Identifier
Mp00126: Permutations cactus evacuationPermutations
Mp00114: Permutations connectivity setBinary words
Mp00104: Binary words reverseBinary words
Images
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[1]=>[1]=>=> [1,2]=>[1,2]=>1=>1 [2,1]=>[2,1]=>0=>0 [1,2,3]=>[1,2,3]=>11=>11 [1,3,2]=>[3,1,2]=>00=>00 [2,1,3]=>[2,3,1]=>00=>00 [2,3,1]=>[2,1,3]=>01=>10 [3,1,2]=>[1,3,2]=>10=>01 [3,2,1]=>[3,2,1]=>00=>00 [1,2,3,4]=>[1,2,3,4]=>111=>111 [1,2,4,3]=>[4,1,2,3]=>000=>000 [1,3,2,4]=>[1,3,2,4]=>101=>101 [1,3,4,2]=>[3,1,2,4]=>001=>100 [1,4,2,3]=>[1,4,2,3]=>100=>001 [1,4,3,2]=>[4,3,1,2]=>000=>000 [2,1,3,4]=>[2,3,4,1]=>000=>000 [2,1,4,3]=>[2,1,4,3]=>010=>010 [2,3,1,4]=>[2,3,1,4]=>001=>100 [2,3,4,1]=>[2,1,3,4]=>011=>110 [2,4,1,3]=>[2,4,1,3]=>000=>000 [2,4,3,1]=>[4,2,1,3]=>000=>000 [3,1,2,4]=>[1,3,4,2]=>100=>001 [3,1,4,2]=>[3,1,4,2]=>000=>000 [3,2,1,4]=>[3,4,2,1]=>000=>000 [3,2,4,1]=>[3,2,4,1]=>000=>000 [3,4,1,2]=>[3,4,1,2]=>000=>000 [3,4,2,1]=>[3,2,1,4]=>001=>100 [4,1,2,3]=>[1,2,4,3]=>110=>011 [4,1,3,2]=>[4,1,3,2]=>000=>000 [4,2,1,3]=>[2,4,3,1]=>000=>000 [4,2,3,1]=>[4,2,3,1]=>000=>000 [4,3,1,2]=>[1,4,3,2]=>100=>001 [4,3,2,1]=>[4,3,2,1]=>000=>000 [1,2,3,4,5]=>[1,2,3,4,5]=>1111=>1111 [1,2,3,5,4]=>[5,1,2,3,4]=>0000=>0000 [1,2,4,3,5]=>[1,4,2,3,5]=>1001=>1001 [1,2,4,5,3]=>[4,1,2,3,5]=>0001=>1000 [1,2,5,3,4]=>[1,5,2,3,4]=>1000=>0001 [1,2,5,4,3]=>[5,4,1,2,3]=>0000=>0000 [1,3,2,4,5]=>[1,3,4,2,5]=>1001=>1001 [1,3,2,5,4]=>[3,1,5,2,4]=>0000=>0000 [1,3,4,2,5]=>[1,3,2,4,5]=>1011=>1101 [1,3,4,5,2]=>[3,1,2,4,5]=>0011=>1100 [1,3,5,2,4]=>[3,5,1,2,4]=>0000=>0000 [1,3,5,4,2]=>[5,3,1,2,4]=>0000=>0000 [1,4,2,3,5]=>[1,2,4,3,5]=>1101=>1011 [1,4,2,5,3]=>[4,1,5,2,3]=>0000=>0000 [1,4,3,2,5]=>[1,4,3,2,5]=>1001=>1001 [1,4,3,5,2]=>[4,1,3,2,5]=>0001=>1000 [1,4,5,2,3]=>[4,5,1,2,3]=>0000=>0000 [1,4,5,3,2]=>[4,3,1,2,5]=>0001=>1000 [1,5,2,3,4]=>[1,2,5,3,4]=>1100=>0011 [1,5,2,4,3]=>[5,1,4,2,3]=>0000=>0000 [1,5,3,2,4]=>[1,5,3,2,4]=>1000=>0001 [1,5,3,4,2]=>[5,1,3,2,4]=>0000=>0000 [1,5,4,2,3]=>[1,5,4,2,3]=>1000=>0001 [1,5,4,3,2]=>[5,4,3,1,2]=>0000=>0000 [2,1,3,4,5]=>[2,3,4,5,1]=>0000=>0000 [2,1,3,5,4]=>[2,1,3,5,4]=>0110=>0110 [2,1,4,3,5]=>[2,4,1,5,3]=>0000=>0000 [2,1,4,5,3]=>[2,1,4,5,3]=>0100=>0010 [2,1,5,3,4]=>[2,3,1,5,4]=>0010=>0100 [2,1,5,4,3]=>[5,2,1,4,3]=>0000=>0000 [2,3,1,4,5]=>[2,3,4,1,5]=>0001=>1000 [2,3,1,5,4]=>[2,1,5,3,4]=>0100=>0010 [2,3,4,1,5]=>[2,3,1,4,5]=>0011=>1100 [2,3,4,5,1]=>[2,1,3,4,5]=>0111=>1110 [2,3,5,1,4]=>[2,5,1,3,4]=>0000=>0000 [2,3,5,4,1]=>[5,2,1,3,4]=>0000=>0000 [2,4,1,3,5]=>[2,4,5,1,3]=>0000=>0000 [2,4,1,5,3]=>[2,1,4,3,5]=>0101=>1010 [2,4,3,1,5]=>[2,4,3,1,5]=>0001=>1000 [2,4,3,5,1]=>[4,2,3,1,5]=>0001=>1000 [2,4,5,1,3]=>[2,4,1,3,5]=>0001=>1000 [2,4,5,3,1]=>[4,2,1,3,5]=>0001=>1000 [2,5,1,3,4]=>[2,3,5,1,4]=>0000=>0000 [2,5,1,4,3]=>[5,2,4,1,3]=>0000=>0000 [2,5,3,1,4]=>[2,5,3,1,4]=>0000=>0000 [2,5,3,4,1]=>[5,2,3,1,4]=>0000=>0000 [2,5,4,1,3]=>[2,5,4,1,3]=>0000=>0000 [2,5,4,3,1]=>[5,4,2,1,3]=>0000=>0000 [3,1,2,4,5]=>[1,3,4,5,2]=>1000=>0001 [3,1,2,5,4]=>[3,1,2,5,4]=>0010=>0100 [3,1,4,2,5]=>[3,4,1,5,2]=>0000=>0000 [3,1,4,5,2]=>[3,1,4,5,2]=>0000=>0000 [3,1,5,2,4]=>[1,3,2,5,4]=>1010=>0101 [3,1,5,4,2]=>[5,3,1,4,2]=>0000=>0000 [3,2,1,4,5]=>[3,4,5,2,1]=>0000=>0000 [3,2,1,5,4]=>[3,2,5,4,1]=>0000=>0000 [3,2,4,1,5]=>[3,4,2,5,1]=>0000=>0000 [3,2,4,5,1]=>[3,2,4,5,1]=>0000=>0000 [3,2,5,1,4]=>[3,5,2,4,1]=>0000=>0000 [3,2,5,4,1]=>[3,2,1,5,4]=>0010=>0100 [3,4,1,2,5]=>[3,4,5,1,2]=>0000=>0000 [3,4,1,5,2]=>[3,1,4,2,5]=>0001=>1000 [3,4,2,1,5]=>[3,4,2,1,5]=>0001=>1000 [3,4,2,5,1]=>[3,2,4,1,5]=>0001=>1000 [3,4,5,1,2]=>[3,4,1,2,5]=>0001=>1000 [3,4,5,2,1]=>[3,2,1,4,5]=>0011=>1100 [3,5,1,2,4]=>[1,3,5,2,4]=>1000=>0001 [3,5,1,4,2]=>[5,3,4,1,2]=>0000=>0000 [3,5,2,1,4]=>[3,5,2,1,4]=>0000=>0000 [3,5,2,4,1]=>[3,2,5,1,4]=>0000=>0000 [3,5,4,1,2]=>[3,5,4,1,2]=>0000=>0000 [3,5,4,2,1]=>[5,3,2,1,4]=>0000=>0000 [4,1,2,3,5]=>[1,2,4,5,3]=>1100=>0011 [4,1,2,5,3]=>[4,1,2,5,3]=>0000=>0000 [4,1,3,2,5]=>[1,4,3,5,2]=>1000=>0001 [4,1,3,5,2]=>[4,1,3,5,2]=>0000=>0000 [4,1,5,2,3]=>[1,4,2,5,3]=>1000=>0001 [4,1,5,3,2]=>[4,3,1,5,2]=>0000=>0000 [4,2,1,3,5]=>[2,4,5,3,1]=>0000=>0000 [4,2,1,5,3]=>[4,2,5,3,1]=>0000=>0000 [4,2,3,1,5]=>[2,4,3,5,1]=>0000=>0000 [4,2,3,5,1]=>[4,2,3,5,1]=>0000=>0000 [4,2,5,1,3]=>[4,5,2,3,1]=>0000=>0000 [4,2,5,3,1]=>[4,2,1,5,3]=>0000=>0000 [4,3,1,2,5]=>[1,4,5,3,2]=>1000=>0001 [4,3,1,5,2]=>[4,1,5,3,2]=>0000=>0000 [4,3,2,1,5]=>[4,5,3,2,1]=>0000=>0000 [4,3,2,5,1]=>[4,3,5,2,1]=>0000=>0000 [4,3,5,1,2]=>[4,5,1,3,2]=>0000=>0000 [4,3,5,2,1]=>[4,3,2,5,1]=>0000=>0000 [4,5,1,2,3]=>[1,4,5,2,3]=>1000=>0001 [4,5,1,3,2]=>[4,3,5,1,2]=>0000=>0000 [4,5,2,1,3]=>[4,5,2,1,3]=>0000=>0000 [4,5,2,3,1]=>[4,2,5,1,3]=>0000=>0000 [4,5,3,1,2]=>[4,5,3,1,2]=>0000=>0000 [4,5,3,2,1]=>[4,3,2,1,5]=>0001=>1000 [5,1,2,3,4]=>[1,2,3,5,4]=>1110=>0111 [5,1,2,4,3]=>[5,1,2,4,3]=>0000=>0000 [5,1,3,2,4]=>[1,5,3,4,2]=>1000=>0001 [5,1,3,4,2]=>[5,1,3,4,2]=>0000=>0000 [5,1,4,2,3]=>[1,5,2,4,3]=>1000=>0001 [5,1,4,3,2]=>[5,4,1,3,2]=>0000=>0000 [5,2,1,3,4]=>[2,3,5,4,1]=>0000=>0000 [5,2,1,4,3]=>[2,1,5,4,3]=>0100=>0010 [5,2,3,1,4]=>[2,5,3,4,1]=>0000=>0000 [5,2,3,4,1]=>[5,2,3,4,1]=>0000=>0000 [5,2,4,1,3]=>[2,5,1,4,3]=>0000=>0000 [5,2,4,3,1]=>[5,4,2,3,1]=>0000=>0000 [5,3,1,2,4]=>[1,3,5,4,2]=>1000=>0001 [5,3,1,4,2]=>[3,1,5,4,2]=>0000=>0000 [5,3,2,1,4]=>[3,5,4,2,1]=>0000=>0000 [5,3,2,4,1]=>[5,3,4,2,1]=>0000=>0000 [5,3,4,1,2]=>[3,5,1,4,2]=>0000=>0000 [5,3,4,2,1]=>[5,3,2,4,1]=>0000=>0000 [5,4,1,2,3]=>[1,2,5,4,3]=>1100=>0011 [5,4,1,3,2]=>[5,1,4,3,2]=>0000=>0000 [5,4,2,1,3]=>[2,5,4,3,1]=>0000=>0000 [5,4,2,3,1]=>[5,2,4,3,1]=>0000=>0000 [5,4,3,1,2]=>[1,5,4,3,2]=>1000=>0001 [5,4,3,2,1]=>[5,4,3,2,1]=>0000=>0000 [1,2,3,4,5,6]=>[1,2,3,4,5,6]=>11111=>11111 [1,2,3,4,6,5]=>[6,1,2,3,4,5]=>00000=>00000 [1,2,3,5,4,6]=>[1,5,2,3,4,6]=>10001=>10001 [1,2,3,5,6,4]=>[5,1,2,3,4,6]=>00001=>10000 [1,2,3,6,4,5]=>[1,6,2,3,4,5]=>10000=>00001 [1,2,3,6,5,4]=>[6,5,1,2,3,4]=>00000=>00000 [1,2,4,3,5,6]=>[1,2,4,3,5,6]=>11011=>11011 [1,2,4,3,6,5]=>[4,1,6,2,3,5]=>00000=>00000 [1,2,4,5,3,6]=>[1,4,2,3,5,6]=>10011=>11001 [1,2,4,5,6,3]=>[4,1,2,3,5,6]=>00011=>11000 [1,2,4,6,3,5]=>[4,6,1,2,3,5]=>00000=>00000 [1,2,4,6,5,3]=>[6,4,1,2,3,5]=>00000=>00000 [1,2,5,3,4,6]=>[1,2,5,3,4,6]=>11001=>10011 [1,2,5,3,6,4]=>[5,1,6,2,3,4]=>00000=>00000 [1,2,5,4,3,6]=>[1,5,4,2,3,6]=>10001=>10001 [1,2,5,4,6,3]=>[5,1,4,2,3,6]=>00001=>10000 [1,2,5,6,3,4]=>[5,6,1,2,3,4]=>00000=>00000 [1,2,5,6,4,3]=>[5,4,1,2,3,6]=>00001=>10000 [1,2,6,3,4,5]=>[1,2,6,3,4,5]=>11000=>00011 [1,2,6,3,5,4]=>[6,1,5,2,3,4]=>00000=>00000 [1,2,6,4,3,5]=>[1,6,4,2,3,5]=>10000=>00001 [1,2,6,4,5,3]=>[6,1,4,2,3,5]=>00000=>00000 [1,2,6,5,3,4]=>[1,6,5,2,3,4]=>10000=>00001 [1,2,6,5,4,3]=>[6,5,4,1,2,3]=>00000=>00000 [1,3,2,4,5,6]=>[1,3,4,5,2,6]=>10001=>10001 [1,3,2,4,6,5]=>[3,1,2,6,4,5]=>00100=>00100 [1,3,2,5,4,6]=>[1,3,2,5,4,6]=>10101=>10101 [1,3,2,5,6,4]=>[3,1,2,5,4,6]=>00101=>10100 [1,3,2,6,4,5]=>[1,3,2,6,4,5]=>10100=>00101 [1,3,2,6,5,4]=>[6,3,1,5,2,4]=>00000=>00000 [1,3,4,2,5,6]=>[1,3,4,2,5,6]=>10011=>11001 [1,3,4,2,6,5]=>[3,1,6,2,4,5]=>00000=>00000 [1,3,4,5,2,6]=>[1,3,2,4,5,6]=>10111=>11101 [1,3,4,5,6,2]=>[3,1,2,4,5,6]=>00111=>11100 [1,3,4,6,2,5]=>[3,6,1,2,4,5]=>00000=>00000 [1,3,4,6,5,2]=>[6,3,1,2,4,5]=>00000=>00000 [1,3,5,2,4,6]=>[1,3,5,2,4,6]=>10001=>10001 [1,3,5,2,6,4]=>[3,1,5,2,4,6]=>00001=>10000 [1,3,5,4,2,6]=>[1,5,3,2,4,6]=>10001=>10001 [1,3,5,4,6,2]=>[5,1,3,2,4,6]=>00001=>10000 [1,3,5,6,2,4]=>[3,5,1,2,4,6]=>00001=>10000 [1,3,5,6,4,2]=>[5,3,1,2,4,6]=>00001=>10000 [1,3,6,2,4,5]=>[1,3,6,2,4,5]=>10000=>00001 [1,3,6,2,5,4]=>[6,3,5,1,2,4]=>00000=>00000 [1,3,6,4,2,5]=>[1,6,3,2,4,5]=>10000=>00001 [1,3,6,4,5,2]=>[6,1,3,2,4,5]=>00000=>00000 [1,3,6,5,2,4]=>[3,6,5,1,2,4]=>00000=>00000 [1,3,6,5,4,2]=>[6,5,3,1,2,4]=>00000=>00000 [1,4,2,3,5,6]=>[1,2,4,5,3,6]=>11001=>10011 [1,4,2,3,6,5]=>[4,1,2,6,3,5]=>00000=>00000 [1,4,2,5,3,6]=>[1,4,2,5,3,6]=>10001=>10001 [1,4,2,5,6,3]=>[4,1,2,5,3,6]=>00001=>10000 [1,4,2,6,3,5]=>[1,4,2,6,3,5]=>10000=>00001 [1,4,2,6,5,3]=>[6,4,1,5,2,3]=>00000=>00000 [1,4,3,2,5,6]=>[1,4,5,3,2,6]=>10001=>10001 [1,4,3,2,6,5]=>[4,1,6,3,2,5]=>00000=>00000 [1,4,3,5,2,6]=>[1,4,3,5,2,6]=>10001=>10001 [1,4,3,5,6,2]=>[4,1,3,5,2,6]=>00001=>10000 [1,4,3,6,2,5]=>[4,6,1,3,2,5]=>00000=>00000 [1,4,3,6,5,2]=>[4,3,1,6,2,5]=>00000=>00000 [1,4,5,2,3,6]=>[1,4,5,2,3,6]=>10001=>10001 [1,4,5,2,6,3]=>[4,1,5,2,3,6]=>00001=>10000 [1,4,5,3,2,6]=>[1,4,3,2,5,6]=>10011=>11001 [1,4,5,3,6,2]=>[4,1,3,2,5,6]=>00011=>11000 [1,4,5,6,2,3]=>[4,5,1,2,3,6]=>00001=>10000 [1,4,5,6,3,2]=>[4,3,1,2,5,6]=>00011=>11000 [1,4,6,2,3,5]=>[1,4,6,2,3,5]=>10000=>00001 [1,4,6,2,5,3]=>[6,4,5,1,2,3]=>00000=>00000 [1,4,6,3,2,5]=>[4,6,3,1,2,5]=>00000=>00000 [1,4,6,3,5,2]=>[4,3,6,1,2,5]=>00000=>00000 [1,4,6,5,2,3]=>[4,6,5,1,2,3]=>00000=>00000 [1,4,6,5,3,2]=>[6,4,3,1,2,5]=>00000=>00000 [1,5,2,3,4,6]=>[1,2,3,5,4,6]=>11101=>10111 [1,5,2,3,6,4]=>[5,1,2,6,3,4]=>00000=>00000 [1,5,2,4,3,6]=>[1,5,2,4,3,6]=>10001=>10001 [1,5,2,4,6,3]=>[5,1,2,4,3,6]=>00001=>10000 [1,5,2,6,3,4]=>[1,5,2,6,3,4]=>10000=>00001 [1,5,2,6,4,3]=>[5,4,1,6,2,3]=>00000=>00000 [1,5,3,2,4,6]=>[1,3,5,4,2,6]=>10001=>10001 [1,5,3,2,6,4]=>[5,1,6,3,2,4]=>00000=>00000 [1,5,3,4,2,6]=>[1,5,3,4,2,6]=>10001=>10001 [1,5,3,4,6,2]=>[5,1,3,4,2,6]=>00001=>10000 [1,5,3,6,2,4]=>[5,6,1,3,2,4]=>00000=>00000 [1,5,3,6,4,2]=>[5,3,1,6,2,4]=>00000=>00000 [1,5,4,2,3,6]=>[1,2,5,4,3,6]=>11001=>10011 [1,5,4,2,6,3]=>[5,1,6,4,2,3]=>00000=>00000 [1,5,4,3,2,6]=>[1,5,4,3,2,6]=>10001=>10001 [1,5,4,3,6,2]=>[5,1,4,3,2,6]=>00001=>10000 [1,5,4,6,2,3]=>[5,6,1,4,2,3]=>00000=>00000 [1,5,4,6,3,2]=>[5,4,1,3,2,6]=>00001=>10000 [1,5,6,2,3,4]=>[1,5,6,2,3,4]=>10000=>00001 [1,5,6,2,4,3]=>[5,4,6,1,2,3]=>00000=>00000 [1,5,6,3,2,4]=>[5,6,3,1,2,4]=>00000=>00000 [1,5,6,3,4,2]=>[5,3,6,1,2,4]=>00000=>00000 [1,5,6,4,2,3]=>[5,6,4,1,2,3]=>00000=>00000 [1,5,6,4,3,2]=>[5,4,3,1,2,6]=>00001=>10000 [1,6,2,3,4,5]=>[1,2,3,6,4,5]=>11100=>00111 [1,6,2,3,5,4]=>[6,1,2,5,3,4]=>00000=>00000 [1,6,2,4,3,5]=>[1,6,2,4,3,5]=>10000=>00001 [1,6,2,4,5,3]=>[6,1,2,4,3,5]=>00000=>00000 [1,6,2,5,3,4]=>[1,6,2,5,3,4]=>10000=>00001 [1,6,2,5,4,3]=>[6,5,1,4,2,3]=>00000=>00000 [1,6,3,2,4,5]=>[1,3,6,4,2,5]=>10000=>00001 [1,6,3,2,5,4]=>[3,1,6,5,2,4]=>00000=>00000 [1,6,3,4,2,5]=>[1,6,3,4,2,5]=>10000=>00001 [1,6,3,4,5,2]=>[6,1,3,4,2,5]=>00000=>00000 [1,6,3,5,2,4]=>[3,6,1,5,2,4]=>00000=>00000 [1,6,3,5,4,2]=>[6,5,1,3,2,4]=>00000=>00000 [1,6,4,2,3,5]=>[1,2,6,4,3,5]=>11000=>00011 [1,6,4,2,5,3]=>[4,1,6,5,2,3]=>00000=>00000 [1,6,4,3,2,5]=>[1,6,4,3,2,5]=>10000=>00001 [1,6,4,3,5,2]=>[6,1,4,3,2,5]=>00000=>00000 [1,6,4,5,2,3]=>[4,6,1,5,2,3]=>00000=>00000 [1,6,4,5,3,2]=>[6,4,1,3,2,5]=>00000=>00000 [1,6,5,2,3,4]=>[1,2,6,5,3,4]=>11000=>00011 [1,6,5,2,4,3]=>[6,1,5,4,2,3]=>00000=>00000 [1,6,5,3,2,4]=>[1,6,5,3,2,4]=>10000=>00001 [1,6,5,3,4,2]=>[6,1,5,3,2,4]=>00000=>00000 [1,6,5,4,2,3]=>[1,6,5,4,2,3]=>10000=>00001 [1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000=>00000 [2,1,3,4,5,6]=>[2,3,4,5,6,1]=>00000=>00000 [2,1,3,4,6,5]=>[2,1,3,4,6,5]=>01110=>01110 [2,1,3,5,4,6]=>[2,3,1,5,6,4]=>00100=>00100 [2,1,3,5,6,4]=>[2,1,3,5,6,4]=>01100=>00110 [2,1,3,6,4,5]=>[2,3,1,4,6,5]=>00110=>01100 [2,1,3,6,5,4]=>[6,2,1,3,5,4]=>00000=>00000 [2,1,4,3,5,6]=>[2,4,5,1,6,3]=>00000=>00000 [2,1,4,3,6,5]=>[2,1,4,3,6,5]=>01010=>01010 [2,1,4,5,3,6]=>[2,4,1,5,6,3]=>00000=>00000 [2,1,4,5,6,3]=>[2,1,4,5,6,3]=>01000=>00010 [2,1,4,6,3,5]=>[2,4,1,3,6,5]=>00010=>01000 [2,1,4,6,5,3]=>[6,2,1,4,5,3]=>00000=>00000 [2,1,5,3,4,6]=>[2,3,5,1,6,4]=>00000=>00000 [2,1,5,3,6,4]=>[2,1,5,3,6,4]=>01000=>00010 [2,1,5,4,3,6]=>[2,5,4,1,6,3]=>00000=>00000 [2,1,5,4,6,3]=>[5,2,4,1,6,3]=>00000=>00000 [2,1,5,6,3,4]=>[2,5,1,3,6,4]=>00000=>00000 [2,1,5,6,4,3]=>[5,2,1,4,6,3]=>00000=>00000 [2,1,6,3,4,5]=>[2,3,4,1,6,5]=>00010=>01000 [2,1,6,3,5,4]=>[6,2,3,1,5,4]=>00000=>00000 [2,1,6,4,3,5]=>[2,6,4,1,5,3]=>00000=>00000 [2,1,6,4,5,3]=>[6,2,4,1,5,3]=>00000=>00000 [2,1,6,5,3,4]=>[2,6,3,1,5,4]=>00000=>00000 [2,1,6,5,4,3]=>[6,5,2,1,4,3]=>00000=>00000 [2,3,1,4,5,6]=>[2,3,4,5,1,6]=>00001=>10000 [2,3,1,4,6,5]=>[2,1,3,6,4,5]=>01100=>00110 [2,3,1,5,4,6]=>[2,3,1,5,4,6]=>00101=>10100 [2,3,1,5,6,4]=>[2,1,3,5,4,6]=>01101=>10110 [2,3,1,6,4,5]=>[2,3,1,6,4,5]=>00100=>00100 [2,3,1,6,5,4]=>[6,2,1,5,3,4]=>00000=>00000 [2,3,4,1,5,6]=>[2,3,4,1,5,6]=>00011=>11000 [2,3,4,1,6,5]=>[2,1,6,3,4,5]=>01000=>00010 [2,3,4,5,1,6]=>[2,3,1,4,5,6]=>00111=>11100 [2,3,4,5,6,1]=>[2,1,3,4,5,6]=>01111=>11110 [2,3,4,6,1,5]=>[2,6,1,3,4,5]=>00000=>00000 [2,3,4,6,5,1]=>[6,2,1,3,4,5]=>00000=>00000 [2,3,5,1,4,6]=>[2,3,5,1,4,6]=>00001=>10000 [2,3,5,1,6,4]=>[2,1,5,3,4,6]=>01001=>10010 [2,3,5,4,1,6]=>[2,5,3,1,4,6]=>00001=>10000 [2,3,5,4,6,1]=>[5,2,3,1,4,6]=>00001=>10000 [2,3,5,6,1,4]=>[2,5,1,3,4,6]=>00001=>10000 [2,3,5,6,4,1]=>[5,2,1,3,4,6]=>00001=>10000 [2,3,6,1,4,5]=>[2,3,6,1,4,5]=>00000=>00000 [2,3,6,1,5,4]=>[6,2,5,1,3,4]=>00000=>00000 [2,3,6,4,1,5]=>[2,6,3,1,4,5]=>00000=>00000 [2,3,6,4,5,1]=>[6,2,3,1,4,5]=>00000=>00000 [2,3,6,5,1,4]=>[2,6,5,1,3,4]=>00000=>00000 [2,3,6,5,4,1]=>[6,5,2,1,3,4]=>00000=>00000 [2,4,1,3,5,6]=>[2,4,5,6,1,3]=>00000=>00000 [2,4,1,3,6,5]=>[2,1,4,6,3,5]=>01000=>00010 [2,4,1,5,3,6]=>[2,4,1,5,3,6]=>00001=>10000 [2,4,1,5,6,3]=>[2,1,4,5,3,6]=>01001=>10010 [2,4,1,6,3,5]=>[2,4,1,6,3,5]=>00000=>00000 [2,4,1,6,5,3]=>[6,2,1,4,3,5]=>00000=>00000 [2,4,3,1,5,6]=>[2,4,5,3,1,6]=>00001=>10000 [2,4,3,1,6,5]=>[4,2,6,3,1,5]=>00000=>00000 [2,4,3,5,1,6]=>[2,4,3,5,1,6]=>00001=>10000 [2,4,3,5,6,1]=>[4,2,3,5,1,6]=>00001=>10000 [2,4,3,6,1,5]=>[4,6,2,3,1,5]=>00000=>00000 [2,4,3,6,5,1]=>[4,2,1,6,3,5]=>00000=>00000 [2,4,5,1,3,6]=>[2,4,5,1,3,6]=>00001=>10000 [2,4,5,1,6,3]=>[2,1,4,3,5,6]=>01011=>11010 [2,4,5,3,1,6]=>[2,4,3,1,5,6]=>00011=>11000 [2,4,5,3,6,1]=>[4,2,3,1,5,6]=>00011=>11000 [2,4,5,6,1,3]=>[2,4,1,3,5,6]=>00011=>11000 [2,4,5,6,3,1]=>[4,2,1,3,5,6]=>00011=>11000 [2,4,6,1,3,5]=>[2,4,6,1,3,5]=>00000=>00000 [2,4,6,1,5,3]=>[6,2,4,1,3,5]=>00000=>00000 [2,4,6,3,1,5]=>[4,6,2,1,3,5]=>00000=>00000 [2,4,6,3,5,1]=>[4,2,6,1,3,5]=>00000=>00000 [2,4,6,5,1,3]=>[2,6,4,1,3,5]=>00000=>00000 [2,4,6,5,3,1]=>[6,4,2,1,3,5]=>00000=>00000 [2,5,1,3,4,6]=>[2,3,5,6,1,4]=>00000=>00000 [2,5,1,3,6,4]=>[2,1,5,6,3,4]=>01000=>00010 [2,5,1,4,3,6]=>[2,5,4,6,1,3]=>00000=>00000 [2,5,1,4,6,3]=>[5,2,4,6,1,3]=>00000=>00000 [2,5,1,6,3,4]=>[2,5,1,6,3,4]=>00000=>00000 [2,5,1,6,4,3]=>[5,2,1,4,3,6]=>00001=>10000 [2,5,3,1,4,6]=>[2,3,5,4,1,6]=>00001=>10000 [2,5,3,1,6,4]=>[5,2,6,3,1,4]=>00000=>00000 [2,5,3,4,1,6]=>[2,5,3,4,1,6]=>00001=>10000 [2,5,3,4,6,1]=>[5,2,3,4,1,6]=>00001=>10000 [2,5,3,6,1,4]=>[5,6,2,3,1,4]=>00000=>00000 [2,5,3,6,4,1]=>[5,2,1,6,3,4]=>00000=>00000 [2,5,4,1,3,6]=>[2,5,6,4,1,3]=>00000=>00000 [2,5,4,1,6,3]=>[2,1,5,4,3,6]=>01001=>10010 [2,5,4,3,1,6]=>[2,5,4,3,1,6]=>00001=>10000 [2,5,4,3,6,1]=>[5,2,4,3,1,6]=>00001=>10000 [2,5,4,6,1,3]=>[2,5,1,4,3,6]=>00001=>10000 [2,5,4,6,3,1]=>[5,4,2,3,1,6]=>00001=>10000 [2,5,6,1,3,4]=>[2,5,6,1,3,4]=>00000=>00000 [2,5,6,1,4,3]=>[5,2,4,1,3,6]=>00001=>10000 [2,5,6,3,1,4]=>[5,6,2,1,3,4]=>00000=>00000 [2,5,6,3,4,1]=>[5,2,6,1,3,4]=>00000=>00000 [2,5,6,4,1,3]=>[2,5,4,1,3,6]=>00001=>10000 [2,5,6,4,3,1]=>[5,4,2,1,3,6]=>00001=>10000 [2,6,1,3,4,5]=>[2,3,4,6,1,5]=>00000=>00000 [2,6,1,3,5,4]=>[6,2,3,5,1,4]=>00000=>00000 [2,6,1,4,3,5]=>[2,6,4,5,1,3]=>00000=>00000 [2,6,1,4,5,3]=>[6,2,4,5,1,3]=>00000=>00000 [2,6,1,5,3,4]=>[2,6,3,5,1,4]=>00000=>00000 [2,6,1,5,4,3]=>[6,5,2,4,1,3]=>00000=>00000 [2,6,3,1,4,5]=>[2,3,6,4,1,5]=>00000=>00000 [2,6,3,1,5,4]=>[2,1,6,5,3,4]=>01000=>00010 [2,6,3,4,1,5]=>[2,6,3,4,1,5]=>00000=>00000 [2,6,3,4,5,1]=>[6,2,3,4,1,5]=>00000=>00000 [2,6,3,5,1,4]=>[2,6,1,5,3,4]=>00000=>00000 [2,6,3,5,4,1]=>[6,5,2,3,1,4]=>00000=>00000 [2,6,4,1,3,5]=>[2,4,6,5,1,3]=>00000=>00000 [2,6,4,1,5,3]=>[2,1,6,4,3,5]=>01000=>00010 [2,6,4,3,1,5]=>[2,6,4,3,1,5]=>00000=>00000 [2,6,4,3,5,1]=>[6,2,4,3,1,5]=>00000=>00000 [2,6,4,5,1,3]=>[2,6,1,4,3,5]=>00000=>00000 [2,6,4,5,3,1]=>[6,4,2,3,1,5]=>00000=>00000 [2,6,5,1,3,4]=>[2,3,6,5,1,4]=>00000=>00000 [2,6,5,1,4,3]=>[6,2,5,4,1,3]=>00000=>00000 [2,6,5,3,1,4]=>[2,6,5,3,1,4]=>00000=>00000 [2,6,5,3,4,1]=>[6,2,5,3,1,4]=>00000=>00000 [2,6,5,4,1,3]=>[2,6,5,4,1,3]=>00000=>00000 [2,6,5,4,3,1]=>[6,5,4,2,1,3]=>00000=>00000 [3,1,2,4,5,6]=>[1,3,4,5,6,2]=>10000=>00001 [3,1,2,4,6,5]=>[3,1,2,4,6,5]=>00110=>01100 [3,1,2,5,4,6]=>[1,3,2,5,6,4]=>10100=>00101 [3,1,2,5,6,4]=>[3,1,2,5,6,4]=>00100=>00100 [3,1,2,6,4,5]=>[1,3,2,4,6,5]=>10110=>01101 [3,1,2,6,5,4]=>[6,3,1,2,5,4]=>00000=>00000 [3,1,4,2,5,6]=>[3,4,5,1,6,2]=>00000=>00000 [3,1,4,2,6,5]=>[3,1,4,2,6,5]=>00010=>01000 [3,1,4,5,2,6]=>[3,4,1,5,6,2]=>00000=>00000 [3,1,4,5,6,2]=>[3,1,4,5,6,2]=>00000=>00000 [3,1,4,6,2,5]=>[3,4,1,2,6,5]=>00010=>01000 [3,1,4,6,5,2]=>[6,3,1,4,5,2]=>00000=>00000 [3,1,5,2,4,6]=>[1,3,5,2,6,4]=>10000=>00001 [3,1,5,2,6,4]=>[3,1,5,2,6,4]=>00000=>00000 [3,1,5,4,2,6]=>[3,5,4,1,6,2]=>00000=>00000 [3,1,5,4,6,2]=>[5,3,4,1,6,2]=>00000=>00000 [3,1,5,6,2,4]=>[3,5,1,2,6,4]=>00000=>00000 [3,1,5,6,4,2]=>[5,3,1,4,6,2]=>00000=>00000 [3,1,6,2,4,5]=>[1,3,4,2,6,5]=>10010=>01001 [3,1,6,2,5,4]=>[6,1,3,2,5,4]=>00000=>00000 [3,1,6,4,2,5]=>[3,6,4,1,5,2]=>00000=>00000 [3,1,6,4,5,2]=>[6,3,4,1,5,2]=>00000=>00000 [3,1,6,5,2,4]=>[1,6,3,2,5,4]=>10000=>00001 [3,1,6,5,4,2]=>[6,5,3,1,4,2]=>00000=>00000 [3,2,1,4,5,6]=>[3,4,5,6,2,1]=>00000=>00000 [3,2,1,4,6,5]=>[3,2,4,6,5,1]=>00000=>00000 [3,2,1,5,4,6]=>[3,5,2,6,4,1]=>00000=>00000 [3,2,1,5,6,4]=>[3,2,5,6,4,1]=>00000=>00000 [3,2,1,6,4,5]=>[3,4,2,6,5,1]=>00000=>00000 [3,2,1,6,5,4]=>[3,2,1,6,5,4]=>00100=>00100 [3,2,4,1,5,6]=>[3,4,5,2,6,1]=>00000=>00000 [3,2,4,1,6,5]=>[3,2,6,4,5,1]=>00000=>00000 [3,2,4,5,1,6]=>[3,4,2,5,6,1]=>00000=>00000 [3,2,4,5,6,1]=>[3,2,4,5,6,1]=>00000=>00000 [3,2,4,6,1,5]=>[3,6,2,4,5,1]=>00000=>00000 [3,2,4,6,5,1]=>[3,2,1,4,6,5]=>00110=>01100 [3,2,5,1,4,6]=>[3,5,6,2,4,1]=>00000=>00000 [3,2,5,1,6,4]=>[3,2,5,4,6,1]=>00000=>00000 [3,2,5,4,1,6]=>[3,5,2,1,6,4]=>00000=>00000 [3,2,5,4,6,1]=>[3,2,5,1,6,4]=>00000=>00000 [3,2,5,6,1,4]=>[3,5,2,4,6,1]=>00000=>00000 [3,2,5,6,4,1]=>[3,2,1,5,6,4]=>00100=>00100 [3,2,6,1,4,5]=>[3,4,6,2,5,1]=>00000=>00000 [3,2,6,1,5,4]=>[3,2,6,1,5,4]=>00000=>00000 [3,2,6,4,1,5]=>[3,4,2,1,6,5]=>00010=>01000 [3,2,6,4,5,1]=>[3,2,4,1,6,5]=>00010=>01000 [3,2,6,5,1,4]=>[3,6,2,1,5,4]=>00000=>00000 [3,2,6,5,4,1]=>[6,3,2,1,5,4]=>00000=>00000 [3,4,1,2,5,6]=>[3,4,5,6,1,2]=>00000=>00000 [3,4,1,2,6,5]=>[3,1,4,6,2,5]=>00000=>00000 [3,4,1,5,2,6]=>[3,4,1,5,2,6]=>00001=>10000 [3,4,1,5,6,2]=>[3,1,4,5,2,6]=>00001=>10000 [3,4,1,6,2,5]=>[3,4,1,6,2,5]=>00000=>00000 [3,4,1,6,5,2]=>[6,3,1,4,2,5]=>00000=>00000 [3,4,2,1,5,6]=>[3,4,5,2,1,6]=>00001=>10000 [3,4,2,1,6,5]=>[3,2,6,4,1,5]=>00000=>00000 [3,4,2,5,1,6]=>[3,4,2,5,1,6]=>00001=>10000 [3,4,2,5,6,1]=>[3,2,4,5,1,6]=>00001=>10000 [3,4,2,6,1,5]=>[3,6,2,4,1,5]=>00000=>00000 [3,4,2,6,5,1]=>[3,2,1,6,4,5]=>00100=>00100 [3,4,5,1,2,6]=>[3,4,5,1,2,6]=>00001=>10000 [3,4,5,1,6,2]=>[3,1,4,2,5,6]=>00011=>11000 [3,4,5,2,1,6]=>[3,4,2,1,5,6]=>00011=>11000 [3,4,5,2,6,1]=>[3,2,4,1,5,6]=>00011=>11000 [3,4,5,6,1,2]=>[3,4,1,2,5,6]=>00011=>11000 [3,4,5,6,2,1]=>[3,2,1,4,5,6]=>00111=>11100 [3,4,6,1,2,5]=>[3,4,6,1,2,5]=>00000=>00000 [3,4,6,1,5,2]=>[6,3,4,1,2,5]=>00000=>00000 [3,4,6,2,1,5]=>[3,6,2,1,4,5]=>00000=>00000 [3,4,6,2,5,1]=>[3,2,6,1,4,5]=>00000=>00000 [3,4,6,5,1,2]=>[3,6,4,1,2,5]=>00000=>00000 [3,4,6,5,2,1]=>[6,3,2,1,4,5]=>00000=>00000 [3,5,1,2,4,6]=>[1,3,5,6,2,4]=>10000=>00001 [3,5,1,2,6,4]=>[3,1,5,6,2,4]=>00000=>00000 [3,5,1,4,2,6]=>[3,5,4,6,1,2]=>00000=>00000 [3,5,1,4,6,2]=>[5,3,4,6,1,2]=>00000=>00000 [3,5,1,6,2,4]=>[3,5,1,6,2,4]=>00000=>00000 [3,5,1,6,4,2]=>[5,3,1,4,2,6]=>00001=>10000 [3,5,2,1,4,6]=>[3,5,6,2,1,4]=>00000=>00000 [3,5,2,1,6,4]=>[3,2,5,4,1,6]=>00001=>10000 [3,5,2,4,1,6]=>[3,5,2,6,1,4]=>00000=>00000 [3,5,2,4,6,1]=>[3,2,5,6,1,4]=>00000=>00000 [3,5,2,6,1,4]=>[3,5,2,4,1,6]=>00001=>10000 [3,5,2,6,4,1]=>[3,2,1,5,4,6]=>00101=>10100 [3,5,4,1,2,6]=>[3,5,6,4,1,2]=>00000=>00000 [3,5,4,1,6,2]=>[3,1,5,4,2,6]=>00001=>10000 [3,5,4,2,1,6]=>[3,5,4,2,1,6]=>00001=>10000 [3,5,4,2,6,1]=>[5,3,4,2,1,6]=>00001=>10000 [3,5,4,6,1,2]=>[3,5,1,4,2,6]=>00001=>10000 [3,5,4,6,2,1]=>[5,3,2,4,1,6]=>00001=>10000 [3,5,6,1,2,4]=>[3,5,6,1,2,4]=>00000=>00000 [3,5,6,1,4,2]=>[5,3,4,1,2,6]=>00001=>10000 [3,5,6,2,1,4]=>[3,5,2,1,4,6]=>00001=>10000 [3,5,6,2,4,1]=>[3,2,5,1,4,6]=>00001=>10000 [3,5,6,4,1,2]=>[3,5,4,1,2,6]=>00001=>10000 [3,5,6,4,2,1]=>[5,3,2,1,4,6]=>00001=>10000 [3,6,1,2,4,5]=>[1,3,4,6,2,5]=>10000=>00001 [3,6,1,2,5,4]=>[6,1,3,5,2,4]=>00000=>00000 [3,6,1,4,2,5]=>[3,6,4,5,1,2]=>00000=>00000 [3,6,1,4,5,2]=>[6,3,4,5,1,2]=>00000=>00000 [3,6,1,5,2,4]=>[1,6,3,5,2,4]=>10000=>00001 [3,6,1,5,4,2]=>[6,5,3,4,1,2]=>00000=>00000 [3,6,2,1,4,5]=>[3,4,6,2,1,5]=>00000=>00000 [3,6,2,1,5,4]=>[3,2,6,5,1,4]=>00000=>00000 [3,6,2,4,1,5]=>[3,4,2,6,1,5]=>00000=>00000 [3,6,2,4,5,1]=>[3,2,4,6,1,5]=>00000=>00000 [3,6,2,5,1,4]=>[3,6,2,5,1,4]=>00000=>00000 [3,6,2,5,4,1]=>[6,3,2,5,1,4]=>00000=>00000 [3,6,4,1,2,5]=>[3,4,6,5,1,2]=>00000=>00000 [3,6,4,1,5,2]=>[3,1,6,4,2,5]=>00000=>00000 [3,6,4,2,1,5]=>[3,6,4,2,1,5]=>00000=>00000 [3,6,4,2,5,1]=>[6,3,4,2,1,5]=>00000=>00000 [3,6,4,5,1,2]=>[3,6,1,4,2,5]=>00000=>00000 [3,6,4,5,2,1]=>[6,3,2,4,1,5]=>00000=>00000 [3,6,5,1,2,4]=>[1,3,6,5,2,4]=>10000=>00001 [3,6,5,1,4,2]=>[6,3,5,4,1,2]=>00000=>00000 [3,6,5,2,1,4]=>[3,6,5,2,1,4]=>00000=>00000 [3,6,5,2,4,1]=>[6,3,5,2,1,4]=>00000=>00000 [3,6,5,4,1,2]=>[3,6,5,4,1,2]=>00000=>00000 [3,6,5,4,2,1]=>[6,5,3,2,1,4]=>00000=>00000 [4,1,2,3,5,6]=>[1,2,4,5,6,3]=>11000=>00011 [4,1,2,3,6,5]=>[4,1,2,3,6,5]=>00010=>01000 [4,1,2,5,3,6]=>[1,4,2,5,6,3]=>10000=>00001 [4,1,2,5,6,3]=>[4,1,2,5,6,3]=>00000=>00000 [4,1,2,6,3,5]=>[1,4,2,3,6,5]=>10010=>01001 [4,1,2,6,5,3]=>[6,4,1,2,5,3]=>00000=>00000 [4,1,3,2,5,6]=>[1,4,5,3,6,2]=>10000=>00001 [4,1,3,2,6,5]=>[4,1,6,3,5,2]=>00000=>00000 [4,1,3,5,2,6]=>[1,4,3,5,6,2]=>10000=>00001 [4,1,3,5,6,2]=>[4,1,3,5,6,2]=>00000=>00000 [4,1,3,6,2,5]=>[4,6,1,3,5,2]=>00000=>00000 [4,1,3,6,5,2]=>[4,3,1,2,6,5]=>00010=>01000 [4,1,5,2,3,6]=>[1,4,5,2,6,3]=>10000=>00001 [4,1,5,2,6,3]=>[4,1,5,2,6,3]=>00000=>00000 [4,1,5,3,2,6]=>[4,5,3,1,6,2]=>00000=>00000 [4,1,5,3,6,2]=>[4,3,5,1,6,2]=>00000=>00000 [4,1,5,6,2,3]=>[4,5,1,2,6,3]=>00000=>00000 [4,1,5,6,3,2]=>[4,3,1,5,6,2]=>00000=>00000 [4,1,6,2,3,5]=>[1,2,4,3,6,5]=>11010=>01011 [4,1,6,2,5,3]=>[6,1,4,2,5,3]=>00000=>00000 [4,1,6,3,2,5]=>[1,4,3,2,6,5]=>10010=>01001 [4,1,6,3,5,2]=>[4,1,3,2,6,5]=>00010=>01000 [4,1,6,5,2,3]=>[1,6,4,2,5,3]=>10000=>00001 [4,1,6,5,3,2]=>[6,4,3,1,5,2]=>00000=>00000 [4,2,1,3,5,6]=>[2,4,5,6,3,1]=>00000=>00000 [4,2,1,3,6,5]=>[4,2,3,6,5,1]=>00000=>00000 [4,2,1,5,3,6]=>[4,5,2,6,3,1]=>00000=>00000 [4,2,1,5,6,3]=>[4,2,5,6,3,1]=>00000=>00000 [4,2,1,6,3,5]=>[2,4,3,6,5,1]=>00000=>00000 [4,2,1,6,5,3]=>[4,2,1,6,5,3]=>00000=>00000 [4,2,3,1,5,6]=>[2,4,5,3,6,1]=>00000=>00000 [4,2,3,1,6,5]=>[4,2,6,3,5,1]=>00000=>00000 [4,2,3,5,1,6]=>[2,4,3,5,6,1]=>00000=>00000 [4,2,3,5,6,1]=>[4,2,3,5,6,1]=>00000=>00000 [4,2,3,6,1,5]=>[4,6,2,3,5,1]=>00000=>00000 [4,2,3,6,5,1]=>[4,2,1,3,6,5]=>00010=>01000 [4,2,5,1,3,6]=>[4,5,6,2,3,1]=>00000=>00000 [4,2,5,1,6,3]=>[4,2,5,3,6,1]=>00000=>00000 [4,2,5,3,1,6]=>[4,5,2,1,6,3]=>00000=>00000 [4,2,5,3,6,1]=>[4,2,5,1,6,3]=>00000=>00000 [4,2,5,6,1,3]=>[4,5,2,3,6,1]=>00000=>00000 [4,2,5,6,3,1]=>[4,2,1,5,6,3]=>00000=>00000 [4,2,6,1,3,5]=>[2,4,6,3,5,1]=>00000=>00000 [4,2,6,1,5,3]=>[4,2,6,1,5,3]=>00000=>00000 [4,2,6,3,1,5]=>[2,4,3,1,6,5]=>00010=>01000 [4,2,6,3,5,1]=>[4,2,3,1,6,5]=>00010=>01000 [4,2,6,5,1,3]=>[4,6,2,1,5,3]=>00000=>00000 [4,2,6,5,3,1]=>[6,4,2,1,5,3]=>00000=>00000 [4,3,1,2,5,6]=>[1,4,5,6,3,2]=>10000=>00001 [4,3,1,2,6,5]=>[4,1,3,6,5,2]=>00000=>00000 [4,3,1,5,2,6]=>[4,5,1,6,3,2]=>00000=>00000 [4,3,1,5,6,2]=>[4,1,5,6,3,2]=>00000=>00000 [4,3,1,6,2,5]=>[1,4,3,6,5,2]=>10000=>00001 [4,3,1,6,5,2]=>[4,3,1,6,5,2]=>00000=>00000 [4,3,2,1,5,6]=>[4,5,6,3,2,1]=>00000=>00000 [4,3,2,1,6,5]=>[4,3,6,5,2,1]=>00000=>00000 [4,3,2,5,1,6]=>[4,5,3,6,2,1]=>00000=>00000 [4,3,2,5,6,1]=>[4,3,5,6,2,1]=>00000=>00000 [4,3,2,6,1,5]=>[4,6,3,5,2,1]=>00000=>00000 [4,3,2,6,5,1]=>[4,3,2,6,5,1]=>00000=>00000 [4,3,5,1,2,6]=>[4,5,6,1,3,2]=>00000=>00000 [4,3,5,1,6,2]=>[4,1,5,3,6,2]=>00000=>00000 [4,3,5,2,1,6]=>[4,5,3,2,6,1]=>00000=>00000 [4,3,5,2,6,1]=>[4,3,5,2,6,1]=>00000=>00000 [4,3,5,6,1,2]=>[4,5,1,3,6,2]=>00000=>00000 [4,3,5,6,2,1]=>[4,3,2,5,6,1]=>00000=>00000 [4,3,6,1,2,5]=>[1,4,6,3,5,2]=>10000=>00001 [4,3,6,1,5,2]=>[4,3,6,1,5,2]=>00000=>00000 [4,3,6,2,1,5]=>[4,6,3,2,5,1]=>00000=>00000 [4,3,6,2,5,1]=>[4,3,6,2,5,1]=>00000=>00000 [4,3,6,5,1,2]=>[4,6,3,1,5,2]=>00000=>00000 [4,3,6,5,2,1]=>[4,3,2,1,6,5]=>00010=>01000 [4,5,1,2,3,6]=>[1,4,5,6,2,3]=>10000=>00001 [4,5,1,2,6,3]=>[4,1,5,6,2,3]=>00000=>00000 [4,5,1,3,2,6]=>[4,5,3,6,1,2]=>00000=>00000 [4,5,1,3,6,2]=>[4,3,5,6,1,2]=>00000=>00000 [4,5,1,6,2,3]=>[4,5,1,6,2,3]=>00000=>00000 [4,5,1,6,3,2]=>[4,3,1,5,2,6]=>00001=>10000 [4,5,2,1,3,6]=>[4,5,6,2,1,3]=>00000=>00000 [4,5,2,1,6,3]=>[4,2,5,3,1,6]=>00001=>10000 [4,5,2,3,1,6]=>[4,5,2,6,1,3]=>00000=>00000 [4,5,2,3,6,1]=>[4,2,5,6,1,3]=>00000=>00000 [4,5,2,6,1,3]=>[4,5,2,3,1,6]=>00001=>10000 [4,5,2,6,3,1]=>[4,2,1,5,3,6]=>00001=>10000 [4,5,3,1,2,6]=>[4,5,6,3,1,2]=>00000=>00000 [4,5,3,1,6,2]=>[4,1,5,3,2,6]=>00001=>10000 [4,5,3,2,1,6]=>[4,5,3,2,1,6]=>00001=>10000 [4,5,3,2,6,1]=>[4,3,5,2,1,6]=>00001=>10000 [4,5,3,6,1,2]=>[4,5,1,3,2,6]=>00001=>10000 [4,5,3,6,2,1]=>[4,3,2,5,1,6]=>00001=>10000 [4,5,6,1,2,3]=>[4,5,6,1,2,3]=>00000=>00000 [4,5,6,1,3,2]=>[4,3,5,1,2,6]=>00001=>10000 [4,5,6,2,1,3]=>[4,5,2,1,3,6]=>00001=>10000 [4,5,6,2,3,1]=>[4,2,5,1,3,6]=>00001=>10000 [4,5,6,3,1,2]=>[4,5,3,1,2,6]=>00001=>10000 [4,5,6,3,2,1]=>[4,3,2,1,5,6]=>00011=>11000 [4,6,1,2,3,5]=>[1,2,4,6,3,5]=>11000=>00011 [4,6,1,2,5,3]=>[6,1,4,5,2,3]=>00000=>00000 [4,6,1,3,2,5]=>[1,4,3,6,2,5]=>10000=>00001 [4,6,1,3,5,2]=>[4,1,3,6,2,5]=>00000=>00000 [4,6,1,5,2,3]=>[1,6,4,5,2,3]=>10000=>00001 [4,6,1,5,3,2]=>[6,4,3,5,1,2]=>00000=>00000 [4,6,2,1,3,5]=>[2,4,6,3,1,5]=>00000=>00000 [4,6,2,1,5,3]=>[4,2,6,5,1,3]=>00000=>00000 [4,6,2,3,1,5]=>[2,4,3,6,1,5]=>00000=>00000 [4,6,2,3,5,1]=>[4,2,3,6,1,5]=>00000=>00000 [4,6,2,5,1,3]=>[4,6,2,5,1,3]=>00000=>00000 [4,6,2,5,3,1]=>[6,4,2,5,1,3]=>00000=>00000 [4,6,3,1,2,5]=>[1,4,6,3,2,5]=>10000=>00001 [4,6,3,1,5,2]=>[4,3,6,5,1,2]=>00000=>00000 [4,6,3,2,1,5]=>[4,6,3,2,1,5]=>00000=>00000 [4,6,3,2,5,1]=>[4,3,6,2,1,5]=>00000=>00000 [4,6,3,5,1,2]=>[4,6,3,5,1,2]=>00000=>00000 [4,6,3,5,2,1]=>[4,3,2,6,1,5]=>00000=>00000 [4,6,5,1,2,3]=>[1,4,6,5,2,3]=>10000=>00001 [4,6,5,1,3,2]=>[6,4,5,3,1,2]=>00000=>00000 [4,6,5,2,1,3]=>[4,6,5,2,1,3]=>00000=>00000 [4,6,5,2,3,1]=>[6,4,5,2,1,3]=>00000=>00000 [4,6,5,3,1,2]=>[4,6,5,3,1,2]=>00000=>00000 [4,6,5,3,2,1]=>[6,4,3,2,1,5]=>00000=>00000 [5,1,2,3,4,6]=>[1,2,3,5,6,4]=>11100=>00111 [5,1,2,3,6,4]=>[5,1,2,3,6,4]=>00000=>00000 [5,1,2,4,3,6]=>[1,5,2,4,6,3]=>10000=>00001 [5,1,2,4,6,3]=>[5,1,2,4,6,3]=>00000=>00000 [5,1,2,6,3,4]=>[1,5,2,3,6,4]=>10000=>00001 [5,1,2,6,4,3]=>[5,4,1,2,6,3]=>00000=>00000 [5,1,3,2,4,6]=>[1,3,5,4,6,2]=>10000=>00001 [5,1,3,2,6,4]=>[5,1,6,3,4,2]=>00000=>00000 [5,1,3,4,2,6]=>[1,5,3,4,6,2]=>10000=>00001 [5,1,3,4,6,2]=>[5,1,3,4,6,2]=>00000=>00000 [5,1,3,6,2,4]=>[5,6,1,3,4,2]=>00000=>00000 [5,1,3,6,4,2]=>[5,3,1,2,6,4]=>00000=>00000 [5,1,4,2,3,6]=>[1,2,5,4,6,3]=>11000=>00011 [5,1,4,2,6,3]=>[5,1,6,2,4,3]=>00000=>00000 [5,1,4,3,2,6]=>[1,5,4,3,6,2]=>10000=>00001 [5,1,4,3,6,2]=>[5,1,4,3,6,2]=>00000=>00000 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[5,4,3,1,6,2]=>[5,1,6,4,3,2]=>00000=>00000 [5,4,3,2,1,6]=>[5,6,4,3,2,1]=>00000=>00000 [5,4,3,2,6,1]=>[5,4,6,3,2,1]=>00000=>00000 [5,4,3,6,1,2]=>[5,6,1,4,3,2]=>00000=>00000 [5,4,3,6,2,1]=>[5,4,3,6,2,1]=>00000=>00000 [5,4,6,1,2,3]=>[1,5,6,2,4,3]=>10000=>00001 [5,4,6,1,3,2]=>[5,4,6,1,3,2]=>00000=>00000 [5,4,6,2,1,3]=>[5,6,4,2,3,1]=>00000=>00000 [5,4,6,2,3,1]=>[5,4,6,2,3,1]=>00000=>00000 [5,4,6,3,1,2]=>[5,6,4,1,3,2]=>00000=>00000 [5,4,6,3,2,1]=>[5,4,3,2,6,1]=>00000=>00000 [5,6,1,2,3,4]=>[1,2,5,6,3,4]=>11000=>00011 [5,6,1,2,4,3]=>[5,1,4,6,2,3]=>00000=>00000 [5,6,1,3,2,4]=>[1,5,3,6,2,4]=>10000=>00001 [5,6,1,3,4,2]=>[5,1,3,6,2,4]=>00000=>00000 [5,6,1,4,2,3]=>[1,5,4,6,2,3]=>10000=>00001 [5,6,1,4,3,2]=>[5,4,3,6,1,2]=>00000=>00000 [5,6,2,1,3,4]=>[2,5,6,3,1,4]=>00000=>00000 [5,6,2,1,4,3]=>[5,2,6,4,1,3]=>00000=>00000 [5,6,2,3,1,4]=>[2,5,3,6,1,4]=>00000=>00000 [5,6,2,3,4,1]=>[5,2,3,6,1,4]=>00000=>00000 [5,6,2,4,1,3]=>[5,6,2,4,1,3]=>00000=>00000 [5,6,2,4,3,1]=>[5,4,2,6,1,3]=>00000=>00000 [5,6,3,1,2,4]=>[1,5,6,3,2,4]=>10000=>00001 [5,6,3,1,4,2]=>[5,3,6,4,1,2]=>00000=>00000 [5,6,3,2,1,4]=>[5,6,3,2,1,4]=>00000=>00000 [5,6,3,2,4,1]=>[5,3,6,2,1,4]=>00000=>00000 [5,6,3,4,1,2]=>[5,6,3,4,1,2]=>00000=>00000 [5,6,3,4,2,1]=>[5,3,2,6,1,4]=>00000=>00000 [5,6,4,1,2,3]=>[1,5,6,4,2,3]=>10000=>00001 [5,6,4,1,3,2]=>[5,4,6,3,1,2]=>00000=>00000 [5,6,4,2,1,3]=>[5,6,4,2,1,3]=>00000=>00000 [5,6,4,2,3,1]=>[5,4,6,2,1,3]=>00000=>00000 [5,6,4,3,1,2]=>[5,6,4,3,1,2]=>00000=>00000 [5,6,4,3,2,1]=>[5,4,3,2,1,6]=>00001=>10000 [6,1,2,3,4,5]=>[1,2,3,4,6,5]=>11110=>01111 [6,1,2,3,5,4]=>[6,1,2,3,5,4]=>00000=>00000 [6,1,2,4,3,5]=>[1,6,2,4,5,3]=>10000=>00001 [6,1,2,4,5,3]=>[6,1,2,4,5,3]=>00000=>00000 [6,1,2,5,3,4]=>[1,6,2,3,5,4]=>10000=>00001 [6,1,2,5,4,3]=>[6,5,1,2,4,3]=>00000=>00000 [6,1,3,2,4,5]=>[1,3,6,4,5,2]=>10000=>00001 [6,1,3,2,5,4]=>[3,1,6,2,5,4]=>00000=>00000 [6,1,3,4,2,5]=>[1,6,3,4,5,2]=>10000=>00001 [6,1,3,4,5,2]=>[6,1,3,4,5,2]=>00000=>00000 [6,1,3,5,2,4]=>[3,6,1,2,5,4]=>00000=>00000 [6,1,3,5,4,2]=>[6,5,1,3,4,2]=>00000=>00000 [6,1,4,2,3,5]=>[1,2,6,4,5,3]=>11000=>00011 [6,1,4,2,5,3]=>[4,1,6,2,5,3]=>00000=>00000 [6,1,4,3,2,5]=>[1,6,4,3,5,2]=>10000=>00001 [6,1,4,3,5,2]=>[6,1,4,3,5,2]=>00000=>00000 [6,1,4,5,2,3]=>[4,6,1,2,5,3]=>00000=>00000 [6,1,4,5,3,2]=>[6,4,1,3,5,2]=>00000=>00000 [6,1,5,2,3,4]=>[1,2,6,3,5,4]=>11000=>00011 [6,1,5,2,4,3]=>[6,1,5,2,4,3]=>00000=>00000 [6,1,5,3,2,4]=>[1,6,5,3,4,2]=>10000=>00001 [6,1,5,3,4,2]=>[6,1,5,3,4,2]=>00000=>00000 [6,1,5,4,2,3]=>[1,6,5,2,4,3]=>10000=>00001 [6,1,5,4,3,2]=>[6,5,4,1,3,2]=>00000=>00000 [6,2,1,3,4,5]=>[2,3,4,6,5,1]=>00000=>00000 [6,2,1,3,5,4]=>[2,1,3,6,5,4]=>01100=>00110 [6,2,1,4,3,5]=>[2,4,1,6,5,3]=>00000=>00000 [6,2,1,4,5,3]=>[2,1,4,6,5,3]=>01000=>00010 [6,2,1,5,3,4]=>[2,3,1,6,5,4]=>00100=>00100 [6,2,1,5,4,3]=>[6,2,1,5,4,3]=>00000=>00000 [6,2,3,1,4,5]=>[2,3,6,4,5,1]=>00000=>00000 [6,2,3,1,5,4]=>[2,1,6,3,5,4]=>01000=>00010 [6,2,3,4,1,5]=>[2,6,3,4,5,1]=>00000=>00000 [6,2,3,4,5,1]=>[6,2,3,4,5,1]=>00000=>00000 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[6,3,2,4,5,1]=>[6,3,4,5,2,1]=>00000=>00000 [6,3,2,5,1,4]=>[3,6,2,5,4,1]=>00000=>00000 [6,3,2,5,4,1]=>[6,3,2,5,4,1]=>00000=>00000 [6,3,4,1,2,5]=>[3,4,6,1,5,2]=>00000=>00000 [6,3,4,1,5,2]=>[3,1,6,4,5,2]=>00000=>00000 [6,3,4,2,1,5]=>[3,6,4,2,5,1]=>00000=>00000 [6,3,4,2,5,1]=>[6,3,4,2,5,1]=>00000=>00000 [6,3,4,5,1,2]=>[3,6,1,4,5,2]=>00000=>00000 [6,3,4,5,2,1]=>[6,3,2,4,5,1]=>00000=>00000 [6,3,5,1,2,4]=>[1,3,6,2,5,4]=>10000=>00001 [6,3,5,1,4,2]=>[6,3,5,1,4,2]=>00000=>00000 [6,3,5,2,1,4]=>[3,6,5,2,4,1]=>00000=>00000 [6,3,5,2,4,1]=>[6,3,5,2,4,1]=>00000=>00000 [6,3,5,4,1,2]=>[3,6,5,1,4,2]=>00000=>00000 [6,3,5,4,2,1]=>[6,5,3,2,4,1]=>00000=>00000 [6,4,1,2,3,5]=>[1,2,4,6,5,3]=>11000=>00011 [6,4,1,2,5,3]=>[4,1,2,6,5,3]=>00000=>00000 [6,4,1,3,2,5]=>[1,6,4,5,3,2]=>10000=>00001 [6,4,1,3,5,2]=>[6,1,4,5,3,2]=>00000=>00000 [6,4,1,5,2,3]=>[1,4,2,6,5,3]=>10000=>00001 [6,4,1,5,3,2]=>[6,4,1,5,3,2]=>00000=>00000 [6,4,2,1,3,5]=>[2,4,6,5,3,1]=>00000=>00000 [6,4,2,1,5,3]=>[4,2,6,5,3,1]=>00000=>00000 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[6,5,2,1,4,3]=>[2,1,6,5,4,3]=>01000=>00010 [6,5,2,3,1,4]=>[2,6,3,5,4,1]=>00000=>00000 [6,5,2,3,4,1]=>[6,2,3,5,4,1]=>00000=>00000 [6,5,2,4,1,3]=>[2,6,1,5,4,3]=>00000=>00000 [6,5,2,4,3,1]=>[6,5,2,4,3,1]=>00000=>00000 [6,5,3,1,2,4]=>[1,3,6,5,4,2]=>10000=>00001 [6,5,3,1,4,2]=>[3,1,6,5,4,2]=>00000=>00000 [6,5,3,2,1,4]=>[3,6,5,4,2,1]=>00000=>00000 [6,5,3,2,4,1]=>[6,3,5,4,2,1]=>00000=>00000 [6,5,3,4,1,2]=>[3,6,1,5,4,2]=>00000=>00000 [6,5,3,4,2,1]=>[6,5,3,4,2,1]=>00000=>00000 [6,5,4,1,2,3]=>[1,2,6,5,4,3]=>11000=>00011 [6,5,4,1,3,2]=>[6,1,5,4,3,2]=>00000=>00000 [6,5,4,2,1,3]=>[2,6,5,4,3,1]=>00000=>00000 [6,5,4,2,3,1]=>[6,2,5,4,3,1]=>00000=>00000 [6,5,4,3,1,2]=>[1,6,5,4,3,2]=>10000=>00001 [6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000=>00000 [1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>111111=>111111 [1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>000000=>000000 [1,2,3,4,6,5,7]=>[1,6,2,3,4,5,7]=>100001=>100001 [1,2,3,4,6,7,5]=>[6,1,2,3,4,5,7]=>000001=>100000 [1,2,3,4,7,5,6]=>[1,7,2,3,4,5,6]=>100000=>000001 [1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>000000=>000000 [1,2,3,5,4,6,7]=>[1,2,5,3,4,6,7]=>110011=>110011 [1,2,3,5,4,7,6]=>[5,1,7,2,3,4,6]=>000000=>000000 [1,2,3,5,6,4,7]=>[1,5,2,3,4,6,7]=>100011=>110001 [1,2,3,5,6,7,4]=>[5,1,2,3,4,6,7]=>000011=>110000 [1,2,3,5,7,4,6]=>[5,7,1,2,3,4,6]=>000000=>000000 [1,2,3,5,7,6,4]=>[7,5,1,2,3,4,6]=>000000=>000000 [1,2,3,6,4,5,7]=>[1,2,6,3,4,5,7]=>110001=>100011 [1,2,3,6,4,7,5]=>[6,1,7,2,3,4,5]=>000000=>000000 [1,2,3,6,5,4,7]=>[1,6,5,2,3,4,7]=>100001=>100001 [1,2,3,6,5,7,4]=>[6,1,5,2,3,4,7]=>000001=>100000 [1,2,3,6,7,4,5]=>[6,7,1,2,3,4,5]=>000000=>000000 [1,2,3,6,7,5,4]=>[6,5,1,2,3,4,7]=>000001=>100000 [1,2,3,7,4,5,6]=>[1,2,7,3,4,5,6]=>110000=>000011 [1,2,3,7,4,6,5]=>[7,1,6,2,3,4,5]=>000000=>000000 [1,2,3,7,5,4,6]=>[1,7,5,2,3,4,6]=>100000=>000001 [1,2,3,7,5,6,4]=>[7,1,5,2,3,4,6]=>000000=>000000 [1,2,3,7,6,4,5]=>[1,7,6,2,3,4,5]=>100000=>000001 [1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>000000=>000000 [1,2,4,3,5,6,7]=>[1,2,4,5,3,6,7]=>110011=>110011 [1,2,4,3,5,7,6]=>[4,1,2,7,3,5,6]=>000000=>000000 [1,2,4,3,6,5,7]=>[1,4,2,6,3,5,7]=>100001=>100001 [1,2,4,3,6,7,5]=>[4,1,2,6,3,5,7]=>000001=>100000 [1,2,4,3,7,5,6]=>[1,4,2,7,3,5,6]=>100000=>000001 [1,2,4,3,7,6,5]=>[7,4,1,6,2,3,5]=>000000=>000000 [1,2,4,5,3,6,7]=>[1,2,4,3,5,6,7]=>110111=>111011 [1,2,4,5,3,7,6]=>[4,1,7,2,3,5,6]=>000000=>000000 [1,2,4,5,6,3,7]=>[1,4,2,3,5,6,7]=>100111=>111001 [1,2,4,5,6,7,3]=>[4,1,2,3,5,6,7]=>000111=>111000 [1,2,4,5,7,3,6]=>[4,7,1,2,3,5,6]=>000000=>000000 [1,2,4,5,7,6,3]=>[7,4,1,2,3,5,6]=>000000=>000000 [1,2,4,6,3,5,7]=>[1,4,6,2,3,5,7]=>100001=>100001 [1,2,4,6,3,7,5]=>[4,1,6,2,3,5,7]=>000001=>100000 [1,2,4,6,5,3,7]=>[1,6,4,2,3,5,7]=>100001=>100001 [1,2,4,6,5,7,3]=>[6,1,4,2,3,5,7]=>000001=>100000 [1,2,4,6,7,3,5]=>[4,6,1,2,3,5,7]=>000001=>100000 [1,2,4,6,7,5,3]=>[6,4,1,2,3,5,7]=>000001=>100000 [1,2,4,7,3,5,6]=>[1,4,7,2,3,5,6]=>100000=>000001 [1,2,4,7,3,6,5]=>[7,4,6,1,2,3,5]=>000000=>000000 [1,2,4,7,5,3,6]=>[1,7,4,2,3,5,6]=>100000=>000001 [1,2,4,7,5,6,3]=>[7,1,4,2,3,5,6]=>000000=>000000 [1,2,4,7,6,3,5]=>[4,7,6,1,2,3,5]=>000000=>000000 [1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>000000=>000000 [1,2,5,3,4,6,7]=>[1,2,3,5,4,6,7]=>111011=>110111 [1,2,5,3,4,7,6]=>[5,1,2,7,3,4,6]=>000000=>000000 [1,2,5,3,6,4,7]=>[1,5,2,6,3,4,7]=>100001=>100001 [1,2,5,3,6,7,4]=>[5,1,2,6,3,4,7]=>000001=>100000 [1,2,5,3,7,4,6]=>[1,5,2,7,3,4,6]=>100000=>000001 [1,2,5,3,7,6,4]=>[7,5,1,6,2,3,4]=>000000=>000000 [1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>110011=>110011 [1,2,5,4,3,7,6]=>[5,1,7,4,2,3,6]=>000000=>000000 [1,2,5,4,6,3,7]=>[1,5,2,4,3,6,7]=>100011=>110001 [1,2,5,4,6,7,3]=>[5,1,2,4,3,6,7]=>000011=>110000 [1,2,5,4,7,3,6]=>[5,7,1,4,2,3,6]=>000000=>000000 [1,2,5,4,7,6,3]=>[5,4,1,7,2,3,6]=>000000=>000000 [1,2,5,6,3,4,7]=>[1,5,6,2,3,4,7]=>100001=>100001 [1,2,5,6,3,7,4]=>[5,1,6,2,3,4,7]=>000001=>100000 [1,2,5,6,4,3,7]=>[1,5,4,2,3,6,7]=>100011=>110001 [1,2,5,6,4,7,3]=>[5,1,4,2,3,6,7]=>000011=>110000 [1,2,5,6,7,3,4]=>[5,6,1,2,3,4,7]=>000001=>100000 [1,2,5,6,7,4,3]=>[5,4,1,2,3,6,7]=>000011=>110000 [1,2,5,7,3,4,6]=>[1,5,7,2,3,4,6]=>100000=>000001 [1,2,5,7,3,6,4]=>[7,5,6,1,2,3,4]=>000000=>000000 [1,2,5,7,4,3,6]=>[5,7,4,1,2,3,6]=>000000=>000000 [1,2,5,7,4,6,3]=>[5,4,7,1,2,3,6]=>000000=>000000 [1,2,5,7,6,3,4]=>[5,7,6,1,2,3,4]=>000000=>000000 [1,2,5,7,6,4,3]=>[7,5,4,1,2,3,6]=>000000=>000000 [1,2,6,3,4,5,7]=>[1,2,3,6,4,5,7]=>111001=>100111 [1,2,6,3,4,7,5]=>[6,1,2,7,3,4,5]=>000000=>000000 [1,2,6,3,5,4,7]=>[1,6,2,5,3,4,7]=>100001=>100001 [1,2,6,3,5,7,4]=>[6,1,2,5,3,4,7]=>000001=>100000 [1,2,6,3,7,4,5]=>[1,6,2,7,3,4,5]=>100000=>000001 [1,2,6,3,7,5,4]=>[6,5,1,7,2,3,4]=>000000=>000000 [1,2,6,4,3,5,7]=>[1,2,6,4,3,5,7]=>110001=>100011 [1,2,6,4,3,7,5]=>[6,1,7,4,2,3,5]=>000000=>000000 [1,2,6,4,5,3,7]=>[1,6,2,4,3,5,7]=>100001=>100001 [1,2,6,4,5,7,3]=>[6,1,2,4,3,5,7]=>000001=>100000 [1,2,6,4,7,3,5]=>[6,7,1,4,2,3,5]=>000000=>000000 [1,2,6,4,7,5,3]=>[6,4,1,7,2,3,5]=>000000=>000000 [1,2,6,5,3,4,7]=>[1,2,6,5,3,4,7]=>110001=>100011 [1,2,6,5,3,7,4]=>[6,1,7,5,2,3,4]=>000000=>000000 [1,2,6,5,4,3,7]=>[1,6,5,4,2,3,7]=>100001=>100001 [1,2,6,5,4,7,3]=>[6,1,5,4,2,3,7]=>000001=>100000 [1,2,6,5,7,3,4]=>[6,7,1,5,2,3,4]=>000000=>000000 [1,2,6,5,7,4,3]=>[6,5,1,4,2,3,7]=>000001=>100000 [1,2,6,7,3,4,5]=>[1,6,7,2,3,4,5]=>100000=>000001 [1,2,6,7,3,5,4]=>[6,5,7,1,2,3,4]=>000000=>000000 [1,2,6,7,4,3,5]=>[6,7,4,1,2,3,5]=>000000=>000000 [1,2,6,7,4,5,3]=>[6,4,7,1,2,3,5]=>000000=>000000 [1,2,6,7,5,3,4]=>[6,7,5,1,2,3,4]=>000000=>000000 [1,2,6,7,5,4,3]=>[6,5,4,1,2,3,7]=>000001=>100000 [1,2,7,3,4,5,6]=>[1,2,3,7,4,5,6]=>111000=>000111 [1,2,7,3,4,6,5]=>[7,1,2,6,3,4,5]=>000000=>000000 [1,2,7,3,5,4,6]=>[1,7,2,5,3,4,6]=>100000=>000001 [1,2,7,3,5,6,4]=>[7,1,2,5,3,4,6]=>000000=>000000 [1,2,7,3,6,4,5]=>[1,7,2,6,3,4,5]=>100000=>000001 [1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>000000=>000000 [1,2,7,4,3,5,6]=>[1,2,7,4,3,5,6]=>110000=>000011 [1,2,7,4,3,6,5]=>[4,1,7,6,2,3,5]=>000000=>000000 [1,2,7,4,5,3,6]=>[1,7,2,4,3,5,6]=>100000=>000001 [1,2,7,4,5,6,3]=>[7,1,2,4,3,5,6]=>000000=>000000 [1,2,7,4,6,3,5]=>[4,7,1,6,2,3,5]=>000000=>000000 [1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>000000=>000000 [1,2,7,5,3,4,6]=>[1,2,7,5,3,4,6]=>110000=>000011 [1,2,7,5,3,6,4]=>[5,1,7,6,2,3,4]=>000000=>000000 [1,2,7,5,4,3,6]=>[1,7,5,4,2,3,6]=>100000=>000001 [1,2,7,5,4,6,3]=>[7,1,5,4,2,3,6]=>000000=>000000 [1,2,7,5,6,3,4]=>[5,7,1,6,2,3,4]=>000000=>000000 [1,2,7,5,6,4,3]=>[7,5,1,4,2,3,6]=>000000=>000000 [1,2,7,6,3,4,5]=>[1,2,7,6,3,4,5]=>110000=>000011 [1,2,7,6,3,5,4]=>[7,1,6,5,2,3,4]=>000000=>000000 [1,2,7,6,4,3,5]=>[1,7,6,4,2,3,5]=>100000=>000001 [1,2,7,6,4,5,3]=>[7,1,6,4,2,3,5]=>000000=>000000 [1,2,7,6,5,3,4]=>[1,7,6,5,2,3,4]=>100000=>000001 [1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000=>000000 [1,3,2,4,5,6,7]=>[1,3,4,5,6,2,7]=>100001=>100001 [1,3,2,4,5,7,6]=>[3,1,2,4,7,5,6]=>001100=>001100 [1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>101101=>101101 [1,3,2,4,6,7,5]=>[3,1,2,4,6,5,7]=>001101=>101100 [1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>101100=>001101 [1,3,2,4,7,6,5]=>[7,3,1,2,6,4,5]=>000000=>000000 [1,3,2,5,4,6,7]=>[1,3,5,2,6,4,7]=>100001=>100001 [1,3,2,5,4,7,6]=>[3,1,5,2,7,4,6]=>000000=>000000 [1,3,2,5,6,4,7]=>[1,3,2,5,6,4,7]=>101001=>100101 [1,3,2,5,6,7,4]=>[3,1,2,5,6,4,7]=>001001=>100100 [1,3,2,5,7,4,6]=>[3,5,1,2,7,4,6]=>000000=>000000 [1,3,2,5,7,6,4]=>[7,3,1,2,5,4,6]=>000000=>000000 [1,3,2,6,4,5,7]=>[1,3,4,2,6,5,7]=>100101=>101001 [1,3,2,6,4,7,5]=>[3,1,6,2,7,4,5]=>000000=>000000 [1,3,2,6,5,4,7]=>[1,6,3,2,5,4,7]=>100001=>100001 [1,3,2,6,5,7,4]=>[6,1,3,2,5,4,7]=>000001=>100000 [1,3,2,6,7,4,5]=>[3,6,1,2,7,4,5]=>000000=>000000 [1,3,2,6,7,5,4]=>[6,3,1,2,5,4,7]=>000001=>100000 [1,3,2,7,4,5,6]=>[1,3,4,2,7,5,6]=>100100=>001001 [1,3,2,7,4,6,5]=>[7,1,3,2,6,4,5]=>000000=>000000 [1,3,2,7,5,4,6]=>[1,7,3,2,5,4,6]=>100000=>000001 [1,3,2,7,5,6,4]=>[7,1,3,2,5,4,6]=>000000=>000000 [1,3,2,7,6,4,5]=>[1,7,3,2,6,4,5]=>100000=>000001 [1,3,2,7,6,5,4]=>[7,6,3,1,5,2,4]=>000000=>000000 [1,3,4,2,5,6,7]=>[1,3,4,5,2,6,7]=>100011=>110001 [1,3,4,2,5,7,6]=>[3,1,2,7,4,5,6]=>001000=>000100 [1,3,4,2,6,5,7]=>[1,3,2,6,4,5,7]=>101001=>100101 [1,3,4,2,6,7,5]=>[3,1,2,6,4,5,7]=>001001=>100100 [1,3,4,2,7,5,6]=>[1,3,2,7,4,5,6]=>101000=>000101 [1,3,4,2,7,6,5]=>[7,3,1,6,2,4,5]=>000000=>000000 [1,3,4,5,2,6,7]=>[1,3,4,2,5,6,7]=>100111=>111001 [1,3,4,5,2,7,6]=>[3,1,7,2,4,5,6]=>000000=>000000 [1,3,4,5,6,2,7]=>[1,3,2,4,5,6,7]=>101111=>111101 [1,3,4,5,6,7,2]=>[3,1,2,4,5,6,7]=>001111=>111100 [1,3,4,5,7,2,6]=>[3,7,1,2,4,5,6]=>000000=>000000 [1,3,4,5,7,6,2]=>[7,3,1,2,4,5,6]=>000000=>000000 [1,3,4,6,2,5,7]=>[1,3,6,2,4,5,7]=>100001=>100001 [1,3,4,6,2,7,5]=>[3,1,6,2,4,5,7]=>000001=>100000 [1,3,4,6,5,2,7]=>[1,6,3,2,4,5,7]=>100001=>100001 [1,3,4,6,5,7,2]=>[6,1,3,2,4,5,7]=>000001=>100000 [1,3,4,6,7,2,5]=>[3,6,1,2,4,5,7]=>000001=>100000 [1,3,4,6,7,5,2]=>[6,3,1,2,4,5,7]=>000001=>100000 [1,3,4,7,2,5,6]=>[1,3,7,2,4,5,6]=>100000=>000001 [1,3,4,7,2,6,5]=>[7,3,6,1,2,4,5]=>000000=>000000 [1,3,4,7,5,2,6]=>[1,7,3,2,4,5,6]=>100000=>000001 [1,3,4,7,5,6,2]=>[7,1,3,2,4,5,6]=>000000=>000000 [1,3,4,7,6,2,5]=>[3,7,6,1,2,4,5]=>000000=>000000 [1,3,4,7,6,5,2]=>[7,6,3,1,2,4,5]=>000000=>000000 [1,3,5,2,4,6,7]=>[1,3,5,6,2,4,7]=>100001=>100001 [1,3,5,2,4,7,6]=>[3,1,5,7,2,4,6]=>000000=>000000 [1,3,5,2,6,4,7]=>[1,3,2,5,4,6,7]=>101011=>110101 [1,3,5,2,6,7,4]=>[3,1,2,5,4,6,7]=>001011=>110100 [1,3,5,2,7,4,6]=>[3,5,1,7,2,4,6]=>000000=>000000 [1,3,5,2,7,6,4]=>[7,3,1,5,2,4,6]=>000000=>000000 [1,3,5,4,2,6,7]=>[1,3,5,4,2,6,7]=>100011=>110001 [1,3,5,4,2,7,6]=>[5,1,7,3,2,4,6]=>000000=>000000 [1,3,5,4,6,2,7]=>[1,5,3,4,2,6,7]=>100011=>110001 [1,3,5,4,6,7,2]=>[5,1,3,4,2,6,7]=>000011=>110000 [1,3,5,4,7,2,6]=>[5,7,1,3,2,4,6]=>000000=>000000 [1,3,5,4,7,6,2]=>[5,3,1,7,2,4,6]=>000000=>000000 [1,3,5,6,2,4,7]=>[1,3,5,2,4,6,7]=>100011=>110001 [1,3,5,6,2,7,4]=>[3,1,5,2,4,6,7]=>000011=>110000 [1,3,5,6,4,2,7]=>[1,5,3,2,4,6,7]=>100011=>110001 [1,3,5,6,4,7,2]=>[5,1,3,2,4,6,7]=>000011=>110000 [1,3,5,6,7,2,4]=>[3,5,1,2,4,6,7]=>000011=>110000 [1,3,5,6,7,4,2]=>[5,3,1,2,4,6,7]=>000011=>110000 [1,3,5,7,2,4,6]=>[3,5,7,1,2,4,6]=>000000=>000000 [1,3,5,7,2,6,4]=>[7,3,5,1,2,4,6]=>000000=>000000 [1,3,5,7,4,2,6]=>[5,7,3,1,2,4,6]=>000000=>000000 [1,3,5,7,4,6,2]=>[5,3,7,1,2,4,6]=>000000=>000000 [1,3,5,7,6,2,4]=>[3,7,5,1,2,4,6]=>000000=>000000 [1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>000000=>000000 [1,3,6,2,4,5,7]=>[1,3,4,6,2,5,7]=>100001=>100001 [1,3,6,2,4,7,5]=>[3,1,6,7,2,4,5]=>000000=>000000 [1,3,6,2,5,4,7]=>[1,6,3,5,2,4,7]=>100001=>100001 [1,3,6,2,5,7,4]=>[6,1,3,5,2,4,7]=>000001=>100000 [1,3,6,2,7,4,5]=>[3,6,1,7,2,4,5]=>000000=>000000 [1,3,6,2,7,5,4]=>[6,3,1,5,2,4,7]=>000001=>100000 [1,3,6,4,2,5,7]=>[1,3,6,4,2,5,7]=>100001=>100001 [1,3,6,4,2,7,5]=>[6,1,7,3,2,4,5]=>000000=>000000 [1,3,6,4,5,2,7]=>[1,6,3,4,2,5,7]=>100001=>100001 [1,3,6,4,5,7,2]=>[6,1,3,4,2,5,7]=>000001=>100000 [1,3,6,4,7,2,5]=>[6,7,1,3,2,4,5]=>000000=>000000 [1,3,6,4,7,5,2]=>[6,3,1,7,2,4,5]=>000000=>000000 [1,3,6,5,2,4,7]=>[1,3,6,5,2,4,7]=>100001=>100001 [1,3,6,5,2,7,4]=>[3,1,6,5,2,4,7]=>000001=>100000 [1,3,6,5,4,2,7]=>[1,6,5,3,2,4,7]=>100001=>100001 [1,3,6,5,4,7,2]=>[6,1,5,3,2,4,7]=>000001=>100000 [1,3,6,5,7,2,4]=>[3,6,1,5,2,4,7]=>000001=>100000 [1,3,6,5,7,4,2]=>[6,5,1,3,2,4,7]=>000001=>100000 [1,3,6,7,2,4,5]=>[3,6,7,1,2,4,5]=>000000=>000000 [1,3,6,7,2,5,4]=>[6,3,5,1,2,4,7]=>000001=>100000 [1,3,6,7,4,2,5]=>[6,7,3,1,2,4,5]=>000000=>000000 [1,3,6,7,4,5,2]=>[6,3,7,1,2,4,5]=>000000=>000000 [1,3,6,7,5,2,4]=>[3,6,5,1,2,4,7]=>000001=>100000 [1,3,6,7,5,4,2]=>[6,5,3,1,2,4,7]=>000001=>100000 [1,3,7,2,4,5,6]=>[1,3,4,7,2,5,6]=>100000=>000001 [1,3,7,2,4,6,5]=>[7,1,3,6,2,4,5]=>000000=>000000 [1,3,7,2,5,4,6]=>[1,7,3,5,2,4,6]=>100000=>000001 [1,3,7,2,5,6,4]=>[7,1,3,5,2,4,6]=>000000=>000000 [1,3,7,2,6,4,5]=>[1,7,3,6,2,4,5]=>100000=>000001 [1,3,7,2,6,5,4]=>[7,6,3,5,1,2,4]=>000000=>000000 [1,3,7,4,2,5,6]=>[1,3,7,4,2,5,6]=>100000=>000001 [1,3,7,4,2,6,5]=>[3,1,7,6,2,4,5]=>000000=>000000 [1,3,7,4,5,2,6]=>[1,7,3,4,2,5,6]=>100000=>000001 [1,3,7,4,5,6,2]=>[7,1,3,4,2,5,6]=>000000=>000000 [1,3,7,4,6,2,5]=>[3,7,1,6,2,4,5]=>000000=>000000 [1,3,7,4,6,5,2]=>[7,6,1,3,2,4,5]=>000000=>000000 [1,3,7,5,2,4,6]=>[1,3,7,5,2,4,6]=>100000=>000001 [1,3,7,5,2,6,4]=>[3,1,7,5,2,4,6]=>000000=>000000 [1,3,7,5,4,2,6]=>[1,7,5,3,2,4,6]=>100000=>000001 [1,3,7,5,4,6,2]=>[7,1,5,3,2,4,6]=>000000=>000000 [1,3,7,5,6,2,4]=>[3,7,1,5,2,4,6]=>000000=>000000 [1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>000000=>000000 [1,3,7,6,2,4,5]=>[1,3,7,6,2,4,5]=>100000=>000001 [1,3,7,6,2,5,4]=>[7,3,6,5,1,2,4]=>000000=>000000 [1,3,7,6,4,2,5]=>[1,7,6,3,2,4,5]=>100000=>000001 [1,3,7,6,4,5,2]=>[7,1,6,3,2,4,5]=>000000=>000000 [1,3,7,6,5,2,4]=>[3,7,6,5,1,2,4]=>000000=>000000 [1,3,7,6,5,4,2]=>[7,6,5,3,1,2,4]=>000000=>000000 [1,4,2,3,5,6,7]=>[1,2,4,5,6,3,7]=>110001=>100011 [1,4,2,3,5,7,6]=>[4,1,2,3,7,5,6]=>000100=>001000 [1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>100101=>101001 [1,4,2,3,6,7,5]=>[4,1,2,3,6,5,7]=>000101=>101000 [1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>100100=>001001 [1,4,2,3,7,6,5]=>[7,4,1,2,6,3,5]=>000000=>000000 [1,4,2,5,3,6,7]=>[1,4,5,2,6,3,7]=>100001=>100001 [1,4,2,5,3,7,6]=>[4,1,5,2,7,3,6]=>000000=>000000 [1,4,2,5,6,3,7]=>[1,4,2,5,6,3,7]=>100001=>100001 [1,4,2,5,6,7,3]=>[4,1,2,5,6,3,7]=>000001=>100000 [1,4,2,5,7,3,6]=>[4,5,1,2,7,3,6]=>000000=>000000 [1,4,2,5,7,6,3]=>[7,4,1,2,5,3,6]=>000000=>000000 [1,4,2,6,3,5,7]=>[1,2,4,3,6,5,7]=>110101=>101011 [1,4,2,6,3,7,5]=>[4,1,6,2,7,3,5]=>000000=>000000 [1,4,2,6,5,3,7]=>[1,6,4,2,5,3,7]=>100001=>100001 [1,4,2,6,5,7,3]=>[6,1,4,2,5,3,7]=>000001=>100000 [1,4,2,6,7,3,5]=>[4,6,1,2,7,3,5]=>000000=>000000 [1,4,2,6,7,5,3]=>[6,4,1,2,5,3,7]=>000001=>100000 [1,4,2,7,3,5,6]=>[1,2,4,3,7,5,6]=>110100=>001011 [1,4,2,7,3,6,5]=>[7,1,4,2,6,3,5]=>000000=>000000 [1,4,2,7,5,3,6]=>[1,7,4,2,5,3,6]=>100000=>000001 [1,4,2,7,5,6,3]=>[7,1,4,2,5,3,6]=>000000=>000000 [1,4,2,7,6,3,5]=>[1,7,4,2,6,3,5]=>100000=>000001 [1,4,2,7,6,5,3]=>[7,6,4,1,5,2,3]=>000000=>000000 [1,4,3,2,5,6,7]=>[1,4,5,6,3,2,7]=>100001=>100001 [1,4,3,2,5,7,6]=>[4,1,3,7,5,2,6]=>000000=>000000 [1,4,3,2,6,5,7]=>[1,4,3,6,5,2,7]=>100001=>100001 [1,4,3,2,6,7,5]=>[4,1,3,6,5,2,7]=>000001=>100000 [1,4,3,2,7,5,6]=>[1,4,3,7,5,2,6]=>100000=>000001 [1,4,3,2,7,6,5]=>[4,3,1,7,6,2,5]=>000000=>000000 [1,4,3,5,2,6,7]=>[1,4,5,3,6,2,7]=>100001=>100001 [1,4,3,5,2,7,6]=>[4,1,7,3,5,2,6]=>000000=>000000 [1,4,3,5,6,2,7]=>[1,4,3,5,6,2,7]=>100001=>100001 [1,4,3,5,6,7,2]=>[4,1,3,5,6,2,7]=>000001=>100000 [1,4,3,5,7,2,6]=>[4,7,1,3,5,2,6]=>000000=>000000 [1,4,3,5,7,6,2]=>[4,3,1,2,7,5,6]=>000100=>001000 [1,4,3,6,2,5,7]=>[1,4,6,3,5,2,7]=>100001=>100001 [1,4,3,6,2,7,5]=>[4,1,6,3,5,2,7]=>000001=>100000 [1,4,3,6,5,2,7]=>[1,4,3,2,6,5,7]=>100101=>101001 [1,4,3,6,5,7,2]=>[4,1,3,2,6,5,7]=>000101=>101000 [1,4,3,6,7,2,5]=>[4,6,1,3,5,2,7]=>000001=>100000 [1,4,3,6,7,5,2]=>[4,3,1,2,6,5,7]=>000101=>101000 [1,4,3,7,2,5,6]=>[1,4,7,3,5,2,6]=>100000=>000001 [1,4,3,7,2,6,5]=>[4,3,7,1,6,2,5]=>000000=>000000 [1,4,3,7,5,2,6]=>[1,4,3,2,7,5,6]=>100100=>001001 [1,4,3,7,5,6,2]=>[4,1,3,2,7,5,6]=>000100=>001000 [1,4,3,7,6,2,5]=>[4,7,3,1,6,2,5]=>000000=>000000 [1,4,3,7,6,5,2]=>[7,4,3,1,6,2,5]=>000000=>000000 [1,4,5,2,3,6,7]=>[1,4,5,6,2,3,7]=>100001=>100001 [1,4,5,2,3,7,6]=>[4,1,5,7,2,3,6]=>000000=>000000 [1,4,5,2,6,3,7]=>[1,4,2,5,3,6,7]=>100011=>110001 [1,4,5,2,6,7,3]=>[4,1,2,5,3,6,7]=>000011=>110000 [1,4,5,2,7,3,6]=>[4,5,1,7,2,3,6]=>000000=>000000 [1,4,5,2,7,6,3]=>[7,4,1,5,2,3,6]=>000000=>000000 [1,4,5,3,2,6,7]=>[1,4,5,3,2,6,7]=>100011=>110001 [1,4,5,3,2,7,6]=>[4,1,7,3,2,5,6]=>000000=>000000 [1,4,5,3,6,2,7]=>[1,4,3,5,2,6,7]=>100011=>110001 [1,4,5,3,6,7,2]=>[4,1,3,5,2,6,7]=>000011=>110000 [1,4,5,3,7,2,6]=>[4,7,1,3,2,5,6]=>000000=>000000 [1,4,5,3,7,6,2]=>[4,3,1,7,2,5,6]=>000000=>000000 [1,4,5,6,2,3,7]=>[1,4,5,2,3,6,7]=>100011=>110001 [1,4,5,6,2,7,3]=>[4,1,5,2,3,6,7]=>000011=>110000 [1,4,5,6,3,2,7]=>[1,4,3,2,5,6,7]=>100111=>111001 [1,4,5,6,3,7,2]=>[4,1,3,2,5,6,7]=>000111=>111000 [1,4,5,6,7,2,3]=>[4,5,1,2,3,6,7]=>000011=>110000 [1,4,5,6,7,3,2]=>[4,3,1,2,5,6,7]=>000111=>111000 [1,4,5,7,2,3,6]=>[4,5,7,1,2,3,6]=>000000=>000000 [1,4,5,7,2,6,3]=>[7,4,5,1,2,3,6]=>000000=>000000 [1,4,5,7,3,2,6]=>[4,7,3,1,2,5,6]=>000000=>000000 [1,4,5,7,3,6,2]=>[4,3,7,1,2,5,6]=>000000=>000000 [1,4,5,7,6,2,3]=>[4,7,5,1,2,3,6]=>000000=>000000 [1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>000000=>000000 [1,4,6,2,3,5,7]=>[1,2,4,6,3,5,7]=>110001=>100011 [1,4,6,2,3,7,5]=>[4,1,6,7,2,3,5]=>000000=>000000 [1,4,6,2,5,3,7]=>[1,6,4,5,2,3,7]=>100001=>100001 [1,4,6,2,5,7,3]=>[6,1,4,5,2,3,7]=>000001=>100000 [1,4,6,2,7,3,5]=>[4,6,1,7,2,3,5]=>000000=>000000 [1,4,6,2,7,5,3]=>[6,4,1,5,2,3,7]=>000001=>100000 [1,4,6,3,2,5,7]=>[1,4,6,3,2,5,7]=>100001=>100001 [1,4,6,3,2,7,5]=>[4,1,6,3,2,5,7]=>000001=>100000 [1,4,6,3,5,2,7]=>[1,4,3,6,2,5,7]=>100001=>100001 [1,4,6,3,5,7,2]=>[4,1,3,6,2,5,7]=>000001=>100000 [1,4,6,3,7,2,5]=>[4,6,1,3,2,5,7]=>000001=>100000 [1,4,6,3,7,5,2]=>[4,3,1,6,2,5,7]=>000001=>100000 [1,4,6,5,2,3,7]=>[1,4,6,5,2,3,7]=>100001=>100001 [1,4,6,5,2,7,3]=>[4,1,6,5,2,3,7]=>000001=>100000 [1,4,6,5,3,2,7]=>[1,6,4,3,2,5,7]=>100001=>100001 [1,4,6,5,3,7,2]=>[6,1,4,3,2,5,7]=>000001=>100000 [1,4,6,5,7,2,3]=>[4,6,1,5,2,3,7]=>000001=>100000 [1,4,6,5,7,3,2]=>[6,4,1,3,2,5,7]=>000001=>100000 [1,4,6,7,2,3,5]=>[4,6,7,1,2,3,5]=>000000=>000000 [1,4,6,7,2,5,3]=>[6,4,5,1,2,3,7]=>000001=>100000 [1,4,6,7,3,2,5]=>[4,6,3,1,2,5,7]=>000001=>100000 [1,4,6,7,3,5,2]=>[4,3,6,1,2,5,7]=>000001=>100000 [1,4,6,7,5,2,3]=>[4,6,5,1,2,3,7]=>000001=>100000 [1,4,6,7,5,3,2]=>[6,4,3,1,2,5,7]=>000001=>100000 [1,4,7,2,3,5,6]=>[1,2,4,7,3,5,6]=>110000=>000011 [1,4,7,2,3,6,5]=>[7,1,4,6,2,3,5]=>000000=>000000 [1,4,7,2,5,3,6]=>[1,7,4,5,2,3,6]=>100000=>000001 [1,4,7,2,5,6,3]=>[7,1,4,5,2,3,6]=>000000=>000000 [1,4,7,2,6,3,5]=>[1,7,4,6,2,3,5]=>100000=>000001 [1,4,7,2,6,5,3]=>[7,6,4,5,1,2,3]=>000000=>000000 [1,4,7,3,2,5,6]=>[1,4,7,3,2,5,6]=>100000=>000001 [1,4,7,3,2,6,5]=>[4,3,7,6,1,2,5]=>000000=>000000 [1,4,7,3,5,2,6]=>[1,4,3,7,2,5,6]=>100000=>000001 [1,4,7,3,5,6,2]=>[4,1,3,7,2,5,6]=>000000=>000000 [1,4,7,3,6,2,5]=>[4,7,3,6,1,2,5]=>000000=>000000 [1,4,7,3,6,5,2]=>[7,4,3,6,1,2,5]=>000000=>000000 [1,4,7,5,2,3,6]=>[1,4,7,5,2,3,6]=>100000=>000001 [1,4,7,5,2,6,3]=>[4,1,7,5,2,3,6]=>000000=>000000 [1,4,7,5,3,2,6]=>[1,7,4,3,2,5,6]=>100000=>000001 [1,4,7,5,3,6,2]=>[7,1,4,3,2,5,6]=>000000=>000000 [1,4,7,5,6,2,3]=>[4,7,1,5,2,3,6]=>000000=>000000 [1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>000000=>000000 [1,4,7,6,2,3,5]=>[1,4,7,6,2,3,5]=>100000=>000001 [1,4,7,6,2,5,3]=>[7,4,6,5,1,2,3]=>000000=>000000 [1,4,7,6,3,2,5]=>[4,7,6,3,1,2,5]=>000000=>000000 [1,4,7,6,3,5,2]=>[7,4,6,3,1,2,5]=>000000=>000000 [1,4,7,6,5,2,3]=>[4,7,6,5,1,2,3]=>000000=>000000 [1,4,7,6,5,3,2]=>[7,6,4,3,1,2,5]=>000000=>000000 [1,5,2,3,4,6,7]=>[1,2,3,5,6,4,7]=>111001=>100111 [1,5,2,3,4,7,6]=>[5,1,2,3,7,4,6]=>000000=>000000 [1,5,2,3,6,4,7]=>[1,5,2,3,6,4,7]=>100001=>100001 [1,5,2,3,6,7,4]=>[5,1,2,3,6,4,7]=>000001=>100000 [1,5,2,3,7,4,6]=>[1,5,2,3,7,4,6]=>100000=>000001 [1,5,2,3,7,6,4]=>[7,5,1,2,6,3,4]=>000000=>000000 [1,5,2,4,3,6,7]=>[1,2,5,4,6,3,7]=>110001=>100011 [1,5,2,4,3,7,6]=>[5,1,7,2,4,3,6]=>000000=>000000 [1,5,2,4,6,3,7]=>[1,5,2,4,6,3,7]=>100001=>100001 [1,5,2,4,6,7,3]=>[5,1,2,4,6,3,7]=>000001=>100000 [1,5,2,4,7,3,6]=>[5,7,1,2,4,3,6]=>000000=>000000 [1,5,2,4,7,6,3]=>[5,4,1,2,7,3,6]=>000000=>000000 [1,5,2,6,3,4,7]=>[1,2,5,3,6,4,7]=>110001=>100011 [1,5,2,6,3,7,4]=>[5,1,6,2,7,3,4]=>000000=>000000 [1,5,2,6,4,3,7]=>[1,5,4,2,6,3,7]=>100001=>100001 [1,5,2,6,4,7,3]=>[5,1,4,2,6,3,7]=>000001=>100000 [1,5,2,6,7,3,4]=>[5,6,1,2,7,3,4]=>000000=>000000 [1,5,2,6,7,4,3]=>[5,4,1,2,6,3,7]=>000001=>100000 [1,5,2,7,3,4,6]=>[1,2,5,3,7,4,6]=>110000=>000011 [1,5,2,7,3,6,4]=>[7,1,5,2,6,3,4]=>000000=>000000 [1,5,2,7,4,3,6]=>[1,5,4,2,7,3,6]=>100000=>000001 [1,5,2,7,4,6,3]=>[5,1,4,2,7,3,6]=>000000=>000000 [1,5,2,7,6,3,4]=>[1,7,5,2,6,3,4]=>100000=>000001 [1,5,2,7,6,4,3]=>[7,5,4,1,6,2,3]=>000000=>000000 [1,5,3,2,4,6,7]=>[1,3,5,6,4,2,7]=>100001=>100001 [1,5,3,2,4,7,6]=>[5,1,3,7,4,2,6]=>000000=>000000 [1,5,3,2,6,4,7]=>[1,5,3,6,4,2,7]=>100001=>100001 [1,5,3,2,6,7,4]=>[5,1,3,6,4,2,7]=>000001=>100000 [1,5,3,2,7,4,6]=>[1,5,3,7,4,2,6]=>100000=>000001 [1,5,3,2,7,6,4]=>[5,3,1,7,6,2,4]=>000000=>000000 [1,5,3,4,2,6,7]=>[1,3,5,4,6,2,7]=>100001=>100001 [1,5,3,4,2,7,6]=>[5,1,7,3,4,2,6]=>000000=>000000 [1,5,3,4,6,2,7]=>[1,5,3,4,6,2,7]=>100001=>100001 [1,5,3,4,6,7,2]=>[5,1,3,4,6,2,7]=>000001=>100000 [1,5,3,4,7,2,6]=>[5,7,1,3,4,2,6]=>000000=>000000 [1,5,3,4,7,6,2]=>[5,3,1,2,7,4,6]=>000000=>000000 [1,5,3,6,2,4,7]=>[1,5,6,3,4,2,7]=>100001=>100001 [1,5,3,6,2,7,4]=>[5,1,6,3,4,2,7]=>000001=>100000 [1,5,3,6,4,2,7]=>[1,5,3,2,6,4,7]=>100001=>100001 [1,5,3,6,4,7,2]=>[5,1,3,2,6,4,7]=>000001=>100000 [1,5,3,6,7,2,4]=>[5,6,1,3,4,2,7]=>000001=>100000 [1,5,3,6,7,4,2]=>[5,3,1,2,6,4,7]=>000001=>100000 [1,5,3,7,2,4,6]=>[1,5,7,3,4,2,6]=>100000=>000001 [1,5,3,7,2,6,4]=>[5,3,7,1,6,2,4]=>000000=>000000 [1,5,3,7,4,2,6]=>[1,5,3,2,7,4,6]=>100000=>000001 [1,5,3,7,4,6,2]=>[5,1,3,2,7,4,6]=>000000=>000000 [1,5,3,7,6,2,4]=>[5,7,3,1,6,2,4]=>000000=>000000 [1,5,3,7,6,4,2]=>[7,5,3,1,6,2,4]=>000000=>000000 [1,5,4,2,3,6,7]=>[1,2,5,6,4,3,7]=>110001=>100011 [1,5,4,2,3,7,6]=>[5,1,2,7,4,3,6]=>000000=>000000 [1,5,4,2,6,3,7]=>[1,5,2,6,4,3,7]=>100001=>100001 [1,5,4,2,6,7,3]=>[5,1,2,6,4,3,7]=>000001=>100000 [1,5,4,2,7,3,6]=>[1,5,2,7,4,3,6]=>100000=>000001 [1,5,4,2,7,6,3]=>[5,4,1,7,6,2,3]=>000000=>000000 [1,5,4,3,2,6,7]=>[1,5,6,4,3,2,7]=>100001=>100001 [1,5,4,3,2,7,6]=>[5,1,7,4,3,2,6]=>000000=>000000 [1,5,4,3,6,2,7]=>[1,5,4,6,3,2,7]=>100001=>100001 [1,5,4,3,6,7,2]=>[5,1,4,6,3,2,7]=>000001=>100000 [1,5,4,3,7,2,6]=>[5,7,1,4,3,2,6]=>000000=>000000 [1,5,4,3,7,6,2]=>[5,4,1,7,3,2,6]=>000000=>000000 [1,5,4,6,2,3,7]=>[1,5,6,2,4,3,7]=>100001=>100001 [1,5,4,6,2,7,3]=>[5,1,6,2,4,3,7]=>000001=>100000 [1,5,4,6,3,2,7]=>[1,5,4,3,6,2,7]=>100001=>100001 [1,5,4,6,3,7,2]=>[5,1,4,3,6,2,7]=>000001=>100000 [1,5,4,6,7,2,3]=>[5,6,1,2,4,3,7]=>000001=>100000 [1,5,4,6,7,3,2]=>[5,4,1,3,6,2,7]=>000001=>100000 [1,5,4,7,2,3,6]=>[1,5,7,2,4,3,6]=>100000=>000001 [1,5,4,7,2,6,3]=>[5,4,7,1,6,2,3]=>000000=>000000 [1,5,4,7,3,2,6]=>[5,7,4,1,3,2,6]=>000000=>000000 [1,5,4,7,3,6,2]=>[5,4,7,1,3,2,6]=>000000=>000000 [1,5,4,7,6,2,3]=>[5,7,4,1,6,2,3]=>000000=>000000 [1,5,4,7,6,3,2]=>[5,4,3,1,7,2,6]=>000000=>000000 [1,5,6,2,3,4,7]=>[1,2,5,6,3,4,7]=>110001=>100011 [1,5,6,2,3,7,4]=>[5,1,6,7,2,3,4]=>000000=>000000 [1,5,6,2,4,3,7]=>[1,5,4,6,2,3,7]=>100001=>100001 [1,5,6,2,4,7,3]=>[5,1,4,6,2,3,7]=>000001=>100000 [1,5,6,2,7,3,4]=>[5,6,1,7,2,3,4]=>000000=>000000 [1,5,6,2,7,4,3]=>[5,4,1,6,2,3,7]=>000001=>100000 [1,5,6,3,2,4,7]=>[1,5,6,3,2,4,7]=>100001=>100001 [1,5,6,3,2,7,4]=>[5,1,6,3,2,4,7]=>000001=>100000 [1,5,6,3,4,2,7]=>[1,5,3,6,2,4,7]=>100001=>100001 [1,5,6,3,4,7,2]=>[5,1,3,6,2,4,7]=>000001=>100000 [1,5,6,3,7,2,4]=>[5,6,1,3,2,4,7]=>000001=>100000 [1,5,6,3,7,4,2]=>[5,3,1,6,2,4,7]=>000001=>100000 [1,5,6,4,2,3,7]=>[1,5,6,4,2,3,7]=>100001=>100001 [1,5,6,4,2,7,3]=>[5,1,6,4,2,3,7]=>000001=>100000 [1,5,6,4,3,2,7]=>[1,5,4,3,2,6,7]=>100011=>110001 [1,5,6,4,3,7,2]=>[5,1,4,3,2,6,7]=>000011=>110000 [1,5,6,4,7,2,3]=>[5,6,1,4,2,3,7]=>000001=>100000 [1,5,6,4,7,3,2]=>[5,4,1,3,2,6,7]=>000011=>110000 [1,5,6,7,2,3,4]=>[5,6,7,1,2,3,4]=>000000=>000000 [1,5,6,7,2,4,3]=>[5,4,6,1,2,3,7]=>000001=>100000 [1,5,6,7,3,2,4]=>[5,6,3,1,2,4,7]=>000001=>100000 [1,5,6,7,3,4,2]=>[5,3,6,1,2,4,7]=>000001=>100000 [1,5,6,7,4,2,3]=>[5,6,4,1,2,3,7]=>000001=>100000 [1,5,6,7,4,3,2]=>[5,4,3,1,2,6,7]=>000011=>110000 [1,5,7,2,3,4,6]=>[1,2,5,7,3,4,6]=>110000=>000011 [1,5,7,2,3,6,4]=>[7,1,5,6,2,3,4]=>000000=>000000 [1,5,7,2,4,3,6]=>[1,5,4,7,2,3,6]=>100000=>000001 [1,5,7,2,4,6,3]=>[5,1,4,7,2,3,6]=>000000=>000000 [1,5,7,2,6,3,4]=>[1,7,5,6,2,3,4]=>100000=>000001 [1,5,7,2,6,4,3]=>[7,5,4,6,1,2,3]=>000000=>000000 [1,5,7,3,2,4,6]=>[1,5,7,3,2,4,6]=>100000=>000001 [1,5,7,3,2,6,4]=>[5,3,7,6,1,2,4]=>000000=>000000 [1,5,7,3,4,2,6]=>[1,5,3,7,2,4,6]=>100000=>000001 [1,5,7,3,4,6,2]=>[5,1,3,7,2,4,6]=>000000=>000000 [1,5,7,3,6,2,4]=>[5,7,3,6,1,2,4]=>000000=>000000 [1,5,7,3,6,4,2]=>[7,5,3,6,1,2,4]=>000000=>000000 [1,5,7,4,2,3,6]=>[1,5,7,4,2,3,6]=>100000=>000001 [1,5,7,4,2,6,3]=>[5,4,7,6,1,2,3]=>000000=>000000 [1,5,7,4,3,2,6]=>[5,7,4,3,1,2,6]=>000000=>000000 [1,5,7,4,3,6,2]=>[5,4,7,3,1,2,6]=>000000=>000000 [1,5,7,4,6,2,3]=>[5,7,4,6,1,2,3]=>000000=>000000 [1,5,7,4,6,3,2]=>[5,4,3,7,1,2,6]=>000000=>000000 [1,5,7,6,2,3,4]=>[1,5,7,6,2,3,4]=>100000=>000001 [1,5,7,6,2,4,3]=>[7,5,6,4,1,2,3]=>000000=>000000 [1,5,7,6,3,2,4]=>[5,7,6,3,1,2,4]=>000000=>000000 [1,5,7,6,3,4,2]=>[7,5,6,3,1,2,4]=>000000=>000000 [1,5,7,6,4,2,3]=>[5,7,6,4,1,2,3]=>000000=>000000 [1,5,7,6,4,3,2]=>[7,5,4,3,1,2,6]=>000000=>000000 [1,6,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>111101=>101111 [1,6,2,3,4,7,5]=>[6,1,2,3,7,4,5]=>000000=>000000 [1,6,2,3,5,4,7]=>[1,6,2,3,5,4,7]=>100001=>100001 [1,6,2,3,5,7,4]=>[6,1,2,3,5,4,7]=>000001=>100000 [1,6,2,3,7,4,5]=>[1,6,2,3,7,4,5]=>100000=>000001 [1,6,2,3,7,5,4]=>[6,5,1,2,7,3,4]=>000000=>000000 [1,6,2,4,3,5,7]=>[1,2,6,4,5,3,7]=>110001=>100011 [1,6,2,4,3,7,5]=>[6,1,7,2,4,3,5]=>000000=>000000 [1,6,2,4,5,3,7]=>[1,6,2,4,5,3,7]=>100001=>100001 [1,6,2,4,5,7,3]=>[6,1,2,4,5,3,7]=>000001=>100000 [1,6,2,4,7,3,5]=>[6,7,1,2,4,3,5]=>000000=>000000 [1,6,2,4,7,5,3]=>[6,4,1,2,7,3,5]=>000000=>000000 [1,6,2,5,3,4,7]=>[1,2,6,3,5,4,7]=>110001=>100011 [1,6,2,5,3,7,4]=>[6,1,7,2,5,3,4]=>000000=>000000 [1,6,2,5,4,3,7]=>[1,6,5,2,4,3,7]=>100001=>100001 [1,6,2,5,4,7,3]=>[6,1,5,2,4,3,7]=>000001=>100000 [1,6,2,5,7,3,4]=>[6,7,1,2,5,3,4]=>000000=>000000 [1,6,2,5,7,4,3]=>[6,5,1,2,4,3,7]=>000001=>100000 [1,6,2,7,3,4,5]=>[1,2,6,3,7,4,5]=>110000=>000011 [1,6,2,7,3,5,4]=>[6,1,5,2,7,3,4]=>000000=>000000 [1,6,2,7,4,3,5]=>[1,6,4,2,7,3,5]=>100000=>000001 [1,6,2,7,4,5,3]=>[6,1,4,2,7,3,5]=>000000=>000000 [1,6,2,7,5,3,4]=>[1,6,5,2,7,3,4]=>100000=>000001 [1,6,2,7,5,4,3]=>[6,5,4,1,7,2,3]=>000000=>000000 [1,6,3,2,4,5,7]=>[1,3,4,6,5,2,7]=>100001=>100001 [1,6,3,2,4,7,5]=>[6,1,3,7,4,2,5]=>000000=>000000 [1,6,3,2,5,4,7]=>[1,3,2,6,5,4,7]=>101001=>100101 [1,6,3,2,5,7,4]=>[3,1,2,6,5,4,7]=>001001=>100100 [1,6,3,2,7,4,5]=>[1,6,3,7,4,2,5]=>100000=>000001 [1,6,3,2,7,5,4]=>[6,3,1,7,5,2,4]=>000000=>000000 [1,6,3,4,2,5,7]=>[1,3,6,4,5,2,7]=>100001=>100001 [1,6,3,4,2,7,5]=>[6,1,7,3,4,2,5]=>000000=>000000 [1,6,3,4,5,2,7]=>[1,6,3,4,5,2,7]=>100001=>100001 [1,6,3,4,5,7,2]=>[6,1,3,4,5,2,7]=>000001=>100000 [1,6,3,4,7,2,5]=>[6,7,1,3,4,2,5]=>000000=>000000 [1,6,3,4,7,5,2]=>[6,3,1,2,7,4,5]=>000000=>000000 [1,6,3,5,2,4,7]=>[1,3,6,2,5,4,7]=>100001=>100001 [1,6,3,5,2,7,4]=>[3,1,6,2,5,4,7]=>000001=>100000 [1,6,3,5,4,2,7]=>[1,6,5,3,4,2,7]=>100001=>100001 [1,6,3,5,4,7,2]=>[6,1,5,3,4,2,7]=>000001=>100000 [1,6,3,5,7,2,4]=>[3,6,1,2,5,4,7]=>000001=>100000 [1,6,3,5,7,4,2]=>[6,5,1,3,4,2,7]=>000001=>100000 [1,6,3,7,2,4,5]=>[1,6,7,3,4,2,5]=>100000=>000001 [1,6,3,7,2,5,4]=>[6,3,7,1,5,2,4]=>000000=>000000 [1,6,3,7,4,2,5]=>[1,6,3,2,7,4,5]=>100000=>000001 [1,6,3,7,4,5,2]=>[6,1,3,2,7,4,5]=>000000=>000000 [1,6,3,7,5,2,4]=>[6,7,3,1,5,2,4]=>000000=>000000 [1,6,3,7,5,4,2]=>[6,5,3,1,7,2,4]=>000000=>000000 [1,6,4,2,3,5,7]=>[1,2,4,6,5,3,7]=>110001=>100011 [1,6,4,2,3,7,5]=>[6,1,2,7,4,3,5]=>000000=>000000 [1,6,4,2,5,3,7]=>[1,4,2,6,5,3,7]=>100001=>100001 [1,6,4,2,5,7,3]=>[4,1,2,6,5,3,7]=>000001=>100000 [1,6,4,2,7,3,5]=>[1,6,2,7,4,3,5]=>100000=>000001 [1,6,4,2,7,5,3]=>[6,4,1,7,5,2,3]=>000000=>000000 [1,6,4,3,2,5,7]=>[1,4,6,5,3,2,7]=>100001=>100001 [1,6,4,3,2,7,5]=>[6,1,7,4,3,2,5]=>000000=>000000 [1,6,4,3,5,2,7]=>[1,6,4,5,3,2,7]=>100001=>100001 [1,6,4,3,5,7,2]=>[6,1,4,5,3,2,7]=>000001=>100000 [1,6,4,3,7,2,5]=>[6,7,1,4,3,2,5]=>000000=>000000 [1,6,4,3,7,5,2]=>[6,4,1,7,3,2,5]=>000000=>000000 [1,6,4,5,2,3,7]=>[1,4,6,2,5,3,7]=>100001=>100001 [1,6,4,5,2,7,3]=>[4,1,6,2,5,3,7]=>000001=>100000 [1,6,4,5,3,2,7]=>[1,6,4,3,5,2,7]=>100001=>100001 [1,6,4,5,3,7,2]=>[6,1,4,3,5,2,7]=>000001=>100000 [1,6,4,5,7,2,3]=>[4,6,1,2,5,3,7]=>000001=>100000 [1,6,4,5,7,3,2]=>[6,4,1,3,5,2,7]=>000001=>100000 [1,6,4,7,2,3,5]=>[1,6,7,2,4,3,5]=>100000=>000001 [1,6,4,7,2,5,3]=>[6,4,7,1,5,2,3]=>000000=>000000 [1,6,4,7,3,2,5]=>[6,7,4,1,3,2,5]=>000000=>000000 [1,6,4,7,3,5,2]=>[6,4,7,1,3,2,5]=>000000=>000000 [1,6,4,7,5,2,3]=>[6,7,4,1,5,2,3]=>000000=>000000 [1,6,4,7,5,3,2]=>[6,4,3,1,7,2,5]=>000000=>000000 [1,6,5,2,3,4,7]=>[1,2,3,6,5,4,7]=>111001=>100111 [1,6,5,2,3,7,4]=>[6,1,2,7,5,3,4]=>000000=>000000 [1,6,5,2,4,3,7]=>[1,6,2,5,4,3,7]=>100001=>100001 [1,6,5,2,4,7,3]=>[6,1,2,5,4,3,7]=>000001=>100000 [1,6,5,2,7,3,4]=>[1,6,2,7,5,3,4]=>100000=>000001 [1,6,5,2,7,4,3]=>[6,5,1,7,4,2,3]=>000000=>000000 [1,6,5,3,2,4,7]=>[1,3,6,5,4,2,7]=>100001=>100001 [1,6,5,3,2,7,4]=>[6,1,7,5,3,2,4]=>000000=>000000 [1,6,5,3,4,2,7]=>[1,6,3,5,4,2,7]=>100001=>100001 [1,6,5,3,4,7,2]=>[6,1,3,5,4,2,7]=>000001=>100000 [1,6,5,3,7,2,4]=>[6,7,1,5,3,2,4]=>000000=>000000 [1,6,5,3,7,4,2]=>[6,5,1,7,3,2,4]=>000000=>000000 [1,6,5,4,2,3,7]=>[1,2,6,5,4,3,7]=>110001=>100011 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[1,6,7,3,4,5,2]=>[6,1,3,7,2,4,5]=>000000=>000000 [1,6,7,3,5,2,4]=>[6,7,3,5,1,2,4]=>000000=>000000 [1,6,7,3,5,4,2]=>[6,5,3,7,1,2,4]=>000000=>000000 [1,6,7,4,2,3,5]=>[1,6,7,4,2,3,5]=>100000=>000001 [1,6,7,4,2,5,3]=>[6,4,7,5,1,2,3]=>000000=>000000 [1,6,7,4,3,2,5]=>[6,7,4,3,1,2,5]=>000000=>000000 [1,6,7,4,3,5,2]=>[6,4,7,3,1,2,5]=>000000=>000000 [1,6,7,4,5,2,3]=>[6,7,4,5,1,2,3]=>000000=>000000 [1,6,7,4,5,3,2]=>[6,4,3,7,1,2,5]=>000000=>000000 [1,6,7,5,2,3,4]=>[1,6,7,5,2,3,4]=>100000=>000001 [1,6,7,5,2,4,3]=>[6,5,7,4,1,2,3]=>000000=>000000 [1,6,7,5,3,2,4]=>[6,7,5,3,1,2,4]=>000000=>000000 [1,6,7,5,3,4,2]=>[6,5,7,3,1,2,4]=>000000=>000000 [1,6,7,5,4,2,3]=>[6,7,5,4,1,2,3]=>000000=>000000 [1,6,7,5,4,3,2]=>[6,5,4,3,1,2,7]=>000001=>100000 [1,7,2,3,4,5,6]=>[1,2,3,4,7,5,6]=>111100=>001111 [1,7,2,3,4,6,5]=>[7,1,2,3,6,4,5]=>000000=>000000 [1,7,2,3,5,4,6]=>[1,7,2,3,5,4,6]=>100000=>000001 [1,7,2,3,5,6,4]=>[7,1,2,3,5,4,6]=>000000=>000000 [1,7,2,3,6,4,5]=>[1,7,2,3,6,4,5]=>100000=>000001 [1,7,2,3,6,5,4]=>[7,6,1,2,5,3,4]=>000000=>000000 [1,7,2,4,3,5,6]=>[1,2,7,4,5,3,6]=>110000=>000011 [1,7,2,4,3,6,5]=>[4,1,7,2,6,3,5]=>000000=>000000 [1,7,2,4,5,3,6]=>[1,7,2,4,5,3,6]=>100000=>000001 [1,7,2,4,5,6,3]=>[7,1,2,4,5,3,6]=>000000=>000000 [1,7,2,4,6,3,5]=>[4,7,1,2,6,3,5]=>000000=>000000 [1,7,2,4,6,5,3]=>[7,6,1,2,4,3,5]=>000000=>000000 [1,7,2,5,3,4,6]=>[1,2,7,3,5,4,6]=>110000=>000011 [1,7,2,5,3,6,4]=>[5,1,7,2,6,3,4]=>000000=>000000 [1,7,2,5,4,3,6]=>[1,7,5,2,4,3,6]=>100000=>000001 [1,7,2,5,4,6,3]=>[7,1,5,2,4,3,6]=>000000=>000000 [1,7,2,5,6,3,4]=>[5,7,1,2,6,3,4]=>000000=>000000 [1,7,2,5,6,4,3]=>[7,5,1,2,4,3,6]=>000000=>000000 [1,7,2,6,3,4,5]=>[1,2,7,3,6,4,5]=>110000=>000011 [1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>000000=>000000 [1,7,2,6,4,3,5]=>[1,7,6,2,4,3,5]=>100000=>000001 [1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>000000=>000000 [1,7,2,6,5,3,4]=>[1,7,6,2,5,3,4]=>100000=>000001 [1,7,2,6,5,4,3]=>[7,6,5,1,4,2,3]=>000000=>000000 [1,7,3,2,4,5,6]=>[1,3,4,7,5,2,6]=>100000=>000001 [1,7,3,2,4,6,5]=>[3,1,2,7,6,4,5]=>001000=>000100 [1,7,3,2,5,4,6]=>[1,3,2,7,5,4,6]=>101000=>000101 [1,7,3,2,5,6,4]=>[3,1,2,7,5,4,6]=>001000=>000100 [1,7,3,2,6,4,5]=>[1,3,2,7,6,4,5]=>101000=>000101 [1,7,3,2,6,5,4]=>[7,3,1,6,5,2,4]=>000000=>000000 [1,7,3,4,2,5,6]=>[1,3,7,4,5,2,6]=>100000=>000001 [1,7,3,4,2,6,5]=>[3,1,7,2,6,4,5]=>000000=>000000 [1,7,3,4,5,2,6]=>[1,7,3,4,5,2,6]=>100000=>000001 [1,7,3,4,5,6,2]=>[7,1,3,4,5,2,6]=>000000=>000000 [1,7,3,4,6,2,5]=>[3,7,1,2,6,4,5]=>000000=>000000 [1,7,3,4,6,5,2]=>[7,6,1,3,4,2,5]=>000000=>000000 [1,7,3,5,2,4,6]=>[1,3,7,2,5,4,6]=>100000=>000001 [1,7,3,5,2,6,4]=>[3,1,7,2,5,4,6]=>000000=>000000 [1,7,3,5,4,2,6]=>[1,7,5,3,4,2,6]=>100000=>000001 [1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>000000=>000000 [1,7,3,5,6,2,4]=>[3,7,1,2,5,4,6]=>000000=>000000 [1,7,3,5,6,4,2]=>[7,5,1,3,4,2,6]=>000000=>000000 [1,7,3,6,2,4,5]=>[1,3,7,2,6,4,5]=>100000=>000001 [1,7,3,6,2,5,4]=>[7,3,6,1,5,2,4]=>000000=>000000 [1,7,3,6,4,2,5]=>[1,7,6,3,4,2,5]=>100000=>000001 [1,7,3,6,4,5,2]=>[7,1,6,3,4,2,5]=>000000=>000000 [1,7,3,6,5,2,4]=>[3,7,6,1,5,2,4]=>000000=>000000 [1,7,3,6,5,4,2]=>[7,6,5,1,3,2,4]=>000000=>000000 [1,7,4,2,3,5,6]=>[1,2,4,7,5,3,6]=>110000=>000011 [1,7,4,2,3,6,5]=>[4,1,2,7,6,3,5]=>000000=>000000 [1,7,4,2,5,3,6]=>[1,4,2,7,5,3,6]=>100000=>000001 [1,7,4,2,5,6,3]=>[4,1,2,7,5,3,6]=>000000=>000000 [1,7,4,2,6,3,5]=>[1,4,2,7,6,3,5]=>100000=>000001 [1,7,4,2,6,5,3]=>[7,4,1,6,5,2,3]=>000000=>000000 [1,7,4,3,2,5,6]=>[1,4,7,5,3,2,6]=>100000=>000001 [1,7,4,3,2,6,5]=>[4,1,7,6,3,2,5]=>000000=>000000 [1,7,4,3,5,2,6]=>[1,7,4,5,3,2,6]=>100000=>000001 [1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>000000=>000000 [1,7,4,3,6,2,5]=>[4,7,1,6,3,2,5]=>000000=>000000 [1,7,4,3,6,5,2]=>[7,4,1,6,3,2,5]=>000000=>000000 [1,7,4,5,2,3,6]=>[1,4,7,2,5,3,6]=>100000=>000001 [1,7,4,5,2,6,3]=>[4,1,7,2,5,3,6]=>000000=>000000 [1,7,4,5,3,2,6]=>[1,7,4,3,5,2,6]=>100000=>000001 [1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>000000=>000000 [1,7,4,5,6,2,3]=>[4,7,1,2,5,3,6]=>000000=>000000 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[2,1,4,3,5,7,6]=>[2,1,4,5,3,7,6]=>010010=>010010 [2,1,4,3,6,5,7]=>[2,4,1,6,3,7,5]=>000000=>000000 [2,1,4,3,6,7,5]=>[2,1,4,6,3,7,5]=>010000=>000010 [2,1,4,3,7,5,6]=>[2,4,1,5,3,7,6]=>000010=>010000 [2,1,4,3,7,6,5]=>[7,2,1,4,3,6,5]=>000000=>000000 [2,1,4,5,3,6,7]=>[2,4,5,1,6,7,3]=>000000=>000000 [2,1,4,5,3,7,6]=>[2,1,4,3,5,7,6]=>010110=>011010 [2,1,4,5,6,3,7]=>[2,4,1,5,6,7,3]=>000000=>000000 [2,1,4,5,6,7,3]=>[2,1,4,5,6,7,3]=>010000=>000010 [2,1,4,5,7,3,6]=>[2,4,1,3,5,7,6]=>000110=>011000 [2,1,4,5,7,6,3]=>[7,2,1,4,5,6,3]=>000000=>000000 [2,1,4,6,3,5,7]=>[2,4,6,1,3,7,5]=>000000=>000000 [2,1,4,6,3,7,5]=>[2,1,4,3,6,7,5]=>010100=>001010 [2,1,4,6,5,3,7]=>[2,6,4,1,5,7,3]=>000000=>000000 [2,1,4,6,5,7,3]=>[6,2,4,1,5,7,3]=>000000=>000000 [2,1,4,6,7,3,5]=>[2,4,1,3,6,7,5]=>000100=>001000 [2,1,4,6,7,5,3]=>[6,2,1,4,5,7,3]=>000000=>000000 [2,1,4,7,3,5,6]=>[2,4,5,1,3,7,6]=>000010=>010000 [2,1,4,7,3,6,5]=>[7,2,4,1,3,6,5]=>000000=>000000 [2,1,4,7,5,3,6]=>[2,7,4,1,5,6,3]=>000000=>000000 [2,1,4,7,5,6,3]=>[7,2,4,1,5,6,3]=>000000=>000000 [2,1,4,7,6,3,5]=>[2,7,4,1,3,6,5]=>000000=>000000 [2,1,4,7,6,5,3]=>[7,6,2,1,4,5,3]=>000000=>000000 [2,1,5,3,4,6,7]=>[2,3,5,6,1,7,4]=>000000=>000000 [2,1,5,3,4,7,6]=>[2,1,3,5,4,7,6]=>011010=>010110 [2,1,5,3,6,4,7]=>[2,5,1,6,3,7,4]=>000000=>000000 [2,1,5,3,6,7,4]=>[2,1,5,6,3,7,4]=>010000=>000010 [2,1,5,3,7,4,6]=>[2,3,1,5,4,7,6]=>001010=>010100 [2,1,5,3,7,6,4]=>[7,2,1,5,3,6,4]=>000000=>000000 [2,1,5,4,3,6,7]=>[2,5,6,4,1,7,3]=>000000=>000000 [2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>010010=>010010 [2,1,5,4,6,3,7]=>[2,5,4,6,1,7,3]=>000000=>000000 [2,1,5,4,6,7,3]=>[5,2,4,6,1,7,3]=>000000=>000000 [2,1,5,4,7,3,6]=>[2,5,1,4,3,7,6]=>000010=>010000 [2,1,5,4,7,6,3]=>[5,2,1,4,3,7,6]=>000010=>010000 [2,1,5,6,3,4,7]=>[2,5,6,1,3,7,4]=>000000=>000000 [2,1,5,6,3,7,4]=>[2,1,5,3,6,7,4]=>010000=>000010 [2,1,5,6,4,3,7]=>[2,5,4,1,6,7,3]=>000000=>000000 [2,1,5,6,4,7,3]=>[5,2,4,1,6,7,3]=>000000=>000000 [2,1,5,6,7,3,4]=>[2,5,1,3,6,7,4]=>000000=>000000 [2,1,5,6,7,4,3]=>[5,2,1,4,6,7,3]=>000000=>000000 [2,1,5,7,3,4,6]=>[2,3,5,1,4,7,6]=>000010=>010000 [2,1,5,7,3,6,4]=>[7,2,5,1,3,6,4]=>000000=>000000 [2,1,5,7,4,3,6]=>[2,5,4,1,3,7,6]=>000010=>010000 [2,1,5,7,4,6,3]=>[5,2,4,1,3,7,6]=>000010=>010000 [2,1,5,7,6,3,4]=>[2,7,5,1,3,6,4]=>000000=>000000 [2,1,5,7,6,4,3]=>[7,5,2,1,4,6,3]=>000000=>000000 [2,1,6,3,4,5,7]=>[2,3,4,6,1,7,5]=>000000=>000000 [2,1,6,3,4,7,5]=>[2,1,3,6,4,7,5]=>011000=>000110 [2,1,6,3,5,4,7]=>[2,6,3,5,1,7,4]=>000000=>000000 [2,1,6,3,5,7,4]=>[6,2,3,5,1,7,4]=>000000=>000000 [2,1,6,3,7,4,5]=>[2,3,1,6,4,7,5]=>001000=>000100 [2,1,6,3,7,5,4]=>[6,2,1,5,3,7,4]=>000000=>000000 [2,1,6,4,3,5,7]=>[2,4,6,5,1,7,3]=>000000=>000000 [2,1,6,4,3,7,5]=>[2,1,6,4,3,7,5]=>010000=>000010 [2,1,6,4,5,3,7]=>[2,6,4,5,1,7,3]=>000000=>000000 [2,1,6,4,5,7,3]=>[6,2,4,5,1,7,3]=>000000=>000000 [2,1,6,4,7,3,5]=>[2,6,1,4,3,7,5]=>000000=>000000 [2,1,6,4,7,5,3]=>[6,2,1,4,3,7,5]=>000000=>000000 [2,1,6,5,3,4,7]=>[2,3,6,5,1,7,4]=>000000=>000000 [2,1,6,5,3,7,4]=>[2,1,6,5,3,7,4]=>010000=>000010 [2,1,6,5,4,3,7]=>[2,6,5,4,1,7,3]=>000000=>000000 [2,1,6,5,4,7,3]=>[6,2,5,4,1,7,3]=>000000=>000000 [2,1,6,5,7,3,4]=>[2,6,1,5,3,7,4]=>000000=>000000 [2,1,6,5,7,4,3]=>[6,5,2,4,1,7,3]=>000000=>000000 [2,1,6,7,3,4,5]=>[2,3,6,1,4,7,5]=>000000=>000000 [2,1,6,7,3,5,4]=>[6,2,5,1,3,7,4]=>000000=>000000 [2,1,6,7,4,3,5]=>[2,6,4,1,3,7,5]=>000000=>000000 [2,1,6,7,4,5,3]=>[6,2,4,1,3,7,5]=>000000=>000000 [2,1,6,7,5,3,4]=>[2,6,5,1,3,7,4]=>000000=>000000 [2,1,6,7,5,4,3]=>[6,5,2,1,4,7,3]=>000000=>000000 [2,1,7,3,4,5,6]=>[2,3,4,5,1,7,6]=>000010=>010000 [2,1,7,3,4,6,5]=>[7,2,3,4,1,6,5]=>000000=>000000 [2,1,7,3,5,4,6]=>[2,7,3,5,1,6,4]=>000000=>000000 [2,1,7,3,5,6,4]=>[7,2,3,5,1,6,4]=>000000=>000000 [2,1,7,3,6,4,5]=>[2,7,3,4,1,6,5]=>000000=>000000 [2,1,7,3,6,5,4]=>[7,6,2,3,1,5,4]=>000000=>000000 [2,1,7,4,3,5,6]=>[2,4,7,5,1,6,3]=>000000=>000000 [2,1,7,4,3,6,5]=>[2,1,7,4,3,6,5]=>010000=>000010 [2,1,7,4,5,3,6]=>[2,7,4,5,1,6,3]=>000000=>000000 [2,1,7,4,5,6,3]=>[7,2,4,5,1,6,3]=>000000=>000000 [2,1,7,4,6,3,5]=>[2,7,1,4,3,6,5]=>000000=>000000 [2,1,7,4,6,5,3]=>[7,6,2,4,1,5,3]=>000000=>000000 [2,1,7,5,3,4,6]=>[2,3,7,5,1,6,4]=>000000=>000000 [2,1,7,5,3,6,4]=>[2,1,7,5,3,6,4]=>010000=>000010 [2,1,7,5,4,3,6]=>[2,7,5,4,1,6,3]=>000000=>000000 [2,1,7,5,4,6,3]=>[7,2,5,4,1,6,3]=>000000=>000000 [2,1,7,5,6,3,4]=>[2,7,1,5,3,6,4]=>000000=>000000 [2,1,7,5,6,4,3]=>[7,5,2,4,1,6,3]=>000000=>000000 [2,1,7,6,3,4,5]=>[2,3,7,4,1,6,5]=>000000=>000000 [2,1,7,6,3,5,4]=>[7,2,6,3,1,5,4]=>000000=>000000 [2,1,7,6,4,3,5]=>[2,7,6,4,1,5,3]=>000000=>000000 [2,1,7,6,4,5,3]=>[7,2,6,4,1,5,3]=>000000=>000000 [2,1,7,6,5,3,4]=>[2,7,6,3,1,5,4]=>000000=>000000 [2,1,7,6,5,4,3]=>[7,6,5,2,1,4,3]=>000000=>000000 [2,3,1,4,5,6,7]=>[2,3,4,5,6,1,7]=>000001=>100000 [2,3,1,4,5,7,6]=>[2,1,3,4,7,5,6]=>011100=>001110 [2,3,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>001101=>101100 [2,3,1,4,6,7,5]=>[2,1,3,4,6,5,7]=>011101=>101110 [2,3,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>001100=>001100 [2,3,1,4,7,6,5]=>[7,2,1,3,6,4,5]=>000000=>000000 [2,3,1,5,4,6,7]=>[2,3,5,1,6,4,7]=>000001=>100000 [2,3,1,5,4,7,6]=>[2,1,5,3,7,4,6]=>010000=>000010 [2,3,1,5,6,4,7]=>[2,3,1,5,6,4,7]=>001001=>100100 [2,3,1,5,6,7,4]=>[2,1,3,5,6,4,7]=>011001=>100110 [2,3,1,5,7,4,6]=>[2,5,1,3,7,4,6]=>000000=>000000 [2,3,1,5,7,6,4]=>[7,2,1,3,5,4,6]=>000000=>000000 [2,3,1,6,4,5,7]=>[2,3,4,1,6,5,7]=>000101=>101000 [2,3,1,6,4,7,5]=>[2,1,6,3,7,4,5]=>010000=>000010 [2,3,1,6,5,4,7]=>[2,6,3,1,5,4,7]=>000001=>100000 [2,3,1,6,5,7,4]=>[6,2,3,1,5,4,7]=>000001=>100000 [2,3,1,6,7,4,5]=>[2,6,1,3,7,4,5]=>000000=>000000 [2,3,1,6,7,5,4]=>[6,2,1,3,5,4,7]=>000001=>100000 [2,3,1,7,4,5,6]=>[2,3,4,1,7,5,6]=>000100=>001000 [2,3,1,7,4,6,5]=>[7,2,3,1,6,4,5]=>000000=>000000 [2,3,1,7,5,4,6]=>[2,7,3,1,5,4,6]=>000000=>000000 [2,3,1,7,5,6,4]=>[7,2,3,1,5,4,6]=>000000=>000000 [2,3,1,7,6,4,5]=>[2,7,3,1,6,4,5]=>000000=>000000 [2,3,1,7,6,5,4]=>[7,6,2,1,5,3,4]=>000000=>000000 [2,3,4,1,5,6,7]=>[2,3,4,5,1,6,7]=>000011=>110000 [2,3,4,1,5,7,6]=>[2,1,3,7,4,5,6]=>011000=>000110 [2,3,4,1,6,5,7]=>[2,3,1,6,4,5,7]=>001001=>100100 [2,3,4,1,6,7,5]=>[2,1,3,6,4,5,7]=>011001=>100110 [2,3,4,1,7,5,6]=>[2,3,1,7,4,5,6]=>001000=>000100 [2,3,4,1,7,6,5]=>[7,2,1,6,3,4,5]=>000000=>000000 [2,3,4,5,1,6,7]=>[2,3,4,1,5,6,7]=>000111=>111000 [2,3,4,5,1,7,6]=>[2,1,7,3,4,5,6]=>010000=>000010 [2,3,4,5,6,1,7]=>[2,3,1,4,5,6,7]=>001111=>111100 [2,3,4,5,6,7,1]=>[2,1,3,4,5,6,7]=>011111=>111110 [2,3,4,5,7,1,6]=>[2,7,1,3,4,5,6]=>000000=>000000 [2,3,4,5,7,6,1]=>[7,2,1,3,4,5,6]=>000000=>000000 [2,3,4,6,1,5,7]=>[2,3,6,1,4,5,7]=>000001=>100000 [2,3,4,6,1,7,5]=>[2,1,6,3,4,5,7]=>010001=>100010 [2,3,4,6,5,1,7]=>[2,6,3,1,4,5,7]=>000001=>100000 [2,3,4,6,5,7,1]=>[6,2,3,1,4,5,7]=>000001=>100000 [2,3,4,6,7,1,5]=>[2,6,1,3,4,5,7]=>000001=>100000 [2,3,4,6,7,5,1]=>[6,2,1,3,4,5,7]=>000001=>100000 [2,3,4,7,1,5,6]=>[2,3,7,1,4,5,6]=>000000=>000000 [2,3,4,7,1,6,5]=>[7,2,6,1,3,4,5]=>000000=>000000 [2,3,4,7,5,1,6]=>[2,7,3,1,4,5,6]=>000000=>000000 [2,3,4,7,5,6,1]=>[7,2,3,1,4,5,6]=>000000=>000000 [2,3,4,7,6,1,5]=>[2,7,6,1,3,4,5]=>000000=>000000 [2,3,4,7,6,5,1]=>[7,6,2,1,3,4,5]=>000000=>000000 [2,3,5,1,4,6,7]=>[2,3,5,6,1,4,7]=>000001=>100000 [2,3,5,1,4,7,6]=>[2,1,5,7,3,4,6]=>010000=>000010 [2,3,5,1,6,4,7]=>[2,3,1,5,4,6,7]=>001011=>110100 [2,3,5,1,6,7,4]=>[2,1,3,5,4,6,7]=>011011=>110110 [2,3,5,1,7,4,6]=>[2,5,1,7,3,4,6]=>000000=>000000 [2,3,5,1,7,6,4]=>[7,2,1,5,3,4,6]=>000000=>000000 [2,3,5,4,1,6,7]=>[2,3,5,4,1,6,7]=>000011=>110000 [2,3,5,4,1,7,6]=>[5,2,7,3,1,4,6]=>000000=>000000 [2,3,5,4,6,1,7]=>[2,5,3,4,1,6,7]=>000011=>110000 [2,3,5,4,6,7,1]=>[5,2,3,4,1,6,7]=>000011=>110000 [2,3,5,4,7,1,6]=>[5,7,2,3,1,4,6]=>000000=>000000 [2,3,5,4,7,6,1]=>[5,2,1,7,3,4,6]=>000000=>000000 [2,3,5,6,1,4,7]=>[2,3,5,1,4,6,7]=>000011=>110000 [2,3,5,6,1,7,4]=>[2,1,5,3,4,6,7]=>010011=>110010 [2,3,5,6,4,1,7]=>[2,5,3,1,4,6,7]=>000011=>110000 [2,3,5,6,4,7,1]=>[5,2,3,1,4,6,7]=>000011=>110000 [2,3,5,6,7,1,4]=>[2,5,1,3,4,6,7]=>000011=>110000 [2,3,5,6,7,4,1]=>[5,2,1,3,4,6,7]=>000011=>110000 [2,3,5,7,1,4,6]=>[2,5,7,1,3,4,6]=>000000=>000000 [2,3,5,7,1,6,4]=>[7,2,5,1,3,4,6]=>000000=>000000 [2,3,5,7,4,1,6]=>[5,7,2,1,3,4,6]=>000000=>000000 [2,3,5,7,4,6,1]=>[5,2,7,1,3,4,6]=>000000=>000000 [2,3,5,7,6,1,4]=>[2,7,5,1,3,4,6]=>000000=>000000 [2,3,5,7,6,4,1]=>[7,5,2,1,3,4,6]=>000000=>000000 [2,3,6,1,4,5,7]=>[2,3,4,6,1,5,7]=>000001=>100000 [2,3,6,1,4,7,5]=>[2,1,6,7,3,4,5]=>010000=>000010 [2,3,6,1,5,4,7]=>[2,6,3,5,1,4,7]=>000001=>100000 [2,3,6,1,5,7,4]=>[6,2,3,5,1,4,7]=>000001=>100000 [2,3,6,1,7,4,5]=>[2,6,1,7,3,4,5]=>000000=>000000 [2,3,6,1,7,5,4]=>[6,2,1,5,3,4,7]=>000001=>100000 [2,3,6,4,1,5,7]=>[2,3,6,4,1,5,7]=>000001=>100000 [2,3,6,4,1,7,5]=>[6,2,7,3,1,4,5]=>000000=>000000 [2,3,6,4,5,1,7]=>[2,6,3,4,1,5,7]=>000001=>100000 [2,3,6,4,5,7,1]=>[6,2,3,4,1,5,7]=>000001=>100000 [2,3,6,4,7,1,5]=>[6,7,2,3,1,4,5]=>000000=>000000 [2,3,6,4,7,5,1]=>[6,2,1,7,3,4,5]=>000000=>000000 [2,3,6,5,1,4,7]=>[2,3,6,5,1,4,7]=>000001=>100000 [2,3,6,5,1,7,4]=>[2,1,6,5,3,4,7]=>010001=>100010 [2,3,6,5,4,1,7]=>[2,6,5,3,1,4,7]=>000001=>100000 [2,3,6,5,4,7,1]=>[6,2,5,3,1,4,7]=>000001=>100000 [2,3,6,5,7,1,4]=>[2,6,1,5,3,4,7]=>000001=>100000 [2,3,6,5,7,4,1]=>[6,5,2,3,1,4,7]=>000001=>100000 [2,3,6,7,1,4,5]=>[2,6,7,1,3,4,5]=>000000=>000000 [2,3,6,7,1,5,4]=>[6,2,5,1,3,4,7]=>000001=>100000 [2,3,6,7,4,1,5]=>[6,7,2,1,3,4,5]=>000000=>000000 [2,3,6,7,4,5,1]=>[6,2,7,1,3,4,5]=>000000=>000000 [2,3,6,7,5,1,4]=>[2,6,5,1,3,4,7]=>000001=>100000 [2,3,6,7,5,4,1]=>[6,5,2,1,3,4,7]=>000001=>100000 [2,3,7,1,4,5,6]=>[2,3,4,7,1,5,6]=>000000=>000000 [2,3,7,1,4,6,5]=>[7,2,3,6,1,4,5]=>000000=>000000 [2,3,7,1,5,4,6]=>[2,7,3,5,1,4,6]=>000000=>000000 [2,3,7,1,5,6,4]=>[7,2,3,5,1,4,6]=>000000=>000000 [2,3,7,1,6,4,5]=>[2,7,3,6,1,4,5]=>000000=>000000 [2,3,7,1,6,5,4]=>[7,6,2,5,1,3,4]=>000000=>000000 [2,3,7,4,1,5,6]=>[2,3,7,4,1,5,6]=>000000=>000000 [2,3,7,4,1,6,5]=>[2,1,7,6,3,4,5]=>010000=>000010 [2,3,7,4,5,1,6]=>[2,7,3,4,1,5,6]=>000000=>000000 [2,3,7,4,5,6,1]=>[7,2,3,4,1,5,6]=>000000=>000000 [2,3,7,4,6,1,5]=>[2,7,1,6,3,4,5]=>000000=>000000 [2,3,7,4,6,5,1]=>[7,6,2,3,1,4,5]=>000000=>000000 [2,3,7,5,1,4,6]=>[2,3,7,5,1,4,6]=>000000=>000000 [2,3,7,5,1,6,4]=>[2,1,7,5,3,4,6]=>010000=>000010 [2,3,7,5,4,1,6]=>[2,7,5,3,1,4,6]=>000000=>000000 [2,3,7,5,4,6,1]=>[7,2,5,3,1,4,6]=>000000=>000000 [2,3,7,5,6,1,4]=>[2,7,1,5,3,4,6]=>000000=>000000 [2,3,7,5,6,4,1]=>[7,5,2,3,1,4,6]=>000000=>000000 [2,3,7,6,1,4,5]=>[2,3,7,6,1,4,5]=>000000=>000000 [2,3,7,6,1,5,4]=>[7,2,6,5,1,3,4]=>000000=>000000 [2,3,7,6,4,1,5]=>[2,7,6,3,1,4,5]=>000000=>000000 [2,3,7,6,4,5,1]=>[7,2,6,3,1,4,5]=>000000=>000000 [2,3,7,6,5,1,4]=>[2,7,6,5,1,3,4]=>000000=>000000 [2,3,7,6,5,4,1]=>[7,6,5,2,1,3,4]=>000000=>000000 [2,4,1,3,5,6,7]=>[2,4,5,6,7,1,3]=>000000=>000000 [2,4,1,3,5,7,6]=>[2,1,4,5,7,3,6]=>010000=>000010 [2,4,1,3,6,5,7]=>[2,4,1,6,7,3,5]=>000000=>000000 [2,4,1,3,6,7,5]=>[2,1,4,6,7,3,5]=>010000=>000010 [2,4,1,3,7,5,6]=>[2,4,1,5,7,3,6]=>000000=>000000 [2,4,1,3,7,6,5]=>[7,2,1,4,6,3,5]=>000000=>000000 [2,4,1,5,3,6,7]=>[2,4,5,1,6,3,7]=>000001=>100000 [2,4,1,5,3,7,6]=>[2,1,4,3,7,5,6]=>010100=>001010 [2,4,1,5,6,3,7]=>[2,4,1,5,6,3,7]=>000001=>100000 [2,4,1,5,6,7,3]=>[2,1,4,5,6,3,7]=>010001=>100010 [2,4,1,5,7,3,6]=>[2,4,1,3,7,5,6]=>000100=>001000 [2,4,1,5,7,6,3]=>[7,2,1,4,5,3,6]=>000000=>000000 [2,4,1,6,3,5,7]=>[2,4,6,1,7,3,5]=>000000=>000000 [2,4,1,6,3,7,5]=>[2,1,4,3,6,5,7]=>010101=>101010 [2,4,1,6,5,3,7]=>[2,6,4,1,5,3,7]=>000001=>100000 [2,4,1,6,5,7,3]=>[6,2,4,1,5,3,7]=>000001=>100000 [2,4,1,6,7,3,5]=>[2,4,1,3,6,5,7]=>000101=>101000 [2,4,1,6,7,5,3]=>[6,2,1,4,5,3,7]=>000001=>100000 [2,4,1,7,3,5,6]=>[2,4,5,1,7,3,6]=>000000=>000000 [2,4,1,7,3,6,5]=>[7,2,4,1,6,3,5]=>000000=>000000 [2,4,1,7,5,3,6]=>[2,7,4,1,5,3,6]=>000000=>000000 [2,4,1,7,5,6,3]=>[7,2,4,1,5,3,6]=>000000=>000000 [2,4,1,7,6,3,5]=>[2,7,4,1,6,3,5]=>000000=>000000 [2,4,1,7,6,5,3]=>[7,6,2,1,4,3,5]=>000000=>000000 [2,4,3,1,5,6,7]=>[2,4,5,6,3,1,7]=>000001=>100000 [2,4,3,1,5,7,6]=>[4,2,3,7,5,1,6]=>000000=>000000 [2,4,3,1,6,5,7]=>[2,4,3,6,5,1,7]=>000001=>100000 [2,4,3,1,6,7,5]=>[4,2,3,6,5,1,7]=>000001=>100000 [2,4,3,1,7,5,6]=>[2,4,3,7,5,1,6]=>000000=>000000 [2,4,3,1,7,6,5]=>[4,2,1,7,6,3,5]=>000000=>000000 [2,4,3,5,1,6,7]=>[2,4,5,3,6,1,7]=>000001=>100000 [2,4,3,5,1,7,6]=>[4,2,7,3,5,1,6]=>000000=>000000 [2,4,3,5,6,1,7]=>[2,4,3,5,6,1,7]=>000001=>100000 [2,4,3,5,6,7,1]=>[4,2,3,5,6,1,7]=>000001=>100000 [2,4,3,5,7,1,6]=>[4,7,2,3,5,1,6]=>000000=>000000 [2,4,3,5,7,6,1]=>[4,2,1,3,7,5,6]=>000100=>001000 [2,4,3,6,1,5,7]=>[2,4,6,3,5,1,7]=>000001=>100000 [2,4,3,6,1,7,5]=>[4,2,6,3,5,1,7]=>000001=>100000 [2,4,3,6,5,1,7]=>[2,4,3,1,6,5,7]=>000101=>101000 [2,4,3,6,5,7,1]=>[4,2,3,1,6,5,7]=>000101=>101000 [2,4,3,6,7,1,5]=>[4,6,2,3,5,1,7]=>000001=>100000 [2,4,3,6,7,5,1]=>[4,2,1,3,6,5,7]=>000101=>101000 [2,4,3,7,1,5,6]=>[2,4,7,3,5,1,6]=>000000=>000000 [2,4,3,7,1,6,5]=>[4,2,7,1,6,3,5]=>000000=>000000 [2,4,3,7,5,1,6]=>[2,4,3,1,7,5,6]=>000100=>001000 [2,4,3,7,5,6,1]=>[4,2,3,1,7,5,6]=>000100=>001000 [2,4,3,7,6,1,5]=>[4,7,2,1,6,3,5]=>000000=>000000 [2,4,3,7,6,5,1]=>[7,4,2,1,6,3,5]=>000000=>000000 [2,4,5,1,3,6,7]=>[2,4,5,6,1,3,7]=>000001=>100000 [2,4,5,1,3,7,6]=>[2,1,4,7,3,5,6]=>010000=>000010 [2,4,5,1,6,3,7]=>[2,4,1,5,3,6,7]=>000011=>110000 [2,4,5,1,6,7,3]=>[2,1,4,5,3,6,7]=>010011=>110010 [2,4,5,1,7,3,6]=>[2,4,1,7,3,5,6]=>000000=>000000 [2,4,5,1,7,6,3]=>[7,2,1,4,3,5,6]=>000000=>000000 [2,4,5,3,1,6,7]=>[2,4,5,3,1,6,7]=>000011=>110000 [2,4,5,3,1,7,6]=>[4,2,7,3,1,5,6]=>000000=>000000 [2,4,5,3,6,1,7]=>[2,4,3,5,1,6,7]=>000011=>110000 [2,4,5,3,6,7,1]=>[4,2,3,5,1,6,7]=>000011=>110000 [2,4,5,3,7,1,6]=>[4,7,2,3,1,5,6]=>000000=>000000 [2,4,5,3,7,6,1]=>[4,2,1,7,3,5,6]=>000000=>000000 [2,4,5,6,1,3,7]=>[2,4,5,1,3,6,7]=>000011=>110000 [2,4,5,6,1,7,3]=>[2,1,4,3,5,6,7]=>010111=>111010 [2,4,5,6,3,1,7]=>[2,4,3,1,5,6,7]=>000111=>111000 [2,4,5,6,3,7,1]=>[4,2,3,1,5,6,7]=>000111=>111000 [2,4,5,6,7,1,3]=>[2,4,1,3,5,6,7]=>000111=>111000 [2,4,5,6,7,3,1]=>[4,2,1,3,5,6,7]=>000111=>111000 [2,4,5,7,1,3,6]=>[2,4,7,1,3,5,6]=>000000=>000000 [2,4,5,7,1,6,3]=>[7,2,4,1,3,5,6]=>000000=>000000 [2,4,5,7,3,1,6]=>[4,7,2,1,3,5,6]=>000000=>000000 [2,4,5,7,3,6,1]=>[4,2,7,1,3,5,6]=>000000=>000000 [2,4,5,7,6,1,3]=>[2,7,4,1,3,5,6]=>000000=>000000 [2,4,5,7,6,3,1]=>[7,4,2,1,3,5,6]=>000000=>000000 [2,4,6,1,3,5,7]=>[2,4,6,7,1,3,5]=>000000=>000000 [2,4,6,1,3,7,5]=>[2,1,4,6,3,5,7]=>010001=>100010 [2,4,6,1,5,3,7]=>[2,6,4,5,1,3,7]=>000001=>100000 [2,4,6,1,5,7,3]=>[6,2,4,5,1,3,7]=>000001=>100000 [2,4,6,1,7,3,5]=>[2,4,1,6,3,5,7]=>000001=>100000 [2,4,6,1,7,5,3]=>[6,2,1,4,3,5,7]=>000001=>100000 [2,4,6,3,1,5,7]=>[2,4,6,3,1,5,7]=>000001=>100000 [2,4,6,3,1,7,5]=>[4,2,6,3,1,5,7]=>000001=>100000 [2,4,6,3,5,1,7]=>[2,4,3,6,1,5,7]=>000001=>100000 [2,4,6,3,5,7,1]=>[4,2,3,6,1,5,7]=>000001=>100000 [2,4,6,3,7,1,5]=>[4,6,2,3,1,5,7]=>000001=>100000 [2,4,6,3,7,5,1]=>[4,2,1,6,3,5,7]=>000001=>100000 [2,4,6,5,1,3,7]=>[2,4,6,5,1,3,7]=>000001=>100000 [2,4,6,5,1,7,3]=>[2,1,6,4,3,5,7]=>010001=>100010 [2,4,6,5,3,1,7]=>[2,6,4,3,1,5,7]=>000001=>100000 [2,4,6,5,3,7,1]=>[6,2,4,3,1,5,7]=>000001=>100000 [2,4,6,5,7,1,3]=>[2,6,1,4,3,5,7]=>000001=>100000 [2,4,6,5,7,3,1]=>[6,4,2,3,1,5,7]=>000001=>100000 [2,4,6,7,1,3,5]=>[2,4,6,1,3,5,7]=>000001=>100000 [2,4,6,7,1,5,3]=>[6,2,4,1,3,5,7]=>000001=>100000 [2,4,6,7,3,1,5]=>[4,6,2,1,3,5,7]=>000001=>100000 [2,4,6,7,3,5,1]=>[4,2,6,1,3,5,7]=>000001=>100000 [2,4,6,7,5,1,3]=>[2,6,4,1,3,5,7]=>000001=>100000 [2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>000001=>100000 [2,4,7,1,3,5,6]=>[2,4,5,7,1,3,6]=>000000=>000000 [2,4,7,1,3,6,5]=>[7,2,4,6,1,3,5]=>000000=>000000 [2,4,7,1,5,3,6]=>[2,7,4,5,1,3,6]=>000000=>000000 [2,4,7,1,5,6,3]=>[7,2,4,5,1,3,6]=>000000=>000000 [2,4,7,1,6,3,5]=>[2,7,4,6,1,3,5]=>000000=>000000 [2,4,7,1,6,5,3]=>[7,6,2,4,1,3,5]=>000000=>000000 [2,4,7,3,1,5,6]=>[2,4,7,3,1,5,6]=>000000=>000000 [2,4,7,3,1,6,5]=>[4,2,7,6,1,3,5]=>000000=>000000 [2,4,7,3,5,1,6]=>[2,4,3,7,1,5,6]=>000000=>000000 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[7,6,5,2,3,4,1]=>[7,2,3,6,5,4,1]=>000000=>000000 [7,6,5,2,4,1,3]=>[2,7,1,6,5,4,3]=>000000=>000000 [7,6,5,2,4,3,1]=>[7,6,2,5,4,3,1]=>000000=>000000 [7,6,5,3,1,2,4]=>[1,3,7,6,5,4,2]=>100000=>000001 [7,6,5,3,1,4,2]=>[3,1,7,6,5,4,2]=>000000=>000000 [7,6,5,3,2,1,4]=>[3,7,6,5,4,2,1]=>000000=>000000 [7,6,5,3,2,4,1]=>[7,3,6,5,4,2,1]=>000000=>000000 [7,6,5,3,4,1,2]=>[3,7,1,6,5,4,2]=>000000=>000000 [7,6,5,3,4,2,1]=>[7,6,3,5,4,2,1]=>000000=>000000 [7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>110000=>000011 [7,6,5,4,1,3,2]=>[7,1,6,5,4,3,2]=>000000=>000000 [7,6,5,4,2,1,3]=>[2,7,6,5,4,3,1]=>000000=>000000 [7,6,5,4,2,3,1]=>[7,2,6,5,4,3,1]=>000000=>000000 [7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>100000=>000001 [7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000=>000000 [8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000=>0000000 [8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>0000000=>0000000 [8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>0000000=>0000000 [8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1]=>0000000=>0000000 [7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>0000000=>0000000 [7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>0000000=>0000000 [7,8,3,4,5,6,1,2]=>[7,8,3,4,5,6,1,2]=>0000000=>0000000 [6,7,8,5,4,1,2,3]=>[6,7,8,5,4,1,2,3]=>0000000=>0000000 [5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>0000000=>0000000 [1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111 [4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>0001000=>0001000 [3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>0011100=>0011100 [2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>0100010=>0100010 [2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>0101010=>0101010 [2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>0111110=>0111110 [1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>1001001=>1001001 [1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>1011101=>1011101 [1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>1101011=>1101011 [4,2,3,1,8,6,7,5]=>[4,2,3,1,8,6,7,5]=>0001000=>0001000 [8,3,2,5,4,7,6,1]=>[8,3,2,5,4,7,6,1]=>0000000=>0000000 [8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>0000000=>0000000 [2,4,1,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>0101000=>0001010 [2,1,4,3,7,8,5,6]=>[2,4,1,3,7,5,8,6]=>0001000=>0001000 [2,1,5,6,3,4,8,7]=>[2,1,5,6,3,4,8,7]=>0100010=>0100010 [2,5,1,7,3,4,8,6]=>[2,1,5,7,3,8,4,6]=>0100000=>0000010 [2,1,5,7,3,8,4,6]=>[2,5,1,7,3,4,8,6]=>0000000=>0000000 [2,6,7,1,3,4,8,5]=>[2,1,6,7,8,3,4,5]=>0100000=>0000010 [2,1,6,7,8,3,4,5]=>[2,6,7,1,3,4,8,5]=>0000000=>0000000 [3,4,1,2,6,5,8,7]=>[3,1,4,2,6,8,5,7]=>0001000=>0001000 [3,1,4,2,6,8,5,7]=>[3,4,1,2,6,5,8,7]=>0001010=>0101000 [3,4,1,2,7,8,5,6]=>[3,4,1,2,7,8,5,6]=>0001000=>0001000 [3,5,1,6,2,4,8,7]=>[3,1,5,6,2,8,4,7]=>0000000=>0000000 [3,1,5,6,2,8,4,7]=>[3,5,1,6,2,4,8,7]=>0000010=>0100000 [3,5,1,7,2,8,4,6]=>[3,5,1,7,2,8,4,6]=>0000000=>0000000 [3,6,7,1,2,8,4,5]=>[3,6,1,7,8,2,4,5]=>0000000=>0000000 [3,6,1,7,8,2,4,5]=>[3,6,7,1,2,8,4,5]=>0000000=>0000000 [4,5,6,1,2,3,8,7]=>[4,1,5,6,8,2,3,7]=>0000000=>0000000 [4,1,5,6,8,2,3,7]=>[4,5,6,1,2,3,8,7]=>0000010=>0100000 [4,5,7,1,2,8,3,6]=>[4,5,1,7,8,2,3,6]=>0000000=>0000000 [4,5,1,7,8,2,3,6]=>[4,5,7,1,2,8,3,6]=>0000000=>0000000 [4,6,7,1,8,2,3,5]=>[4,6,7,1,8,2,3,5]=>0000000=>0000000 [1,2,5,6,3,4,7,8]=>[1,2,5,6,3,4,7,8]=>1100011=>1100011 [3,7,1,5,4,8,2,6]=>[3,7,1,5,4,8,2,6]=>0000000=>0000000 [5,8,4,3,1,7,6,2]=>[5,4,3,8,7,6,1,2]=>0000000=>0000000 [6,8,4,3,7,1,5,2]=>[6,4,8,3,7,5,1,2]=>0000000=>0000000 [7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>0000000=>0000000 [6,8,5,7,3,1,4,2]=>[6,5,8,7,3,4,1,2]=>0000000=>0000000 [4,7,6,1,8,3,2,5]=>[4,7,6,1,8,3,2,5]=>0000000=>0000000 [5,7,6,8,1,3,2,4]=>[5,7,6,8,1,3,2,4]=>0000000=>0000000 [8,4,6,2,7,3,5,1]=>[8,4,6,2,7,3,5,1]=>0000000=>0000000 [5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>0000000=>0000000 [6,3,2,8,7,1,5,4]=>[6,3,8,2,1,7,5,4]=>0000000=>0000000 [7,3,2,8,6,5,1,4]=>[7,8,3,2,1,6,5,4]=>0000000=>0000000 [7,4,8,2,6,5,1,3]=>[7,8,4,2,6,1,5,3]=>0000000=>0000000 [6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>0000000=>0000000 [5,4,8,2,1,7,6,3]=>[5,4,2,8,7,1,6,3]=>0000000=>0000000 [6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>0000000=>0000000 [7,5,8,6,2,4,1,3]=>[7,8,5,6,2,1,4,3]=>0000000=>0000000 [6,5,8,7,3,4,1,2]=>[6,8,5,7,3,1,4,2]=>0000000=>0000000 [1,6,7,4,5,2,3,8]=>[1,6,7,4,5,2,3,8]=>1000001=>1000001 [5,4,3,8,7,6,1,2]=>[5,8,4,3,1,7,6,2]=>0000000=>0000000 [6,4,8,3,7,5,1,2]=>[6,8,4,3,7,1,5,2]=>0000000=>0000000 [6,2,8,4,5,1,7,3]=>[6,2,8,4,5,1,7,3]=>0000000=>0000000 [5,2,3,8,1,6,7,4]=>[5,2,3,8,1,6,7,4]=>0000000=>0000000 [6,3,8,2,1,7,5,4]=>[6,3,2,8,7,1,5,4]=>0000000=>0000000 [7,8,3,2,1,6,5,4]=>[7,3,2,8,6,5,1,4]=>0000000=>0000000 [7,8,4,2,6,1,5,3]=>[7,4,8,2,6,5,1,3]=>0000000=>0000000 [5,4,2,8,7,1,6,3]=>[5,4,8,2,1,7,6,3]=>0000000=>0000000 [1,5,3,7,2,6,4,8]=>[1,5,3,7,2,6,4,8]=>1000001=>1000001 [7,8,5,6,2,1,4,3]=>[7,5,8,6,2,4,1,3]=>0000000=>0000000
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
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
reverse
Description
Return the reversal of a binary word.