Identifier
Mp00326: Permutations —weak order rowmotion⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
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[1]=>[1]=>=> [1,2]=>[2,1]=>0=>0 [2,1]=>[1,2]=>1=>1 [1,2,3]=>[3,2,1]=>00=>00 [1,3,2]=>[2,3,1]=>00=>00 [2,1,3]=>[3,1,2]=>00=>00 [2,3,1]=>[2,1,3]=>01=>10 [3,1,2]=>[1,3,2]=>10=>01 [3,2,1]=>[1,2,3]=>11=>11 [1,2,3,4]=>[4,3,2,1]=>000=>000 [1,2,4,3]=>[3,4,2,1]=>000=>000 [1,3,2,4]=>[4,2,3,1]=>000=>000 [1,3,4,2]=>[3,2,4,1]=>000=>000 [1,4,2,3]=>[2,4,3,1]=>000=>000 [1,4,3,2]=>[2,3,4,1]=>000=>000 [2,1,3,4]=>[4,3,1,2]=>000=>000 [2,1,4,3]=>[3,4,1,2]=>000=>000 [2,3,1,4]=>[4,2,1,3]=>000=>000 [2,3,4,1]=>[3,2,1,4]=>001=>100 [2,4,1,3]=>[2,1,4,3]=>010=>010 [2,4,3,1]=>[2,1,3,4]=>011=>110 [3,1,2,4]=>[4,1,3,2]=>000=>000 [3,1,4,2]=>[1,3,2,4]=>101=>101 [3,2,1,4]=>[4,1,2,3]=>000=>000 [3,2,4,1]=>[2,3,1,4]=>001=>100 [3,4,1,2]=>[3,1,4,2]=>000=>000 [3,4,2,1]=>[3,1,2,4]=>001=>100 [4,1,2,3]=>[1,4,3,2]=>100=>001 [4,1,3,2]=>[1,4,2,3]=>100=>001 [4,2,1,3]=>[1,2,4,3]=>110=>011 [4,2,3,1]=>[2,4,1,3]=>000=>000 [4,3,1,2]=>[1,3,4,2]=>100=>001 [4,3,2,1]=>[1,2,3,4]=>111=>111 [1,2,3,4,5]=>[5,4,3,2,1]=>0000=>0000 [1,2,3,5,4]=>[4,5,3,2,1]=>0000=>0000 [1,2,4,3,5]=>[5,3,4,2,1]=>0000=>0000 [1,2,4,5,3]=>[4,3,5,2,1]=>0000=>0000 [1,2,5,3,4]=>[3,5,4,2,1]=>0000=>0000 [1,2,5,4,3]=>[3,4,5,2,1]=>0000=>0000 [1,3,2,4,5]=>[5,4,2,3,1]=>0000=>0000 [1,3,2,5,4]=>[4,5,2,3,1]=>0000=>0000 [1,3,4,2,5]=>[5,3,2,4,1]=>0000=>0000 [1,3,4,5,2]=>[4,3,2,5,1]=>0000=>0000 [1,3,5,2,4]=>[3,2,5,4,1]=>0000=>0000 [1,3,5,4,2]=>[3,2,4,5,1]=>0000=>0000 [1,4,2,3,5]=>[5,2,4,3,1]=>0000=>0000 [1,4,2,5,3]=>[2,4,3,5,1]=>0000=>0000 [1,4,3,2,5]=>[5,2,3,4,1]=>0000=>0000 [1,4,3,5,2]=>[3,4,2,5,1]=>0000=>0000 [1,4,5,2,3]=>[4,2,5,3,1]=>0000=>0000 [1,4,5,3,2]=>[4,2,3,5,1]=>0000=>0000 [1,5,2,3,4]=>[2,5,4,3,1]=>0000=>0000 [1,5,2,4,3]=>[2,5,3,4,1]=>0000=>0000 [1,5,3,2,4]=>[2,3,5,4,1]=>0000=>0000 [1,5,3,4,2]=>[3,5,2,4,1]=>0000=>0000 [1,5,4,2,3]=>[2,4,5,3,1]=>0000=>0000 [1,5,4,3,2]=>[2,3,4,5,1]=>0000=>0000 [2,1,3,4,5]=>[5,4,3,1,2]=>0000=>0000 [2,1,3,5,4]=>[4,5,3,1,2]=>0000=>0000 [2,1,4,3,5]=>[5,3,4,1,2]=>0000=>0000 [2,1,4,5,3]=>[4,3,5,1,2]=>0000=>0000 [2,1,5,3,4]=>[3,5,4,1,2]=>0000=>0000 [2,1,5,4,3]=>[3,4,5,1,2]=>0000=>0000 [2,3,1,4,5]=>[5,4,2,1,3]=>0000=>0000 [2,3,1,5,4]=>[4,5,2,1,3]=>0000=>0000 [2,3,4,1,5]=>[5,3,2,1,4]=>0000=>0000 [2,3,4,5,1]=>[4,3,2,1,5]=>0001=>1000 [2,3,5,1,4]=>[3,2,1,5,4]=>0010=>0100 [2,3,5,4,1]=>[3,2,1,4,5]=>0011=>1100 [2,4,1,3,5]=>[5,2,1,4,3]=>0000=>0000 [2,4,1,5,3]=>[2,1,4,3,5]=>0101=>1010 [2,4,3,1,5]=>[5,2,1,3,4]=>0000=>0000 [2,4,3,5,1]=>[3,4,2,1,5]=>0001=>1000 [2,4,5,1,3]=>[4,2,1,5,3]=>0000=>0000 [2,4,5,3,1]=>[4,2,1,3,5]=>0001=>1000 [2,5,1,3,4]=>[2,1,5,4,3]=>0100=>0010 [2,5,1,4,3]=>[2,1,5,3,4]=>0100=>0010 [2,5,3,1,4]=>[2,1,3,5,4]=>0110=>0110 [2,5,3,4,1]=>[3,5,2,1,4]=>0000=>0000 [2,5,4,1,3]=>[2,1,4,5,3]=>0100=>0010 [2,5,4,3,1]=>[2,1,3,4,5]=>0111=>1110 [3,1,2,4,5]=>[5,4,1,3,2]=>0000=>0000 [3,1,2,5,4]=>[4,5,1,3,2]=>0000=>0000 [3,1,4,2,5]=>[5,1,3,2,4]=>0000=>0000 [3,1,4,5,2]=>[4,1,3,2,5]=>0001=>1000 [3,1,5,2,4]=>[1,3,2,5,4]=>1010=>0101 [3,1,5,4,2]=>[1,3,2,4,5]=>1011=>1101 [3,2,1,4,5]=>[5,4,1,2,3]=>0000=>0000 [3,2,1,5,4]=>[4,5,1,2,3]=>0000=>0000 [3,2,4,1,5]=>[5,2,3,1,4]=>0000=>0000 [3,2,4,5,1]=>[4,2,3,1,5]=>0001=>1000 [3,2,5,1,4]=>[2,3,1,5,4]=>0010=>0100 [3,2,5,4,1]=>[2,3,1,4,5]=>0011=>1100 [3,4,1,2,5]=>[5,3,1,4,2]=>0000=>0000 [3,4,1,5,2]=>[3,1,4,2,5]=>0001=>1000 [3,4,2,1,5]=>[5,3,1,2,4]=>0000=>0000 [3,4,2,5,1]=>[3,2,4,1,5]=>0001=>1000 [3,4,5,1,2]=>[4,3,1,5,2]=>0000=>0000 [3,4,5,2,1]=>[4,3,1,2,5]=>0001=>1000 [3,5,1,2,4]=>[3,1,5,4,2]=>0000=>0000 [3,5,1,4,2]=>[3,1,5,2,4]=>0000=>0000 [3,5,2,1,4]=>[3,1,2,5,4]=>0010=>0100 [3,5,2,4,1]=>[3,2,5,1,4]=>0000=>0000 [3,5,4,1,2]=>[3,1,4,5,2]=>0000=>0000 [3,5,4,2,1]=>[3,1,2,4,5]=>0011=>1100 [4,1,2,3,5]=>[5,1,4,3,2]=>0000=>0000 [4,1,2,5,3]=>[1,4,3,5,2]=>1000=>0001 [4,1,3,2,5]=>[5,1,4,2,3]=>0000=>0000 [4,1,3,5,2]=>[1,4,3,2,5]=>1001=>1001 [4,1,5,2,3]=>[1,4,2,5,3]=>1000=>0001 [4,1,5,3,2]=>[1,4,2,3,5]=>1001=>1001 [4,2,1,3,5]=>[5,1,2,4,3]=>0000=>0000 [4,2,1,5,3]=>[1,2,4,3,5]=>1101=>1011 [4,2,3,1,5]=>[5,2,4,1,3]=>0000=>0000 [4,2,3,5,1]=>[2,4,3,1,5]=>0001=>1000 [4,2,5,1,3]=>[2,4,1,5,3]=>0000=>0000 [4,2,5,3,1]=>[2,4,1,3,5]=>0001=>1000 [4,3,1,2,5]=>[5,1,3,4,2]=>0000=>0000 [4,3,1,5,2]=>[1,3,4,2,5]=>1001=>1001 [4,3,2,1,5]=>[5,1,2,3,4]=>0000=>0000 [4,3,2,5,1]=>[2,3,4,1,5]=>0001=>1000 [4,3,5,1,2]=>[3,4,1,5,2]=>0000=>0000 [4,3,5,2,1]=>[3,4,1,2,5]=>0001=>1000 [4,5,1,2,3]=>[4,1,5,3,2]=>0000=>0000 [4,5,1,3,2]=>[4,1,5,2,3]=>0000=>0000 [4,5,2,1,3]=>[4,1,2,5,3]=>0000=>0000 [4,5,2,3,1]=>[4,2,5,1,3]=>0000=>0000 [4,5,3,1,2]=>[4,1,3,5,2]=>0000=>0000 [4,5,3,2,1]=>[4,1,2,3,5]=>0001=>1000 [5,1,2,3,4]=>[1,5,4,3,2]=>1000=>0001 [5,1,2,4,3]=>[1,5,3,4,2]=>1000=>0001 [5,1,3,2,4]=>[1,5,4,2,3]=>1000=>0001 [5,1,3,4,2]=>[1,5,3,2,4]=>1000=>0001 [5,1,4,2,3]=>[1,5,2,4,3]=>1000=>0001 [5,1,4,3,2]=>[1,5,2,3,4]=>1000=>0001 [5,2,1,3,4]=>[1,2,5,4,3]=>1100=>0011 [5,2,1,4,3]=>[1,2,5,3,4]=>1100=>0011 [5,2,3,1,4]=>[2,5,4,1,3]=>0000=>0000 [5,2,3,4,1]=>[2,5,3,1,4]=>0000=>0000 [5,2,4,1,3]=>[2,5,1,4,3]=>0000=>0000 [5,2,4,3,1]=>[2,5,1,3,4]=>0000=>0000 [5,3,1,2,4]=>[1,3,5,4,2]=>1000=>0001 [5,3,1,4,2]=>[1,3,5,2,4]=>1000=>0001 [5,3,2,1,4]=>[1,2,3,5,4]=>1110=>0111 [5,3,2,4,1]=>[2,3,5,1,4]=>0000=>0000 [5,3,4,1,2]=>[3,5,1,4,2]=>0000=>0000 [5,3,4,2,1]=>[3,5,1,2,4]=>0000=>0000 [5,4,1,2,3]=>[1,4,5,3,2]=>1000=>0001 [5,4,1,3,2]=>[1,4,5,2,3]=>1000=>0001 [5,4,2,1,3]=>[1,2,4,5,3]=>1100=>0011 [5,4,2,3,1]=>[2,4,5,1,3]=>0000=>0000 [5,4,3,1,2]=>[1,3,4,5,2]=>1000=>0001 [5,4,3,2,1]=>[1,2,3,4,5]=>1111=>1111 [1,2,3,4,5,6]=>[6,5,4,3,2,1]=>00000=>00000 [1,2,3,4,6,5]=>[5,6,4,3,2,1]=>00000=>00000 [1,2,3,5,4,6]=>[6,4,5,3,2,1]=>00000=>00000 [1,2,3,5,6,4]=>[5,4,6,3,2,1]=>00000=>00000 [1,2,3,6,4,5]=>[4,6,5,3,2,1]=>00000=>00000 [1,2,3,6,5,4]=>[4,5,6,3,2,1]=>00000=>00000 [1,2,4,3,5,6]=>[6,5,3,4,2,1]=>00000=>00000 [1,2,4,3,6,5]=>[5,6,3,4,2,1]=>00000=>00000 [1,2,4,5,3,6]=>[6,4,3,5,2,1]=>00000=>00000 [1,2,4,5,6,3]=>[5,4,3,6,2,1]=>00000=>00000 [1,2,4,6,3,5]=>[4,3,6,5,2,1]=>00000=>00000 [1,2,4,6,5,3]=>[4,3,5,6,2,1]=>00000=>00000 [1,2,5,3,4,6]=>[6,3,5,4,2,1]=>00000=>00000 [1,2,5,3,6,4]=>[3,5,4,6,2,1]=>00000=>00000 [1,2,5,4,3,6]=>[6,3,4,5,2,1]=>00000=>00000 [1,2,5,4,6,3]=>[4,5,3,6,2,1]=>00000=>00000 [1,2,5,6,3,4]=>[5,3,6,4,2,1]=>00000=>00000 [1,2,5,6,4,3]=>[5,3,4,6,2,1]=>00000=>00000 [1,2,6,3,4,5]=>[3,6,5,4,2,1]=>00000=>00000 [1,2,6,3,5,4]=>[3,6,4,5,2,1]=>00000=>00000 [1,2,6,4,3,5]=>[3,4,6,5,2,1]=>00000=>00000 [1,2,6,4,5,3]=>[4,6,3,5,2,1]=>00000=>00000 [1,2,6,5,3,4]=>[3,5,6,4,2,1]=>00000=>00000 [1,2,6,5,4,3]=>[3,4,5,6,2,1]=>00000=>00000 [1,3,2,4,5,6]=>[6,5,4,2,3,1]=>00000=>00000 [1,3,2,4,6,5]=>[5,6,4,2,3,1]=>00000=>00000 [1,3,2,5,4,6]=>[6,4,5,2,3,1]=>00000=>00000 [1,3,2,5,6,4]=>[5,4,6,2,3,1]=>00000=>00000 [1,3,2,6,4,5]=>[4,6,5,2,3,1]=>00000=>00000 [1,3,2,6,5,4]=>[4,5,6,2,3,1]=>00000=>00000 [1,3,4,2,5,6]=>[6,5,3,2,4,1]=>00000=>00000 [1,3,4,2,6,5]=>[5,6,3,2,4,1]=>00000=>00000 [1,3,4,5,2,6]=>[6,4,3,2,5,1]=>00000=>00000 [1,3,4,5,6,2]=>[5,4,3,2,6,1]=>00000=>00000 [1,3,4,6,2,5]=>[4,3,2,6,5,1]=>00000=>00000 [1,3,4,6,5,2]=>[4,3,2,5,6,1]=>00000=>00000 [1,3,5,2,4,6]=>[6,3,2,5,4,1]=>00000=>00000 [1,3,5,2,6,4]=>[3,2,5,4,6,1]=>00000=>00000 [1,3,5,4,2,6]=>[6,3,2,4,5,1]=>00000=>00000 [1,3,5,4,6,2]=>[4,5,3,2,6,1]=>00000=>00000 [1,3,5,6,2,4]=>[5,3,2,6,4,1]=>00000=>00000 [1,3,5,6,4,2]=>[5,3,2,4,6,1]=>00000=>00000 [1,3,6,2,4,5]=>[3,2,6,5,4,1]=>00000=>00000 [1,3,6,2,5,4]=>[3,2,6,4,5,1]=>00000=>00000 [1,3,6,4,2,5]=>[3,2,4,6,5,1]=>00000=>00000 [1,3,6,4,5,2]=>[4,6,3,2,5,1]=>00000=>00000 [1,3,6,5,2,4]=>[3,2,5,6,4,1]=>00000=>00000 [1,3,6,5,4,2]=>[3,2,4,5,6,1]=>00000=>00000 [1,4,2,3,5,6]=>[6,5,2,4,3,1]=>00000=>00000 [1,4,2,3,6,5]=>[5,6,2,4,3,1]=>00000=>00000 [1,4,2,5,3,6]=>[6,2,4,3,5,1]=>00000=>00000 [1,4,2,5,6,3]=>[5,2,4,3,6,1]=>00000=>00000 [1,4,2,6,3,5]=>[2,4,3,6,5,1]=>00000=>00000 [1,4,2,6,5,3]=>[2,4,3,5,6,1]=>00000=>00000 [1,4,3,2,5,6]=>[6,5,2,3,4,1]=>00000=>00000 [1,4,3,2,6,5]=>[5,6,2,3,4,1]=>00000=>00000 [1,4,3,5,2,6]=>[6,3,4,2,5,1]=>00000=>00000 [1,4,3,5,6,2]=>[5,3,4,2,6,1]=>00000=>00000 [1,4,3,6,2,5]=>[3,4,2,6,5,1]=>00000=>00000 [1,4,3,6,5,2]=>[3,4,2,5,6,1]=>00000=>00000 [1,4,5,2,3,6]=>[6,4,2,5,3,1]=>00000=>00000 [1,4,5,2,6,3]=>[4,2,5,3,6,1]=>00000=>00000 [1,4,5,3,2,6]=>[6,4,2,3,5,1]=>00000=>00000 [1,4,5,3,6,2]=>[4,3,5,2,6,1]=>00000=>00000 [1,4,5,6,2,3]=>[5,4,2,6,3,1]=>00000=>00000 [1,4,5,6,3,2]=>[5,4,2,3,6,1]=>00000=>00000 [1,4,6,2,3,5]=>[4,2,6,5,3,1]=>00000=>00000 [1,4,6,2,5,3]=>[4,2,6,3,5,1]=>00000=>00000 [1,4,6,3,2,5]=>[4,2,3,6,5,1]=>00000=>00000 [1,4,6,3,5,2]=>[4,3,6,2,5,1]=>00000=>00000 [1,4,6,5,2,3]=>[4,2,5,6,3,1]=>00000=>00000 [1,4,6,5,3,2]=>[4,2,3,5,6,1]=>00000=>00000 [1,5,2,3,4,6]=>[6,2,5,4,3,1]=>00000=>00000 [1,5,2,3,6,4]=>[2,5,4,6,3,1]=>00000=>00000 [1,5,2,4,3,6]=>[6,2,5,3,4,1]=>00000=>00000 [1,5,2,4,6,3]=>[2,5,4,3,6,1]=>00000=>00000 [1,5,2,6,3,4]=>[2,5,3,6,4,1]=>00000=>00000 [1,5,2,6,4,3]=>[2,5,3,4,6,1]=>00000=>00000 [1,5,3,2,4,6]=>[6,2,3,5,4,1]=>00000=>00000 [1,5,3,2,6,4]=>[2,3,5,4,6,1]=>00000=>00000 [1,5,3,4,2,6]=>[6,3,5,2,4,1]=>00000=>00000 [1,5,3,4,6,2]=>[3,5,4,2,6,1]=>00000=>00000 [1,5,3,6,2,4]=>[3,5,2,6,4,1]=>00000=>00000 [1,5,3,6,4,2]=>[3,5,2,4,6,1]=>00000=>00000 [1,5,4,2,3,6]=>[6,2,4,5,3,1]=>00000=>00000 [1,5,4,2,6,3]=>[2,4,5,3,6,1]=>00000=>00000 [1,5,4,3,2,6]=>[6,2,3,4,5,1]=>00000=>00000 [1,5,4,3,6,2]=>[3,4,5,2,6,1]=>00000=>00000 [1,5,4,6,2,3]=>[4,5,2,6,3,1]=>00000=>00000 [1,5,4,6,3,2]=>[4,5,2,3,6,1]=>00000=>00000 [1,5,6,2,3,4]=>[5,2,6,4,3,1]=>00000=>00000 [1,5,6,2,4,3]=>[5,2,6,3,4,1]=>00000=>00000 [1,5,6,3,2,4]=>[5,2,3,6,4,1]=>00000=>00000 [1,5,6,3,4,2]=>[5,3,6,2,4,1]=>00000=>00000 [1,5,6,4,2,3]=>[5,2,4,6,3,1]=>00000=>00000 [1,5,6,4,3,2]=>[5,2,3,4,6,1]=>00000=>00000 [1,6,2,3,4,5]=>[2,6,5,4,3,1]=>00000=>00000 [1,6,2,3,5,4]=>[2,6,4,5,3,1]=>00000=>00000 [1,6,2,4,3,5]=>[2,6,5,3,4,1]=>00000=>00000 [1,6,2,4,5,3]=>[2,6,4,3,5,1]=>00000=>00000 [1,6,2,5,3,4]=>[2,6,3,5,4,1]=>00000=>00000 [1,6,2,5,4,3]=>[2,6,3,4,5,1]=>00000=>00000 [1,6,3,2,4,5]=>[2,3,6,5,4,1]=>00000=>00000 [1,6,3,2,5,4]=>[2,3,6,4,5,1]=>00000=>00000 [1,6,3,4,2,5]=>[3,6,5,2,4,1]=>00000=>00000 [1,6,3,4,5,2]=>[3,6,4,2,5,1]=>00000=>00000 [1,6,3,5,2,4]=>[3,6,2,5,4,1]=>00000=>00000 [1,6,3,5,4,2]=>[3,6,2,4,5,1]=>00000=>00000 [1,6,4,2,3,5]=>[2,4,6,5,3,1]=>00000=>00000 [1,6,4,2,5,3]=>[2,4,6,3,5,1]=>00000=>00000 [1,6,4,3,2,5]=>[2,3,4,6,5,1]=>00000=>00000 [1,6,4,3,5,2]=>[3,4,6,2,5,1]=>00000=>00000 [1,6,4,5,2,3]=>[4,6,2,5,3,1]=>00000=>00000 [1,6,4,5,3,2]=>[4,6,2,3,5,1]=>00000=>00000 [1,6,5,2,3,4]=>[2,5,6,4,3,1]=>00000=>00000 [1,6,5,2,4,3]=>[2,5,6,3,4,1]=>00000=>00000 [1,6,5,3,2,4]=>[2,3,5,6,4,1]=>00000=>00000 [1,6,5,3,4,2]=>[3,5,6,2,4,1]=>00000=>00000 [1,6,5,4,2,3]=>[2,4,5,6,3,1]=>00000=>00000 [1,6,5,4,3,2]=>[2,3,4,5,6,1]=>00000=>00000 [2,1,3,4,5,6]=>[6,5,4,3,1,2]=>00000=>00000 [2,1,3,4,6,5]=>[5,6,4,3,1,2]=>00000=>00000 [2,1,3,5,4,6]=>[6,4,5,3,1,2]=>00000=>00000 [2,1,3,5,6,4]=>[5,4,6,3,1,2]=>00000=>00000 [2,1,3,6,4,5]=>[4,6,5,3,1,2]=>00000=>00000 [2,1,3,6,5,4]=>[4,5,6,3,1,2]=>00000=>00000 [2,1,4,3,5,6]=>[6,5,3,4,1,2]=>00000=>00000 [2,1,4,3,6,5]=>[5,6,3,4,1,2]=>00000=>00000 [2,1,4,5,3,6]=>[6,4,3,5,1,2]=>00000=>00000 [2,1,4,5,6,3]=>[5,4,3,6,1,2]=>00000=>00000 [2,1,4,6,3,5]=>[4,3,6,5,1,2]=>00000=>00000 [2,1,4,6,5,3]=>[4,3,5,6,1,2]=>00000=>00000 [2,1,5,3,4,6]=>[6,3,5,4,1,2]=>00000=>00000 [2,1,5,3,6,4]=>[3,5,4,6,1,2]=>00000=>00000 [2,1,5,4,3,6]=>[6,3,4,5,1,2]=>00000=>00000 [2,1,5,4,6,3]=>[4,5,3,6,1,2]=>00000=>00000 [2,1,5,6,3,4]=>[5,3,6,4,1,2]=>00000=>00000 [2,1,5,6,4,3]=>[5,3,4,6,1,2]=>00000=>00000 [2,1,6,3,4,5]=>[3,6,5,4,1,2]=>00000=>00000 [2,1,6,3,5,4]=>[3,6,4,5,1,2]=>00000=>00000 [2,1,6,4,3,5]=>[3,4,6,5,1,2]=>00000=>00000 [2,1,6,4,5,3]=>[4,6,3,5,1,2]=>00000=>00000 [2,1,6,5,3,4]=>[3,5,6,4,1,2]=>00000=>00000 [2,1,6,5,4,3]=>[3,4,5,6,1,2]=>00000=>00000 [2,3,1,4,5,6]=>[6,5,4,2,1,3]=>00000=>00000 [2,3,1,4,6,5]=>[5,6,4,2,1,3]=>00000=>00000 [2,3,1,5,4,6]=>[6,4,5,2,1,3]=>00000=>00000 [2,3,1,5,6,4]=>[5,4,6,2,1,3]=>00000=>00000 [2,3,1,6,4,5]=>[4,6,5,2,1,3]=>00000=>00000 [2,3,1,6,5,4]=>[4,5,6,2,1,3]=>00000=>00000 [2,3,4,1,5,6]=>[6,5,3,2,1,4]=>00000=>00000 [2,3,4,1,6,5]=>[5,6,3,2,1,4]=>00000=>00000 [2,3,4,5,1,6]=>[6,4,3,2,1,5]=>00000=>00000 [2,3,4,5,6,1]=>[5,4,3,2,1,6]=>00001=>10000 [2,3,4,6,1,5]=>[4,3,2,1,6,5]=>00010=>01000 [2,3,4,6,5,1]=>[4,3,2,1,5,6]=>00011=>11000 [2,3,5,1,4,6]=>[6,3,2,1,5,4]=>00000=>00000 [2,3,5,1,6,4]=>[3,2,1,5,4,6]=>00101=>10100 [2,3,5,4,1,6]=>[6,3,2,1,4,5]=>00000=>00000 [2,3,5,4,6,1]=>[4,5,3,2,1,6]=>00001=>10000 [2,3,5,6,1,4]=>[5,3,2,1,6,4]=>00000=>00000 [2,3,5,6,4,1]=>[5,3,2,1,4,6]=>00001=>10000 [2,3,6,1,4,5]=>[3,2,1,6,5,4]=>00100=>00100 [2,3,6,1,5,4]=>[3,2,1,6,4,5]=>00100=>00100 [2,3,6,4,1,5]=>[3,2,1,4,6,5]=>00110=>01100 [2,3,6,4,5,1]=>[4,6,3,2,1,5]=>00000=>00000 [2,3,6,5,1,4]=>[3,2,1,5,6,4]=>00100=>00100 [2,3,6,5,4,1]=>[3,2,1,4,5,6]=>00111=>11100 [2,4,1,3,5,6]=>[6,5,2,1,4,3]=>00000=>00000 [2,4,1,3,6,5]=>[5,6,2,1,4,3]=>00000=>00000 [2,4,1,5,3,6]=>[6,2,1,4,3,5]=>00000=>00000 [2,4,1,5,6,3]=>[5,2,1,4,3,6]=>00001=>10000 [2,4,1,6,3,5]=>[2,1,4,3,6,5]=>01010=>01010 [2,4,1,6,5,3]=>[2,1,4,3,5,6]=>01011=>11010 [2,4,3,1,5,6]=>[6,5,2,1,3,4]=>00000=>00000 [2,4,3,1,6,5]=>[5,6,2,1,3,4]=>00000=>00000 [2,4,3,5,1,6]=>[6,3,4,2,1,5]=>00000=>00000 [2,4,3,5,6,1]=>[5,3,4,2,1,6]=>00001=>10000 [2,4,3,6,1,5]=>[3,4,2,1,6,5]=>00010=>01000 [2,4,3,6,5,1]=>[3,4,2,1,5,6]=>00011=>11000 [2,4,5,1,3,6]=>[6,4,2,1,5,3]=>00000=>00000 [2,4,5,1,6,3]=>[4,2,1,5,3,6]=>00001=>10000 [2,4,5,3,1,6]=>[6,4,2,1,3,5]=>00000=>00000 [2,4,5,3,6,1]=>[4,3,5,2,1,6]=>00001=>10000 [2,4,5,6,1,3]=>[5,4,2,1,6,3]=>00000=>00000 [2,4,5,6,3,1]=>[5,4,2,1,3,6]=>00001=>10000 [2,4,6,1,3,5]=>[4,2,1,6,5,3]=>00000=>00000 [2,4,6,1,5,3]=>[4,2,1,6,3,5]=>00000=>00000 [2,4,6,3,1,5]=>[4,2,1,3,6,5]=>00010=>01000 [2,4,6,3,5,1]=>[4,3,6,2,1,5]=>00000=>00000 [2,4,6,5,1,3]=>[4,2,1,5,6,3]=>00000=>00000 [2,4,6,5,3,1]=>[4,2,1,3,5,6]=>00011=>11000 [2,5,1,3,4,6]=>[6,2,1,5,4,3]=>00000=>00000 [2,5,1,3,6,4]=>[2,1,5,4,6,3]=>01000=>00010 [2,5,1,4,3,6]=>[6,2,1,5,3,4]=>00000=>00000 [2,5,1,4,6,3]=>[2,1,5,4,3,6]=>01001=>10010 [2,5,1,6,3,4]=>[2,1,5,3,6,4]=>01000=>00010 [2,5,1,6,4,3]=>[2,1,5,3,4,6]=>01001=>10010 [2,5,3,1,4,6]=>[6,2,1,3,5,4]=>00000=>00000 [2,5,3,1,6,4]=>[2,1,3,5,4,6]=>01101=>10110 [2,5,3,4,1,6]=>[6,3,5,2,1,4]=>00000=>00000 [2,5,3,4,6,1]=>[3,5,4,2,1,6]=>00001=>10000 [2,5,3,6,1,4]=>[3,5,2,1,6,4]=>00000=>00000 [2,5,3,6,4,1]=>[3,5,2,1,4,6]=>00001=>10000 [2,5,4,1,3,6]=>[6,2,1,4,5,3]=>00000=>00000 [2,5,4,1,6,3]=>[2,1,4,5,3,6]=>01001=>10010 [2,5,4,3,1,6]=>[6,2,1,3,4,5]=>00000=>00000 [2,5,4,3,6,1]=>[3,4,5,2,1,6]=>00001=>10000 [2,5,4,6,1,3]=>[4,5,2,1,6,3]=>00000=>00000 [2,5,4,6,3,1]=>[4,5,2,1,3,6]=>00001=>10000 [2,5,6,1,3,4]=>[5,2,1,6,4,3]=>00000=>00000 [2,5,6,1,4,3]=>[5,2,1,6,3,4]=>00000=>00000 [2,5,6,3,1,4]=>[5,2,1,3,6,4]=>00000=>00000 [2,5,6,3,4,1]=>[5,3,6,2,1,4]=>00000=>00000 [2,5,6,4,1,3]=>[5,2,1,4,6,3]=>00000=>00000 [2,5,6,4,3,1]=>[5,2,1,3,4,6]=>00001=>10000 [2,6,1,3,4,5]=>[2,1,6,5,4,3]=>01000=>00010 [2,6,1,3,5,4]=>[2,1,6,4,5,3]=>01000=>00010 [2,6,1,4,3,5]=>[2,1,6,5,3,4]=>01000=>00010 [2,6,1,4,5,3]=>[2,1,6,4,3,5]=>01000=>00010 [2,6,1,5,3,4]=>[2,1,6,3,5,4]=>01000=>00010 [2,6,1,5,4,3]=>[2,1,6,3,4,5]=>01000=>00010 [2,6,3,1,4,5]=>[2,1,3,6,5,4]=>01100=>00110 [2,6,3,1,5,4]=>[2,1,3,6,4,5]=>01100=>00110 [2,6,3,4,1,5]=>[3,6,5,2,1,4]=>00000=>00000 [2,6,3,4,5,1]=>[3,6,4,2,1,5]=>00000=>00000 [2,6,3,5,1,4]=>[3,6,2,1,5,4]=>00000=>00000 [2,6,3,5,4,1]=>[3,6,2,1,4,5]=>00000=>00000 [2,6,4,1,3,5]=>[2,1,4,6,5,3]=>01000=>00010 [2,6,4,1,5,3]=>[2,1,4,6,3,5]=>01000=>00010 [2,6,4,3,1,5]=>[2,1,3,4,6,5]=>01110=>01110 [2,6,4,3,5,1]=>[3,4,6,2,1,5]=>00000=>00000 [2,6,4,5,1,3]=>[4,6,2,1,5,3]=>00000=>00000 [2,6,4,5,3,1]=>[4,6,2,1,3,5]=>00000=>00000 [2,6,5,1,3,4]=>[2,1,5,6,4,3]=>01000=>00010 [2,6,5,1,4,3]=>[2,1,5,6,3,4]=>01000=>00010 [2,6,5,3,1,4]=>[2,1,3,5,6,4]=>01100=>00110 [2,6,5,3,4,1]=>[3,5,6,2,1,4]=>00000=>00000 [2,6,5,4,1,3]=>[2,1,4,5,6,3]=>01000=>00010 [2,6,5,4,3,1]=>[2,1,3,4,5,6]=>01111=>11110 [3,1,2,4,5,6]=>[6,5,4,1,3,2]=>00000=>00000 [3,1,2,4,6,5]=>[5,6,4,1,3,2]=>00000=>00000 [3,1,2,5,4,6]=>[6,4,5,1,3,2]=>00000=>00000 [3,1,2,5,6,4]=>[5,4,6,1,3,2]=>00000=>00000 [3,1,2,6,4,5]=>[4,6,5,1,3,2]=>00000=>00000 [3,1,2,6,5,4]=>[4,5,6,1,3,2]=>00000=>00000 [3,1,4,2,5,6]=>[6,5,1,3,2,4]=>00000=>00000 [3,1,4,2,6,5]=>[5,6,1,3,2,4]=>00000=>00000 [3,1,4,5,2,6]=>[6,4,1,3,2,5]=>00000=>00000 [3,1,4,5,6,2]=>[5,4,1,3,2,6]=>00001=>10000 [3,1,4,6,2,5]=>[4,1,3,2,6,5]=>00010=>01000 [3,1,4,6,5,2]=>[4,1,3,2,5,6]=>00011=>11000 [3,1,5,2,4,6]=>[6,1,3,2,5,4]=>00000=>00000 [3,1,5,2,6,4]=>[1,3,2,5,4,6]=>10101=>10101 [3,1,5,4,2,6]=>[6,1,3,2,4,5]=>00000=>00000 [3,1,5,4,6,2]=>[4,5,1,3,2,6]=>00001=>10000 [3,1,5,6,2,4]=>[5,1,3,2,6,4]=>00000=>00000 [3,1,5,6,4,2]=>[5,1,3,2,4,6]=>00001=>10000 [3,1,6,2,4,5]=>[1,3,2,6,5,4]=>10100=>00101 [3,1,6,2,5,4]=>[1,3,2,6,4,5]=>10100=>00101 [3,1,6,4,2,5]=>[1,3,2,4,6,5]=>10110=>01101 [3,1,6,4,5,2]=>[4,6,1,3,2,5]=>00000=>00000 [3,1,6,5,2,4]=>[1,3,2,5,6,4]=>10100=>00101 [3,1,6,5,4,2]=>[1,3,2,4,5,6]=>10111=>11101 [3,2,1,4,5,6]=>[6,5,4,1,2,3]=>00000=>00000 [3,2,1,4,6,5]=>[5,6,4,1,2,3]=>00000=>00000 [3,2,1,5,4,6]=>[6,4,5,1,2,3]=>00000=>00000 [3,2,1,5,6,4]=>[5,4,6,1,2,3]=>00000=>00000 [3,2,1,6,4,5]=>[4,6,5,1,2,3]=>00000=>00000 [3,2,1,6,5,4]=>[4,5,6,1,2,3]=>00000=>00000 [3,2,4,1,5,6]=>[6,5,2,3,1,4]=>00000=>00000 [3,2,4,1,6,5]=>[5,6,2,3,1,4]=>00000=>00000 [3,2,4,5,1,6]=>[6,4,2,3,1,5]=>00000=>00000 [3,2,4,5,6,1]=>[5,4,2,3,1,6]=>00001=>10000 [3,2,4,6,1,5]=>[4,2,3,1,6,5]=>00010=>01000 [3,2,4,6,5,1]=>[4,2,3,1,5,6]=>00011=>11000 [3,2,5,1,4,6]=>[6,2,3,1,5,4]=>00000=>00000 [3,2,5,1,6,4]=>[2,3,1,5,4,6]=>00101=>10100 [3,2,5,4,1,6]=>[6,2,3,1,4,5]=>00000=>00000 [3,2,5,4,6,1]=>[4,5,2,3,1,6]=>00001=>10000 [3,2,5,6,1,4]=>[5,2,3,1,6,4]=>00000=>00000 [3,2,5,6,4,1]=>[5,2,3,1,4,6]=>00001=>10000 [3,2,6,1,4,5]=>[2,3,1,6,5,4]=>00100=>00100 [3,2,6,1,5,4]=>[2,3,1,6,4,5]=>00100=>00100 [3,2,6,4,1,5]=>[2,3,1,4,6,5]=>00110=>01100 [3,2,6,4,5,1]=>[4,6,2,3,1,5]=>00000=>00000 [3,2,6,5,1,4]=>[2,3,1,5,6,4]=>00100=>00100 [3,2,6,5,4,1]=>[2,3,1,4,5,6]=>00111=>11100 [3,4,1,2,5,6]=>[6,5,3,1,4,2]=>00000=>00000 [3,4,1,2,6,5]=>[5,6,3,1,4,2]=>00000=>00000 [3,4,1,5,2,6]=>[6,3,1,4,2,5]=>00000=>00000 [3,4,1,5,6,2]=>[5,3,1,4,2,6]=>00001=>10000 [3,4,1,6,2,5]=>[3,1,4,2,6,5]=>00010=>01000 [3,4,1,6,5,2]=>[3,1,4,2,5,6]=>00011=>11000 [3,4,2,1,5,6]=>[6,5,3,1,2,4]=>00000=>00000 [3,4,2,1,6,5]=>[5,6,3,1,2,4]=>00000=>00000 [3,4,2,5,1,6]=>[6,3,2,4,1,5]=>00000=>00000 [3,4,2,5,6,1]=>[5,3,2,4,1,6]=>00001=>10000 [3,4,2,6,1,5]=>[3,2,4,1,6,5]=>00010=>01000 [3,4,2,6,5,1]=>[3,2,4,1,5,6]=>00011=>11000 [3,4,5,1,2,6]=>[6,4,3,1,5,2]=>00000=>00000 [3,4,5,1,6,2]=>[4,3,1,5,2,6]=>00001=>10000 [3,4,5,2,1,6]=>[6,4,3,1,2,5]=>00000=>00000 [3,4,5,2,6,1]=>[4,3,2,5,1,6]=>00001=>10000 [3,4,5,6,1,2]=>[5,4,3,1,6,2]=>00000=>00000 [3,4,5,6,2,1]=>[5,4,3,1,2,6]=>00001=>10000 [3,4,6,1,2,5]=>[4,3,1,6,5,2]=>00000=>00000 [3,4,6,1,5,2]=>[4,3,1,6,2,5]=>00000=>00000 [3,4,6,2,1,5]=>[4,3,1,2,6,5]=>00010=>01000 [3,4,6,2,5,1]=>[4,3,2,6,1,5]=>00000=>00000 [3,4,6,5,1,2]=>[4,3,1,5,6,2]=>00000=>00000 [3,4,6,5,2,1]=>[4,3,1,2,5,6]=>00011=>11000 [3,5,1,2,4,6]=>[6,3,1,5,4,2]=>00000=>00000 [3,5,1,2,6,4]=>[3,1,5,4,6,2]=>00000=>00000 [3,5,1,4,2,6]=>[6,3,1,5,2,4]=>00000=>00000 [3,5,1,4,6,2]=>[3,1,5,4,2,6]=>00001=>10000 [3,5,1,6,2,4]=>[3,1,5,2,6,4]=>00000=>00000 [3,5,1,6,4,2]=>[3,1,5,2,4,6]=>00001=>10000 [3,5,2,1,4,6]=>[6,3,1,2,5,4]=>00000=>00000 [3,5,2,1,6,4]=>[3,1,2,5,4,6]=>00101=>10100 [3,5,2,4,1,6]=>[6,3,2,5,1,4]=>00000=>00000 [3,5,2,4,6,1]=>[3,2,5,4,1,6]=>00001=>10000 [3,5,2,6,1,4]=>[3,2,5,1,6,4]=>00000=>00000 [3,5,2,6,4,1]=>[3,2,5,1,4,6]=>00001=>10000 [3,5,4,1,2,6]=>[6,3,1,4,5,2]=>00000=>00000 [3,5,4,1,6,2]=>[3,1,4,5,2,6]=>00001=>10000 [3,5,4,2,1,6]=>[6,3,1,2,4,5]=>00000=>00000 [3,5,4,2,6,1]=>[3,2,4,5,1,6]=>00001=>10000 [3,5,4,6,1,2]=>[4,5,3,1,6,2]=>00000=>00000 [3,5,4,6,2,1]=>[4,5,3,1,2,6]=>00001=>10000 [3,5,6,1,2,4]=>[5,3,1,6,4,2]=>00000=>00000 [3,5,6,1,4,2]=>[5,3,1,6,2,4]=>00000=>00000 [3,5,6,2,1,4]=>[5,3,1,2,6,4]=>00000=>00000 [3,5,6,2,4,1]=>[5,3,2,6,1,4]=>00000=>00000 [3,5,6,4,1,2]=>[5,3,1,4,6,2]=>00000=>00000 [3,5,6,4,2,1]=>[5,3,1,2,4,6]=>00001=>10000 [3,6,1,2,4,5]=>[3,1,6,5,4,2]=>00000=>00000 [3,6,1,2,5,4]=>[3,1,6,4,5,2]=>00000=>00000 [3,6,1,4,2,5]=>[3,1,6,5,2,4]=>00000=>00000 [3,6,1,4,5,2]=>[3,1,6,4,2,5]=>00000=>00000 [3,6,1,5,2,4]=>[3,1,6,2,5,4]=>00000=>00000 [3,6,1,5,4,2]=>[3,1,6,2,4,5]=>00000=>00000 [3,6,2,1,4,5]=>[3,1,2,6,5,4]=>00100=>00100 [3,6,2,1,5,4]=>[3,1,2,6,4,5]=>00100=>00100 [3,6,2,4,1,5]=>[3,2,6,5,1,4]=>00000=>00000 [3,6,2,4,5,1]=>[3,2,6,4,1,5]=>00000=>00000 [3,6,2,5,1,4]=>[3,2,6,1,5,4]=>00000=>00000 [3,6,2,5,4,1]=>[3,2,6,1,4,5]=>00000=>00000 [3,6,4,1,2,5]=>[3,1,4,6,5,2]=>00000=>00000 [3,6,4,1,5,2]=>[3,1,4,6,2,5]=>00000=>00000 [3,6,4,2,1,5]=>[3,1,2,4,6,5]=>00110=>01100 [3,6,4,2,5,1]=>[3,2,4,6,1,5]=>00000=>00000 [3,6,4,5,1,2]=>[4,6,3,1,5,2]=>00000=>00000 [3,6,4,5,2,1]=>[4,6,3,1,2,5]=>00000=>00000 [3,6,5,1,2,4]=>[3,1,5,6,4,2]=>00000=>00000 [3,6,5,1,4,2]=>[3,1,5,6,2,4]=>00000=>00000 [3,6,5,2,1,4]=>[3,1,2,5,6,4]=>00100=>00100 [3,6,5,2,4,1]=>[3,2,5,6,1,4]=>00000=>00000 [3,6,5,4,1,2]=>[3,1,4,5,6,2]=>00000=>00000 [3,6,5,4,2,1]=>[3,1,2,4,5,6]=>00111=>11100 [4,1,2,3,5,6]=>[6,5,1,4,3,2]=>00000=>00000 [4,1,2,3,6,5]=>[5,6,1,4,3,2]=>00000=>00000 [4,1,2,5,3,6]=>[6,1,4,3,5,2]=>00000=>00000 [4,1,2,5,6,3]=>[5,1,4,3,6,2]=>00000=>00000 [4,1,2,6,3,5]=>[1,4,3,6,5,2]=>10000=>00001 [4,1,2,6,5,3]=>[1,4,3,5,6,2]=>10000=>00001 [4,1,3,2,5,6]=>[6,5,1,4,2,3]=>00000=>00000 [4,1,3,2,6,5]=>[5,6,1,4,2,3]=>00000=>00000 [4,1,3,5,2,6]=>[6,1,4,3,2,5]=>00000=>00000 [4,1,3,5,6,2]=>[5,1,4,3,2,6]=>00001=>10000 [4,1,3,6,2,5]=>[1,4,3,2,6,5]=>10010=>01001 [4,1,3,6,5,2]=>[1,4,3,2,5,6]=>10011=>11001 [4,1,5,2,3,6]=>[6,1,4,2,5,3]=>00000=>00000 [4,1,5,2,6,3]=>[1,4,2,5,3,6]=>10001=>10001 [4,1,5,3,2,6]=>[6,1,4,2,3,5]=>00000=>00000 [4,1,5,3,6,2]=>[1,4,3,5,2,6]=>10001=>10001 [4,1,5,6,2,3]=>[5,1,4,2,6,3]=>00000=>00000 [4,1,5,6,3,2]=>[5,1,4,2,3,6]=>00001=>10000 [4,1,6,2,3,5]=>[1,4,2,6,5,3]=>10000=>00001 [4,1,6,2,5,3]=>[1,4,2,6,3,5]=>10000=>00001 [4,1,6,3,2,5]=>[1,4,2,3,6,5]=>10010=>01001 [4,1,6,3,5,2]=>[1,4,3,6,2,5]=>10000=>00001 [4,1,6,5,2,3]=>[1,4,2,5,6,3]=>10000=>00001 [4,1,6,5,3,2]=>[1,4,2,3,5,6]=>10011=>11001 [4,2,1,3,5,6]=>[6,5,1,2,4,3]=>00000=>00000 [4,2,1,3,6,5]=>[5,6,1,2,4,3]=>00000=>00000 [4,2,1,5,3,6]=>[6,1,2,4,3,5]=>00000=>00000 [4,2,1,5,6,3]=>[5,1,2,4,3,6]=>00001=>10000 [4,2,1,6,3,5]=>[1,2,4,3,6,5]=>11010=>01011 [4,2,1,6,5,3]=>[1,2,4,3,5,6]=>11011=>11011 [4,2,3,1,5,6]=>[6,5,2,4,1,3]=>00000=>00000 [4,2,3,1,6,5]=>[5,6,2,4,1,3]=>00000=>00000 [4,2,3,5,1,6]=>[6,2,4,3,1,5]=>00000=>00000 [4,2,3,5,6,1]=>[5,2,4,3,1,6]=>00001=>10000 [4,2,3,6,1,5]=>[2,4,3,1,6,5]=>00010=>01000 [4,2,3,6,5,1]=>[2,4,3,1,5,6]=>00011=>11000 [4,2,5,1,3,6]=>[6,2,4,1,5,3]=>00000=>00000 [4,2,5,1,6,3]=>[2,4,1,5,3,6]=>00001=>10000 [4,2,5,3,1,6]=>[6,2,4,1,3,5]=>00000=>00000 [4,2,5,3,6,1]=>[2,4,3,5,1,6]=>00001=>10000 [4,2,5,6,1,3]=>[5,2,4,1,6,3]=>00000=>00000 [4,2,5,6,3,1]=>[5,2,4,1,3,6]=>00001=>10000 [4,2,6,1,3,5]=>[2,4,1,6,5,3]=>00000=>00000 [4,2,6,1,5,3]=>[2,4,1,6,3,5]=>00000=>00000 [4,2,6,3,1,5]=>[2,4,1,3,6,5]=>00010=>01000 [4,2,6,3,5,1]=>[2,4,3,6,1,5]=>00000=>00000 [4,2,6,5,1,3]=>[2,4,1,5,6,3]=>00000=>00000 [4,2,6,5,3,1]=>[2,4,1,3,5,6]=>00011=>11000 [4,3,1,2,5,6]=>[6,5,1,3,4,2]=>00000=>00000 [4,3,1,2,6,5]=>[5,6,1,3,4,2]=>00000=>00000 [4,3,1,5,2,6]=>[6,1,3,4,2,5]=>00000=>00000 [4,3,1,5,6,2]=>[5,1,3,4,2,6]=>00001=>10000 [4,3,1,6,2,5]=>[1,3,4,2,6,5]=>10010=>01001 [4,3,1,6,5,2]=>[1,3,4,2,5,6]=>10011=>11001 [4,3,2,1,5,6]=>[6,5,1,2,3,4]=>00000=>00000 [4,3,2,1,6,5]=>[5,6,1,2,3,4]=>00000=>00000 [4,3,2,5,1,6]=>[6,2,3,4,1,5]=>00000=>00000 [4,3,2,5,6,1]=>[5,2,3,4,1,6]=>00001=>10000 [4,3,2,6,1,5]=>[2,3,4,1,6,5]=>00010=>01000 [4,3,2,6,5,1]=>[2,3,4,1,5,6]=>00011=>11000 [4,3,5,1,2,6]=>[6,3,4,1,5,2]=>00000=>00000 [4,3,5,1,6,2]=>[3,4,1,5,2,6]=>00001=>10000 [4,3,5,2,1,6]=>[6,3,4,1,2,5]=>00000=>00000 [4,3,5,2,6,1]=>[3,4,2,5,1,6]=>00001=>10000 [4,3,5,6,1,2]=>[5,3,4,1,6,2]=>00000=>00000 [4,3,5,6,2,1]=>[5,3,4,1,2,6]=>00001=>10000 [4,3,6,1,2,5]=>[3,4,1,6,5,2]=>00000=>00000 [4,3,6,1,5,2]=>[3,4,1,6,2,5]=>00000=>00000 [4,3,6,2,1,5]=>[3,4,1,2,6,5]=>00010=>01000 [4,3,6,2,5,1]=>[3,4,2,6,1,5]=>00000=>00000 [4,3,6,5,1,2]=>[3,4,1,5,6,2]=>00000=>00000 [4,3,6,5,2,1]=>[3,4,1,2,5,6]=>00011=>11000 [4,5,1,2,3,6]=>[6,4,1,5,3,2]=>00000=>00000 [4,5,1,2,6,3]=>[4,1,5,3,6,2]=>00000=>00000 [4,5,1,3,2,6]=>[6,4,1,5,2,3]=>00000=>00000 [4,5,1,3,6,2]=>[4,1,5,3,2,6]=>00001=>10000 [4,5,1,6,2,3]=>[4,1,5,2,6,3]=>00000=>00000 [4,5,1,6,3,2]=>[4,1,5,2,3,6]=>00001=>10000 [4,5,2,1,3,6]=>[6,4,1,2,5,3]=>00000=>00000 [4,5,2,1,6,3]=>[4,1,2,5,3,6]=>00001=>10000 [4,5,2,3,1,6]=>[6,4,2,5,1,3]=>00000=>00000 [4,5,2,3,6,1]=>[4,2,5,3,1,6]=>00001=>10000 [4,5,2,6,1,3]=>[4,2,5,1,6,3]=>00000=>00000 [4,5,2,6,3,1]=>[4,2,5,1,3,6]=>00001=>10000 [4,5,3,1,2,6]=>[6,4,1,3,5,2]=>00000=>00000 [4,5,3,1,6,2]=>[4,1,3,5,2,6]=>00001=>10000 [4,5,3,2,1,6]=>[6,4,1,2,3,5]=>00000=>00000 [4,5,3,2,6,1]=>[4,2,3,5,1,6]=>00001=>10000 [4,5,3,6,1,2]=>[4,3,5,1,6,2]=>00000=>00000 [4,5,3,6,2,1]=>[4,3,5,1,2,6]=>00001=>10000 [4,5,6,1,2,3]=>[5,4,1,6,3,2]=>00000=>00000 [4,5,6,1,3,2]=>[5,4,1,6,2,3]=>00000=>00000 [4,5,6,2,1,3]=>[5,4,1,2,6,3]=>00000=>00000 [4,5,6,2,3,1]=>[5,4,2,6,1,3]=>00000=>00000 [4,5,6,3,1,2]=>[5,4,1,3,6,2]=>00000=>00000 [4,5,6,3,2,1]=>[5,4,1,2,3,6]=>00001=>10000 [4,6,1,2,3,5]=>[4,1,6,5,3,2]=>00000=>00000 [4,6,1,2,5,3]=>[4,1,6,3,5,2]=>00000=>00000 [4,6,1,3,2,5]=>[4,1,6,5,2,3]=>00000=>00000 [4,6,1,3,5,2]=>[4,1,6,3,2,5]=>00000=>00000 [4,6,1,5,2,3]=>[4,1,6,2,5,3]=>00000=>00000 [4,6,1,5,3,2]=>[4,1,6,2,3,5]=>00000=>00000 [4,6,2,1,3,5]=>[4,1,2,6,5,3]=>00000=>00000 [4,6,2,1,5,3]=>[4,1,2,6,3,5]=>00000=>00000 [4,6,2,3,1,5]=>[4,2,6,5,1,3]=>00000=>00000 [4,6,2,3,5,1]=>[4,2,6,3,1,5]=>00000=>00000 [4,6,2,5,1,3]=>[4,2,6,1,5,3]=>00000=>00000 [4,6,2,5,3,1]=>[4,2,6,1,3,5]=>00000=>00000 [4,6,3,1,2,5]=>[4,1,3,6,5,2]=>00000=>00000 [4,6,3,1,5,2]=>[4,1,3,6,2,5]=>00000=>00000 [4,6,3,2,1,5]=>[4,1,2,3,6,5]=>00010=>01000 [4,6,3,2,5,1]=>[4,2,3,6,1,5]=>00000=>00000 [4,6,3,5,1,2]=>[4,3,6,1,5,2]=>00000=>00000 [4,6,3,5,2,1]=>[4,3,6,1,2,5]=>00000=>00000 [4,6,5,1,2,3]=>[4,1,5,6,3,2]=>00000=>00000 [4,6,5,1,3,2]=>[4,1,5,6,2,3]=>00000=>00000 [4,6,5,2,1,3]=>[4,1,2,5,6,3]=>00000=>00000 [4,6,5,2,3,1]=>[4,2,5,6,1,3]=>00000=>00000 [4,6,5,3,1,2]=>[4,1,3,5,6,2]=>00000=>00000 [4,6,5,3,2,1]=>[4,1,2,3,5,6]=>00011=>11000 [5,1,2,3,4,6]=>[6,1,5,4,3,2]=>00000=>00000 [5,1,2,3,6,4]=>[1,5,4,6,3,2]=>10000=>00001 [5,1,2,4,3,6]=>[6,1,5,3,4,2]=>00000=>00000 [5,1,2,4,6,3]=>[1,5,4,3,6,2]=>10000=>00001 [5,1,2,6,3,4]=>[1,5,3,6,4,2]=>10000=>00001 [5,1,2,6,4,3]=>[1,5,3,4,6,2]=>10000=>00001 [5,1,3,2,4,6]=>[6,1,5,4,2,3]=>00000=>00000 [5,1,3,2,6,4]=>[1,5,4,6,2,3]=>10000=>00001 [5,1,3,4,2,6]=>[6,1,5,3,2,4]=>00000=>00000 [5,1,3,4,6,2]=>[1,5,4,3,2,6]=>10001=>10001 [5,1,3,6,2,4]=>[1,5,3,2,6,4]=>10000=>00001 [5,1,3,6,4,2]=>[1,5,3,2,4,6]=>10001=>10001 [5,1,4,2,3,6]=>[6,1,5,2,4,3]=>00000=>00000 [5,1,4,2,6,3]=>[1,5,2,4,3,6]=>10001=>10001 [5,1,4,3,2,6]=>[6,1,5,2,3,4]=>00000=>00000 [5,1,4,3,6,2]=>[1,5,3,4,2,6]=>10001=>10001 [5,1,4,6,2,3]=>[1,5,4,2,6,3]=>10000=>00001 [5,1,4,6,3,2]=>[1,5,4,2,3,6]=>10001=>10001 [5,1,6,2,3,4]=>[1,5,2,6,4,3]=>10000=>00001 [5,1,6,2,4,3]=>[1,5,2,6,3,4]=>10000=>00001 [5,1,6,3,2,4]=>[1,5,2,3,6,4]=>10000=>00001 [5,1,6,3,4,2]=>[1,5,3,6,2,4]=>10000=>00001 [5,1,6,4,2,3]=>[1,5,2,4,6,3]=>10000=>00001 [5,1,6,4,3,2]=>[1,5,2,3,4,6]=>10001=>10001 [5,2,1,3,4,6]=>[6,1,2,5,4,3]=>00000=>00000 [5,2,1,3,6,4]=>[1,2,5,4,6,3]=>11000=>00011 [5,2,1,4,3,6]=>[6,1,2,5,3,4]=>00000=>00000 [5,2,1,4,6,3]=>[1,2,5,4,3,6]=>11001=>10011 [5,2,1,6,3,4]=>[1,2,5,3,6,4]=>11000=>00011 [5,2,1,6,4,3]=>[1,2,5,3,4,6]=>11001=>10011 [5,2,3,1,4,6]=>[6,2,5,4,1,3]=>00000=>00000 [5,2,3,1,6,4]=>[2,5,4,6,1,3]=>00000=>00000 [5,2,3,4,1,6]=>[6,2,5,3,1,4]=>00000=>00000 [5,2,3,4,6,1]=>[2,5,4,3,1,6]=>00001=>10000 [5,2,3,6,1,4]=>[2,5,3,1,6,4]=>00000=>00000 [5,2,3,6,4,1]=>[2,5,3,1,4,6]=>00001=>10000 [5,2,4,1,3,6]=>[6,2,5,1,4,3]=>00000=>00000 [5,2,4,1,6,3]=>[2,5,1,4,3,6]=>00001=>10000 [5,2,4,3,1,6]=>[6,2,5,1,3,4]=>00000=>00000 [5,2,4,3,6,1]=>[2,5,3,4,1,6]=>00001=>10000 [5,2,4,6,1,3]=>[2,5,4,1,6,3]=>00000=>00000 [5,2,4,6,3,1]=>[2,5,4,1,3,6]=>00001=>10000 [5,2,6,1,3,4]=>[2,5,1,6,4,3]=>00000=>00000 [5,2,6,1,4,3]=>[2,5,1,6,3,4]=>00000=>00000 [5,2,6,3,1,4]=>[2,5,1,3,6,4]=>00000=>00000 [5,2,6,3,4,1]=>[2,5,3,6,1,4]=>00000=>00000 [5,2,6,4,1,3]=>[2,5,1,4,6,3]=>00000=>00000 [5,2,6,4,3,1]=>[2,5,1,3,4,6]=>00001=>10000 [5,3,1,2,4,6]=>[6,1,3,5,4,2]=>00000=>00000 [5,3,1,2,6,4]=>[1,3,5,4,6,2]=>10000=>00001 [5,3,1,4,2,6]=>[6,1,3,5,2,4]=>00000=>00000 [5,3,1,4,6,2]=>[1,3,5,4,2,6]=>10001=>10001 [5,3,1,6,2,4]=>[1,3,5,2,6,4]=>10000=>00001 [5,3,1,6,4,2]=>[1,3,5,2,4,6]=>10001=>10001 [5,3,2,1,4,6]=>[6,1,2,3,5,4]=>00000=>00000 [5,3,2,1,6,4]=>[1,2,3,5,4,6]=>11101=>10111 [5,3,2,4,1,6]=>[6,2,3,5,1,4]=>00000=>00000 [5,3,2,4,6,1]=>[2,3,5,4,1,6]=>00001=>10000 [5,3,2,6,1,4]=>[2,3,5,1,6,4]=>00000=>00000 [5,3,2,6,4,1]=>[2,3,5,1,4,6]=>00001=>10000 [5,3,4,1,2,6]=>[6,3,5,1,4,2]=>00000=>00000 [5,3,4,1,6,2]=>[3,5,1,4,2,6]=>00001=>10000 [5,3,4,2,1,6]=>[6,3,5,1,2,4]=>00000=>00000 [5,3,4,2,6,1]=>[3,5,2,4,1,6]=>00001=>10000 [5,3,4,6,1,2]=>[3,5,4,1,6,2]=>00000=>00000 [5,3,4,6,2,1]=>[3,5,4,1,2,6]=>00001=>10000 [5,3,6,1,2,4]=>[3,5,1,6,4,2]=>00000=>00000 [5,3,6,1,4,2]=>[3,5,1,6,2,4]=>00000=>00000 [5,3,6,2,1,4]=>[3,5,1,2,6,4]=>00000=>00000 [5,3,6,2,4,1]=>[3,5,2,6,1,4]=>00000=>00000 [5,3,6,4,1,2]=>[3,5,1,4,6,2]=>00000=>00000 [5,3,6,4,2,1]=>[3,5,1,2,4,6]=>00001=>10000 [5,4,1,2,3,6]=>[6,1,4,5,3,2]=>00000=>00000 [5,4,1,2,6,3]=>[1,4,5,3,6,2]=>10000=>00001 [5,4,1,3,2,6]=>[6,1,4,5,2,3]=>00000=>00000 [5,4,1,3,6,2]=>[1,4,5,3,2,6]=>10001=>10001 [5,4,1,6,2,3]=>[1,4,5,2,6,3]=>10000=>00001 [5,4,1,6,3,2]=>[1,4,5,2,3,6]=>10001=>10001 [5,4,2,1,3,6]=>[6,1,2,4,5,3]=>00000=>00000 [5,4,2,1,6,3]=>[1,2,4,5,3,6]=>11001=>10011 [5,4,2,3,1,6]=>[6,2,4,5,1,3]=>00000=>00000 [5,4,2,3,6,1]=>[2,4,5,3,1,6]=>00001=>10000 [5,4,2,6,1,3]=>[2,4,5,1,6,3]=>00000=>00000 [5,4,2,6,3,1]=>[2,4,5,1,3,6]=>00001=>10000 [5,4,3,1,2,6]=>[6,1,3,4,5,2]=>00000=>00000 [5,4,3,1,6,2]=>[1,3,4,5,2,6]=>10001=>10001 [5,4,3,2,1,6]=>[6,1,2,3,4,5]=>00000=>00000 [5,4,3,2,6,1]=>[2,3,4,5,1,6]=>00001=>10000 [5,4,3,6,1,2]=>[3,4,5,1,6,2]=>00000=>00000 [5,4,3,6,2,1]=>[3,4,5,1,2,6]=>00001=>10000 [5,4,6,1,2,3]=>[4,5,1,6,3,2]=>00000=>00000 [5,4,6,1,3,2]=>[4,5,1,6,2,3]=>00000=>00000 [5,4,6,2,1,3]=>[4,5,1,2,6,3]=>00000=>00000 [5,4,6,2,3,1]=>[4,5,2,6,1,3]=>00000=>00000 [5,4,6,3,1,2]=>[4,5,1,3,6,2]=>00000=>00000 [5,4,6,3,2,1]=>[4,5,1,2,3,6]=>00001=>10000 [5,6,1,2,3,4]=>[5,1,6,4,3,2]=>00000=>00000 [5,6,1,2,4,3]=>[5,1,6,3,4,2]=>00000=>00000 [5,6,1,3,2,4]=>[5,1,6,4,2,3]=>00000=>00000 [5,6,1,3,4,2]=>[5,1,6,3,2,4]=>00000=>00000 [5,6,1,4,2,3]=>[5,1,6,2,4,3]=>00000=>00000 [5,6,1,4,3,2]=>[5,1,6,2,3,4]=>00000=>00000 [5,6,2,1,3,4]=>[5,1,2,6,4,3]=>00000=>00000 [5,6,2,1,4,3]=>[5,1,2,6,3,4]=>00000=>00000 [5,6,2,3,1,4]=>[5,2,6,4,1,3]=>00000=>00000 [5,6,2,3,4,1]=>[5,2,6,3,1,4]=>00000=>00000 [5,6,2,4,1,3]=>[5,2,6,1,4,3]=>00000=>00000 [5,6,2,4,3,1]=>[5,2,6,1,3,4]=>00000=>00000 [5,6,3,1,2,4]=>[5,1,3,6,4,2]=>00000=>00000 [5,6,3,1,4,2]=>[5,1,3,6,2,4]=>00000=>00000 [5,6,3,2,1,4]=>[5,1,2,3,6,4]=>00000=>00000 [5,6,3,2,4,1]=>[5,2,3,6,1,4]=>00000=>00000 [5,6,3,4,1,2]=>[5,3,6,1,4,2]=>00000=>00000 [5,6,3,4,2,1]=>[5,3,6,1,2,4]=>00000=>00000 [5,6,4,1,2,3]=>[5,1,4,6,3,2]=>00000=>00000 [5,6,4,1,3,2]=>[5,1,4,6,2,3]=>00000=>00000 [5,6,4,2,1,3]=>[5,1,2,4,6,3]=>00000=>00000 [5,6,4,2,3,1]=>[5,2,4,6,1,3]=>00000=>00000 [5,6,4,3,1,2]=>[5,1,3,4,6,2]=>00000=>00000 [5,6,4,3,2,1]=>[5,1,2,3,4,6]=>00001=>10000 [6,1,2,3,4,5]=>[1,6,5,4,3,2]=>10000=>00001 [6,1,2,3,5,4]=>[1,6,4,5,3,2]=>10000=>00001 [6,1,2,4,3,5]=>[1,6,5,3,4,2]=>10000=>00001 [6,1,2,4,5,3]=>[1,6,4,3,5,2]=>10000=>00001 [6,1,2,5,3,4]=>[1,6,3,5,4,2]=>10000=>00001 [6,1,2,5,4,3]=>[1,6,3,4,5,2]=>10000=>00001 [6,1,3,2,4,5]=>[1,6,5,4,2,3]=>10000=>00001 [6,1,3,2,5,4]=>[1,6,4,5,2,3]=>10000=>00001 [6,1,3,4,2,5]=>[1,6,5,3,2,4]=>10000=>00001 [6,1,3,4,5,2]=>[1,6,4,3,2,5]=>10000=>00001 [6,1,3,5,2,4]=>[1,6,3,2,5,4]=>10000=>00001 [6,1,3,5,4,2]=>[1,6,3,2,4,5]=>10000=>00001 [6,1,4,2,3,5]=>[1,6,5,2,4,3]=>10000=>00001 [6,1,4,2,5,3]=>[1,6,2,4,3,5]=>10000=>00001 [6,1,4,3,2,5]=>[1,6,5,2,3,4]=>10000=>00001 [6,1,4,3,5,2]=>[1,6,3,4,2,5]=>10000=>00001 [6,1,4,5,2,3]=>[1,6,4,2,5,3]=>10000=>00001 [6,1,4,5,3,2]=>[1,6,4,2,3,5]=>10000=>00001 [6,1,5,2,3,4]=>[1,6,2,5,4,3]=>10000=>00001 [6,1,5,2,4,3]=>[1,6,2,5,3,4]=>10000=>00001 [6,1,5,3,2,4]=>[1,6,2,3,5,4]=>10000=>00001 [6,1,5,3,4,2]=>[1,6,3,5,2,4]=>10000=>00001 [6,1,5,4,2,3]=>[1,6,2,4,5,3]=>10000=>00001 [6,1,5,4,3,2]=>[1,6,2,3,4,5]=>10000=>00001 [6,2,1,3,4,5]=>[1,2,6,5,4,3]=>11000=>00011 [6,2,1,3,5,4]=>[1,2,6,4,5,3]=>11000=>00011 [6,2,1,4,3,5]=>[1,2,6,5,3,4]=>11000=>00011 [6,2,1,4,5,3]=>[1,2,6,4,3,5]=>11000=>00011 [6,2,1,5,3,4]=>[1,2,6,3,5,4]=>11000=>00011 [6,2,1,5,4,3]=>[1,2,6,3,4,5]=>11000=>00011 [6,2,3,1,4,5]=>[2,6,5,4,1,3]=>00000=>00000 [6,2,3,1,5,4]=>[2,6,4,5,1,3]=>00000=>00000 [6,2,3,4,1,5]=>[2,6,5,3,1,4]=>00000=>00000 [6,2,3,4,5,1]=>[2,6,4,3,1,5]=>00000=>00000 [6,2,3,5,1,4]=>[2,6,3,1,5,4]=>00000=>00000 [6,2,3,5,4,1]=>[2,6,3,1,4,5]=>00000=>00000 [6,2,4,1,3,5]=>[2,6,5,1,4,3]=>00000=>00000 [6,2,4,1,5,3]=>[2,6,1,4,3,5]=>00000=>00000 [6,2,4,3,1,5]=>[2,6,5,1,3,4]=>00000=>00000 [6,2,4,3,5,1]=>[2,6,3,4,1,5]=>00000=>00000 [6,2,4,5,1,3]=>[2,6,4,1,5,3]=>00000=>00000 [6,2,4,5,3,1]=>[2,6,4,1,3,5]=>00000=>00000 [6,2,5,1,3,4]=>[2,6,1,5,4,3]=>00000=>00000 [6,2,5,1,4,3]=>[2,6,1,5,3,4]=>00000=>00000 [6,2,5,3,1,4]=>[2,6,1,3,5,4]=>00000=>00000 [6,2,5,3,4,1]=>[2,6,3,5,1,4]=>00000=>00000 [6,2,5,4,1,3]=>[2,6,1,4,5,3]=>00000=>00000 [6,2,5,4,3,1]=>[2,6,1,3,4,5]=>00000=>00000 [6,3,1,2,4,5]=>[1,3,6,5,4,2]=>10000=>00001 [6,3,1,2,5,4]=>[1,3,6,4,5,2]=>10000=>00001 [6,3,1,4,2,5]=>[1,3,6,5,2,4]=>10000=>00001 [6,3,1,4,5,2]=>[1,3,6,4,2,5]=>10000=>00001 [6,3,1,5,2,4]=>[1,3,6,2,5,4]=>10000=>00001 [6,3,1,5,4,2]=>[1,3,6,2,4,5]=>10000=>00001 [6,3,2,1,4,5]=>[1,2,3,6,5,4]=>11100=>00111 [6,3,2,1,5,4]=>[1,2,3,6,4,5]=>11100=>00111 [6,3,2,4,1,5]=>[2,3,6,5,1,4]=>00000=>00000 [6,3,2,4,5,1]=>[2,3,6,4,1,5]=>00000=>00000 [6,3,2,5,1,4]=>[2,3,6,1,5,4]=>00000=>00000 [6,3,2,5,4,1]=>[2,3,6,1,4,5]=>00000=>00000 [6,3,4,1,2,5]=>[3,6,5,1,4,2]=>00000=>00000 [6,3,4,1,5,2]=>[3,6,1,4,2,5]=>00000=>00000 [6,3,4,2,1,5]=>[3,6,5,1,2,4]=>00000=>00000 [6,3,4,2,5,1]=>[3,6,2,4,1,5]=>00000=>00000 [6,3,4,5,1,2]=>[3,6,4,1,5,2]=>00000=>00000 [6,3,4,5,2,1]=>[3,6,4,1,2,5]=>00000=>00000 [6,3,5,1,2,4]=>[3,6,1,5,4,2]=>00000=>00000 [6,3,5,1,4,2]=>[3,6,1,5,2,4]=>00000=>00000 [6,3,5,2,1,4]=>[3,6,1,2,5,4]=>00000=>00000 [6,3,5,2,4,1]=>[3,6,2,5,1,4]=>00000=>00000 [6,3,5,4,1,2]=>[3,6,1,4,5,2]=>00000=>00000 [6,3,5,4,2,1]=>[3,6,1,2,4,5]=>00000=>00000 [6,4,1,2,3,5]=>[1,4,6,5,3,2]=>10000=>00001 [6,4,1,2,5,3]=>[1,4,6,3,5,2]=>10000=>00001 [6,4,1,3,2,5]=>[1,4,6,5,2,3]=>10000=>00001 [6,4,1,3,5,2]=>[1,4,6,3,2,5]=>10000=>00001 [6,4,1,5,2,3]=>[1,4,6,2,5,3]=>10000=>00001 [6,4,1,5,3,2]=>[1,4,6,2,3,5]=>10000=>00001 [6,4,2,1,3,5]=>[1,2,4,6,5,3]=>11000=>00011 [6,4,2,1,5,3]=>[1,2,4,6,3,5]=>11000=>00011 [6,4,2,3,1,5]=>[2,4,6,5,1,3]=>00000=>00000 [6,4,2,3,5,1]=>[2,4,6,3,1,5]=>00000=>00000 [6,4,2,5,1,3]=>[2,4,6,1,5,3]=>00000=>00000 [6,4,2,5,3,1]=>[2,4,6,1,3,5]=>00000=>00000 [6,4,3,1,2,5]=>[1,3,4,6,5,2]=>10000=>00001 [6,4,3,1,5,2]=>[1,3,4,6,2,5]=>10000=>00001 [6,4,3,2,1,5]=>[1,2,3,4,6,5]=>11110=>01111 [6,4,3,2,5,1]=>[2,3,4,6,1,5]=>00000=>00000 [6,4,3,5,1,2]=>[3,4,6,1,5,2]=>00000=>00000 [6,4,3,5,2,1]=>[3,4,6,1,2,5]=>00000=>00000 [6,4,5,1,2,3]=>[4,6,1,5,3,2]=>00000=>00000 [6,4,5,1,3,2]=>[4,6,1,5,2,3]=>00000=>00000 [6,4,5,2,1,3]=>[4,6,1,2,5,3]=>00000=>00000 [6,4,5,2,3,1]=>[4,6,2,5,1,3]=>00000=>00000 [6,4,5,3,1,2]=>[4,6,1,3,5,2]=>00000=>00000 [6,4,5,3,2,1]=>[4,6,1,2,3,5]=>00000=>00000 [6,5,1,2,3,4]=>[1,5,6,4,3,2]=>10000=>00001 [6,5,1,2,4,3]=>[1,5,6,3,4,2]=>10000=>00001 [6,5,1,3,2,4]=>[1,5,6,4,2,3]=>10000=>00001 [6,5,1,3,4,2]=>[1,5,6,3,2,4]=>10000=>00001 [6,5,1,4,2,3]=>[1,5,6,2,4,3]=>10000=>00001 [6,5,1,4,3,2]=>[1,5,6,2,3,4]=>10000=>00001 [6,5,2,1,3,4]=>[1,2,5,6,4,3]=>11000=>00011 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[2,5,3,7,4,6,1]=>[3,5,4,7,2,1,6]=>000000=>000000 [2,5,3,7,6,1,4]=>[3,5,2,1,6,7,4]=>000000=>000000 [2,5,3,7,6,4,1]=>[3,5,2,1,4,6,7]=>000011=>110000 [2,5,4,1,3,6,7]=>[7,6,2,1,4,5,3]=>000000=>000000 [2,5,4,1,3,7,6]=>[6,7,2,1,4,5,3]=>000000=>000000 [2,5,4,1,6,3,7]=>[7,2,1,4,5,3,6]=>000000=>000000 [2,5,4,1,6,7,3]=>[6,2,1,4,5,3,7]=>000001=>100000 [2,5,4,1,7,3,6]=>[2,1,4,5,3,7,6]=>010010=>010010 [2,5,4,1,7,6,3]=>[2,1,4,5,3,6,7]=>010011=>110010 [2,5,4,3,1,6,7]=>[7,6,2,1,3,4,5]=>000000=>000000 [2,5,4,3,1,7,6]=>[6,7,2,1,3,4,5]=>000000=>000000 [2,5,4,3,6,1,7]=>[7,3,4,5,2,1,6]=>000000=>000000 [2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>000001=>100000 [2,5,4,3,7,1,6]=>[3,4,5,2,1,7,6]=>000010=>010000 [2,5,4,3,7,6,1]=>[3,4,5,2,1,6,7]=>000011=>110000 [2,5,4,6,1,3,7]=>[7,4,5,2,1,6,3]=>000000=>000000 [2,5,4,6,1,7,3]=>[4,5,2,1,6,3,7]=>000001=>100000 [2,5,4,6,3,1,7]=>[7,4,5,2,1,3,6]=>000000=>000000 [2,5,4,6,3,7,1]=>[4,5,3,6,2,1,7]=>000001=>100000 [2,5,4,6,7,1,3]=>[6,4,5,2,1,7,3]=>000000=>000000 [2,5,4,6,7,3,1]=>[6,4,5,2,1,3,7]=>000001=>100000 [2,5,4,7,1,3,6]=>[4,5,2,1,7,6,3]=>000000=>000000 [2,5,4,7,1,6,3]=>[4,5,2,1,7,3,6]=>000000=>000000 [2,5,4,7,3,1,6]=>[4,5,2,1,3,7,6]=>000010=>010000 [2,5,4,7,3,6,1]=>[4,5,3,7,2,1,6]=>000000=>000000 [2,5,4,7,6,1,3]=>[4,5,2,1,6,7,3]=>000000=>000000 [2,5,4,7,6,3,1]=>[4,5,2,1,3,6,7]=>000011=>110000 [2,5,6,1,3,4,7]=>[7,5,2,1,6,4,3]=>000000=>000000 [2,5,6,1,3,7,4]=>[5,2,1,6,4,7,3]=>000000=>000000 [2,5,6,1,4,3,7]=>[7,5,2,1,6,3,4]=>000000=>000000 [2,5,6,1,4,7,3]=>[5,2,1,6,4,3,7]=>000001=>100000 [2,5,6,1,7,3,4]=>[5,2,1,6,3,7,4]=>000000=>000000 [2,5,6,1,7,4,3]=>[5,2,1,6,3,4,7]=>000001=>100000 [2,5,6,3,1,4,7]=>[7,5,2,1,3,6,4]=>000000=>000000 [2,5,6,3,1,7,4]=>[5,2,1,3,6,4,7]=>000001=>100000 [2,5,6,3,4,1,7]=>[7,5,3,6,2,1,4]=>000000=>000000 [2,5,6,3,4,7,1]=>[5,3,6,4,2,1,7]=>000001=>100000 [2,5,6,3,7,1,4]=>[5,3,6,2,1,7,4]=>000000=>000000 [2,5,6,3,7,4,1]=>[5,3,6,2,1,4,7]=>000001=>100000 [2,5,6,4,1,3,7]=>[7,5,2,1,4,6,3]=>000000=>000000 [2,5,6,4,1,7,3]=>[5,2,1,4,6,3,7]=>000001=>100000 [2,5,6,4,3,1,7]=>[7,5,2,1,3,4,6]=>000000=>000000 [2,5,6,4,3,7,1]=>[5,3,4,6,2,1,7]=>000001=>100000 [2,5,6,4,7,1,3]=>[5,4,6,2,1,7,3]=>000000=>000000 [2,5,6,4,7,3,1]=>[5,4,6,2,1,3,7]=>000001=>100000 [2,5,6,7,1,3,4]=>[6,5,2,1,7,4,3]=>000000=>000000 [2,5,6,7,1,4,3]=>[6,5,2,1,7,3,4]=>000000=>000000 [2,5,6,7,3,1,4]=>[6,5,2,1,3,7,4]=>000000=>000000 [2,5,6,7,3,4,1]=>[6,5,3,7,2,1,4]=>000000=>000000 [2,5,6,7,4,1,3]=>[6,5,2,1,4,7,3]=>000000=>000000 [2,5,6,7,4,3,1]=>[6,5,2,1,3,4,7]=>000001=>100000 [2,5,7,1,3,4,6]=>[5,2,1,7,6,4,3]=>000000=>000000 [2,5,7,1,3,6,4]=>[5,2,1,7,4,6,3]=>000000=>000000 [2,5,7,1,4,3,6]=>[5,2,1,7,6,3,4]=>000000=>000000 [2,5,7,1,4,6,3]=>[5,2,1,7,4,3,6]=>000000=>000000 [2,5,7,1,6,3,4]=>[5,2,1,7,3,6,4]=>000000=>000000 [2,5,7,1,6,4,3]=>[5,2,1,7,3,4,6]=>000000=>000000 [2,5,7,3,1,4,6]=>[5,2,1,3,7,6,4]=>000000=>000000 [2,5,7,3,1,6,4]=>[5,2,1,3,7,4,6]=>000000=>000000 [2,5,7,3,4,1,6]=>[5,3,7,6,2,1,4]=>000000=>000000 [2,5,7,3,4,6,1]=>[5,3,7,4,2,1,6]=>000000=>000000 [2,5,7,3,6,1,4]=>[5,3,7,2,1,6,4]=>000000=>000000 [2,5,7,3,6,4,1]=>[5,3,7,2,1,4,6]=>000000=>000000 [2,5,7,4,1,3,6]=>[5,2,1,4,7,6,3]=>000000=>000000 [2,5,7,4,1,6,3]=>[5,2,1,4,7,3,6]=>000000=>000000 [2,5,7,4,3,1,6]=>[5,2,1,3,4,7,6]=>000010=>010000 [2,5,7,4,3,6,1]=>[5,3,4,7,2,1,6]=>000000=>000000 [2,5,7,4,6,1,3]=>[5,4,7,2,1,6,3]=>000000=>000000 [2,5,7,4,6,3,1]=>[5,4,7,2,1,3,6]=>000000=>000000 [2,5,7,6,1,3,4]=>[5,2,1,6,7,4,3]=>000000=>000000 [2,5,7,6,1,4,3]=>[5,2,1,6,7,3,4]=>000000=>000000 [2,5,7,6,3,1,4]=>[5,2,1,3,6,7,4]=>000000=>000000 [2,5,7,6,3,4,1]=>[5,3,6,7,2,1,4]=>000000=>000000 [2,5,7,6,4,1,3]=>[5,2,1,4,6,7,3]=>000000=>000000 [2,5,7,6,4,3,1]=>[5,2,1,3,4,6,7]=>000011=>110000 [2,6,1,3,4,5,7]=>[7,2,1,6,5,4,3]=>000000=>000000 [2,6,1,3,4,7,5]=>[2,1,6,5,7,4,3]=>010000=>000010 [2,6,1,3,5,4,7]=>[7,2,1,6,4,5,3]=>000000=>000000 [2,6,1,3,5,7,4]=>[2,1,6,5,4,7,3]=>010000=>000010 [2,6,1,3,7,4,5]=>[2,1,6,4,7,5,3]=>010000=>000010 [2,6,1,3,7,5,4]=>[2,1,6,4,5,7,3]=>010000=>000010 [2,6,1,4,3,5,7]=>[7,2,1,6,5,3,4]=>000000=>000000 [2,6,1,4,3,7,5]=>[2,1,6,5,7,3,4]=>010000=>000010 [2,6,1,4,5,3,7]=>[7,2,1,6,4,3,5]=>000000=>000000 [2,6,1,4,5,7,3]=>[2,1,6,5,4,3,7]=>010001=>100010 [2,6,1,4,7,3,5]=>[2,1,6,4,3,7,5]=>010000=>000010 [2,6,1,4,7,5,3]=>[2,1,6,4,3,5,7]=>010001=>100010 [2,6,1,5,3,4,7]=>[7,2,1,6,3,5,4]=>000000=>000000 [2,6,1,5,3,7,4]=>[2,1,6,3,5,4,7]=>010001=>100010 [2,6,1,5,4,3,7]=>[7,2,1,6,3,4,5]=>000000=>000000 [2,6,1,5,4,7,3]=>[2,1,6,4,5,3,7]=>010001=>100010 [2,6,1,5,7,3,4]=>[2,1,6,5,3,7,4]=>010000=>000010 [2,6,1,5,7,4,3]=>[2,1,6,5,3,4,7]=>010001=>100010 [2,6,1,7,3,4,5]=>[2,1,6,3,7,5,4]=>010000=>000010 [2,6,1,7,3,5,4]=>[2,1,6,3,7,4,5]=>010000=>000010 [2,6,1,7,4,3,5]=>[2,1,6,3,4,7,5]=>010000=>000010 [2,6,1,7,4,5,3]=>[2,1,6,4,7,3,5]=>010000=>000010 [2,6,1,7,5,3,4]=>[2,1,6,3,5,7,4]=>010000=>000010 [2,6,1,7,5,4,3]=>[2,1,6,3,4,5,7]=>010001=>100010 [2,6,3,1,4,5,7]=>[7,2,1,3,6,5,4]=>000000=>000000 [2,6,3,1,4,7,5]=>[2,1,3,6,5,7,4]=>011000=>000110 [2,6,3,1,5,4,7]=>[7,2,1,3,6,4,5]=>000000=>000000 [2,6,3,1,5,7,4]=>[2,1,3,6,5,4,7]=>011001=>100110 [2,6,3,1,7,4,5]=>[2,1,3,6,4,7,5]=>011000=>000110 [2,6,3,1,7,5,4]=>[2,1,3,6,4,5,7]=>011001=>100110 [2,6,3,4,1,5,7]=>[7,3,6,5,2,1,4]=>000000=>000000 [2,6,3,4,1,7,5]=>[3,6,5,7,2,1,4]=>000000=>000000 [2,6,3,4,5,1,7]=>[7,3,6,4,2,1,5]=>000000=>000000 [2,6,3,4,5,7,1]=>[3,6,5,4,2,1,7]=>000001=>100000 [2,6,3,4,7,1,5]=>[3,6,4,2,1,7,5]=>000000=>000000 [2,6,3,4,7,5,1]=>[3,6,4,2,1,5,7]=>000001=>100000 [2,6,3,5,1,4,7]=>[7,3,6,2,1,5,4]=>000000=>000000 [2,6,3,5,1,7,4]=>[3,6,2,1,5,4,7]=>000001=>100000 [2,6,3,5,4,1,7]=>[7,3,6,2,1,4,5]=>000000=>000000 [2,6,3,5,4,7,1]=>[3,6,4,5,2,1,7]=>000001=>100000 [2,6,3,5,7,1,4]=>[3,6,5,2,1,7,4]=>000000=>000000 [2,6,3,5,7,4,1]=>[3,6,5,2,1,4,7]=>000001=>100000 [2,6,3,7,1,4,5]=>[3,6,2,1,7,5,4]=>000000=>000000 [2,6,3,7,1,5,4]=>[3,6,2,1,7,4,5]=>000000=>000000 [2,6,3,7,4,1,5]=>[3,6,2,1,4,7,5]=>000000=>000000 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[7,5,2,6,3,4,1]=>[2,5,7,3,6,1,4]=>000000=>000000 [7,5,2,6,4,1,3]=>[2,5,7,1,4,6,3]=>000000=>000000 [7,5,2,6,4,3,1]=>[2,5,7,1,3,4,6]=>000000=>000000 [7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>100000=>000001 [7,5,3,1,2,6,4]=>[1,3,5,7,4,6,2]=>100000=>000001 [7,5,3,1,4,2,6]=>[1,3,5,7,6,2,4]=>100000=>000001 [7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>100000=>000001 [7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>100000=>000001 [7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>100000=>000001 [7,5,3,2,1,4,6]=>[1,2,3,5,7,6,4]=>111000=>000111 [7,5,3,2,1,6,4]=>[1,2,3,5,7,4,6]=>111000=>000111 [7,5,3,2,4,1,6]=>[2,3,5,7,6,1,4]=>000000=>000000 [7,5,3,2,4,6,1]=>[2,3,5,7,4,1,6]=>000000=>000000 [7,5,3,2,6,1,4]=>[2,3,5,7,1,6,4]=>000000=>000000 [7,5,3,2,6,4,1]=>[2,3,5,7,1,4,6]=>000000=>000000 [7,5,3,4,1,2,6]=>[3,5,7,6,1,4,2]=>000000=>000000 [7,5,3,4,1,6,2]=>[3,5,7,1,4,2,6]=>000000=>000000 [7,5,3,4,2,1,6]=>[3,5,7,6,1,2,4]=>000000=>000000 [7,5,3,4,2,6,1]=>[3,5,7,2,4,1,6]=>000000=>000000 [7,5,3,4,6,1,2]=>[3,5,7,4,1,6,2]=>000000=>000000 [7,5,3,4,6,2,1]=>[3,5,7,4,1,2,6]=>000000=>000000 [7,5,3,6,1,2,4]=>[3,5,7,1,6,4,2]=>000000=>000000 [7,5,3,6,1,4,2]=>[3,5,7,1,6,2,4]=>000000=>000000 [7,5,3,6,2,1,4]=>[3,5,7,1,2,6,4]=>000000=>000000 [7,5,3,6,2,4,1]=>[3,5,7,2,6,1,4]=>000000=>000000 [7,5,3,6,4,1,2]=>[3,5,7,1,4,6,2]=>000000=>000000 [7,5,3,6,4,2,1]=>[3,5,7,1,2,4,6]=>000000=>000000 [7,5,4,1,2,3,6]=>[1,4,5,7,6,3,2]=>100000=>000001 [7,5,4,1,2,6,3]=>[1,4,5,7,3,6,2]=>100000=>000001 [7,5,4,1,3,2,6]=>[1,4,5,7,6,2,3]=>100000=>000001 [7,5,4,1,3,6,2]=>[1,4,5,7,3,2,6]=>100000=>000001 [7,5,4,1,6,2,3]=>[1,4,5,7,2,6,3]=>100000=>000001 [7,5,4,1,6,3,2]=>[1,4,5,7,2,3,6]=>100000=>000001 [7,5,4,2,1,3,6]=>[1,2,4,5,7,6,3]=>110000=>000011 [7,5,4,2,1,6,3]=>[1,2,4,5,7,3,6]=>110000=>000011 [7,5,4,2,3,1,6]=>[2,4,5,7,6,1,3]=>000000=>000000 [7,5,4,2,3,6,1]=>[2,4,5,7,3,1,6]=>000000=>000000 [7,5,4,2,6,1,3]=>[2,4,5,7,1,6,3]=>000000=>000000 [7,5,4,2,6,3,1]=>[2,4,5,7,1,3,6]=>000000=>000000 [7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>100000=>000001 [7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>100000=>000001 [7,5,4,3,2,1,6]=>[1,2,3,4,5,7,6]=>111110=>011111 [7,5,4,3,2,6,1]=>[2,3,4,5,7,1,6]=>000000=>000000 [7,5,4,3,6,1,2]=>[3,4,5,7,1,6,2]=>000000=>000000 [7,5,4,3,6,2,1]=>[3,4,5,7,1,2,6]=>000000=>000000 [7,5,4,6,1,2,3]=>[4,5,7,1,6,3,2]=>000000=>000000 [7,5,4,6,1,3,2]=>[4,5,7,1,6,2,3]=>000000=>000000 [7,5,4,6,2,1,3]=>[4,5,7,1,2,6,3]=>000000=>000000 [7,5,4,6,2,3,1]=>[4,5,7,2,6,1,3]=>000000=>000000 [7,5,4,6,3,1,2]=>[4,5,7,1,3,6,2]=>000000=>000000 [7,5,4,6,3,2,1]=>[4,5,7,1,2,3,6]=>000000=>000000 [7,5,6,1,2,3,4]=>[5,7,1,6,4,3,2]=>000000=>000000 [7,5,6,1,2,4,3]=>[5,7,1,6,3,4,2]=>000000=>000000 [7,5,6,1,3,2,4]=>[5,7,1,6,4,2,3]=>000000=>000000 [7,5,6,1,3,4,2]=>[5,7,1,6,3,2,4]=>000000=>000000 [7,5,6,1,4,2,3]=>[5,7,1,6,2,4,3]=>000000=>000000 [7,5,6,1,4,3,2]=>[5,7,1,6,2,3,4]=>000000=>000000 [7,5,6,2,1,3,4]=>[5,7,1,2,6,4,3]=>000000=>000000 [7,5,6,2,1,4,3]=>[5,7,1,2,6,3,4]=>000000=>000000 [7,5,6,2,3,1,4]=>[5,7,2,6,4,1,3]=>000000=>000000 [7,5,6,2,3,4,1]=>[5,7,2,6,3,1,4]=>000000=>000000 [7,5,6,2,4,1,3]=>[5,7,2,6,1,4,3]=>000000=>000000 [7,5,6,2,4,3,1]=>[5,7,2,6,1,3,4]=>000000=>000000 [7,5,6,3,1,2,4]=>[5,7,1,3,6,4,2]=>000000=>000000 [7,5,6,3,1,4,2]=>[5,7,1,3,6,2,4]=>000000=>000000 [7,5,6,3,2,1,4]=>[5,7,1,2,3,6,4]=>000000=>000000 [7,5,6,3,2,4,1]=>[5,7,2,3,6,1,4]=>000000=>000000 [7,5,6,3,4,1,2]=>[5,7,3,6,1,4,2]=>000000=>000000 [7,5,6,3,4,2,1]=>[5,7,3,6,1,2,4]=>000000=>000000 [7,5,6,4,1,2,3]=>[5,7,1,4,6,3,2]=>000000=>000000 [7,5,6,4,1,3,2]=>[5,7,1,4,6,2,3]=>000000=>000000 [7,5,6,4,2,1,3]=>[5,7,1,2,4,6,3]=>000000=>000000 [7,5,6,4,2,3,1]=>[5,7,2,4,6,1,3]=>000000=>000000 [7,5,6,4,3,1,2]=>[5,7,1,3,4,6,2]=>000000=>000000 [7,5,6,4,3,2,1]=>[5,7,1,2,3,4,6]=>000000=>000000 [7,6,1,2,3,4,5]=>[1,6,7,5,4,3,2]=>100000=>000001 [7,6,1,2,3,5,4]=>[1,6,7,4,5,3,2]=>100000=>000001 [7,6,1,2,4,3,5]=>[1,6,7,5,3,4,2]=>100000=>000001 [7,6,1,2,4,5,3]=>[1,6,7,4,3,5,2]=>100000=>000001 [7,6,1,2,5,3,4]=>[1,6,7,3,5,4,2]=>100000=>000001 [7,6,1,2,5,4,3]=>[1,6,7,3,4,5,2]=>100000=>000001 [7,6,1,3,2,4,5]=>[1,6,7,5,4,2,3]=>100000=>000001 [7,6,1,3,2,5,4]=>[1,6,7,4,5,2,3]=>100000=>000001 [7,6,1,3,4,2,5]=>[1,6,7,5,3,2,4]=>100000=>000001 [7,6,1,3,4,5,2]=>[1,6,7,4,3,2,5]=>100000=>000001 [7,6,1,3,5,2,4]=>[1,6,7,3,2,5,4]=>100000=>000001 [7,6,1,3,5,4,2]=>[1,6,7,3,2,4,5]=>100000=>000001 [7,6,1,4,2,3,5]=>[1,6,7,5,2,4,3]=>100000=>000001 [7,6,1,4,2,5,3]=>[1,6,7,2,4,3,5]=>100000=>000001 [7,6,1,4,3,2,5]=>[1,6,7,5,2,3,4]=>100000=>000001 [7,6,1,4,3,5,2]=>[1,6,7,3,4,2,5]=>100000=>000001 [7,6,1,4,5,2,3]=>[1,6,7,4,2,5,3]=>100000=>000001 [7,6,1,4,5,3,2]=>[1,6,7,4,2,3,5]=>100000=>000001 [7,6,1,5,2,3,4]=>[1,6,7,2,5,4,3]=>100000=>000001 [7,6,1,5,2,4,3]=>[1,6,7,2,5,3,4]=>100000=>000001 [7,6,1,5,3,2,4]=>[1,6,7,2,3,5,4]=>100000=>000001 [7,6,1,5,3,4,2]=>[1,6,7,3,5,2,4]=>100000=>000001 [7,6,1,5,4,2,3]=>[1,6,7,2,4,5,3]=>100000=>000001 [7,6,1,5,4,3,2]=>[1,6,7,2,3,4,5]=>100000=>000001 [7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>110000=>000011 [7,6,2,1,3,5,4]=>[1,2,6,7,4,5,3]=>110000=>000011 [7,6,2,1,4,3,5]=>[1,2,6,7,5,3,4]=>110000=>000011 [7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>110000=>000011 [7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>110000=>000011 [7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>110000=>000011 [7,6,2,3,1,4,5]=>[2,6,7,5,4,1,3]=>000000=>000000 [7,6,2,3,1,5,4]=>[2,6,7,4,5,1,3]=>000000=>000000 [7,6,2,3,4,1,5]=>[2,6,7,5,3,1,4]=>000000=>000000 [7,6,2,3,4,5,1]=>[2,6,7,4,3,1,5]=>000000=>000000 [7,6,2,3,5,1,4]=>[2,6,7,3,1,5,4]=>000000=>000000 [7,6,2,3,5,4,1]=>[2,6,7,3,1,4,5]=>000000=>000000 [7,6,2,4,1,3,5]=>[2,6,7,5,1,4,3]=>000000=>000000 [7,6,2,4,1,5,3]=>[2,6,7,1,4,3,5]=>000000=>000000 [7,6,2,4,3,1,5]=>[2,6,7,5,1,3,4]=>000000=>000000 [7,6,2,4,3,5,1]=>[2,6,7,3,4,1,5]=>000000=>000000 [7,6,2,4,5,1,3]=>[2,6,7,4,1,5,3]=>000000=>000000 [7,6,2,4,5,3,1]=>[2,6,7,4,1,3,5]=>000000=>000000 [7,6,2,5,1,3,4]=>[2,6,7,1,5,4,3]=>000000=>000000 [7,6,2,5,1,4,3]=>[2,6,7,1,5,3,4]=>000000=>000000 [7,6,2,5,3,1,4]=>[2,6,7,1,3,5,4]=>000000=>000000 [7,6,2,5,3,4,1]=>[2,6,7,3,5,1,4]=>000000=>000000 [7,6,2,5,4,1,3]=>[2,6,7,1,4,5,3]=>000000=>000000 [7,6,2,5,4,3,1]=>[2,6,7,1,3,4,5]=>000000=>000000 [7,6,3,1,2,4,5]=>[1,3,6,7,5,4,2]=>100000=>000001 [7,6,3,1,2,5,4]=>[1,3,6,7,4,5,2]=>100000=>000001 [7,6,3,1,4,2,5]=>[1,3,6,7,5,2,4]=>100000=>000001 [7,6,3,1,4,5,2]=>[1,3,6,7,4,2,5]=>100000=>000001 [7,6,3,1,5,2,4]=>[1,3,6,7,2,5,4]=>100000=>000001 [7,6,3,1,5,4,2]=>[1,3,6,7,2,4,5]=>100000=>000001 [7,6,3,2,1,4,5]=>[1,2,3,6,7,5,4]=>111000=>000111 [7,6,3,2,1,5,4]=>[1,2,3,6,7,4,5]=>111000=>000111 [7,6,3,2,4,1,5]=>[2,3,6,7,5,1,4]=>000000=>000000 [7,6,3,2,4,5,1]=>[2,3,6,7,4,1,5]=>000000=>000000 [7,6,3,2,5,1,4]=>[2,3,6,7,1,5,4]=>000000=>000000 [7,6,3,2,5,4,1]=>[2,3,6,7,1,4,5]=>000000=>000000 [7,6,3,4,1,2,5]=>[3,6,7,5,1,4,2]=>000000=>000000 [7,6,3,4,1,5,2]=>[3,6,7,1,4,2,5]=>000000=>000000 [7,6,3,4,2,1,5]=>[3,6,7,5,1,2,4]=>000000=>000000 [7,6,3,4,2,5,1]=>[3,6,7,2,4,1,5]=>000000=>000000 [7,6,3,4,5,1,2]=>[3,6,7,4,1,5,2]=>000000=>000000 [7,6,3,4,5,2,1]=>[3,6,7,4,1,2,5]=>000000=>000000 [7,6,3,5,1,2,4]=>[3,6,7,1,5,4,2]=>000000=>000000 [7,6,3,5,1,4,2]=>[3,6,7,1,5,2,4]=>000000=>000000 [7,6,3,5,2,1,4]=>[3,6,7,1,2,5,4]=>000000=>000000 [7,6,3,5,2,4,1]=>[3,6,7,2,5,1,4]=>000000=>000000 [7,6,3,5,4,1,2]=>[3,6,7,1,4,5,2]=>000000=>000000 [7,6,3,5,4,2,1]=>[3,6,7,1,2,4,5]=>000000=>000000 [7,6,4,1,2,3,5]=>[1,4,6,7,5,3,2]=>100000=>000001 [7,6,4,1,2,5,3]=>[1,4,6,7,3,5,2]=>100000=>000001 [7,6,4,1,3,2,5]=>[1,4,6,7,5,2,3]=>100000=>000001 [7,6,4,1,3,5,2]=>[1,4,6,7,3,2,5]=>100000=>000001 [7,6,4,1,5,2,3]=>[1,4,6,7,2,5,3]=>100000=>000001 [7,6,4,1,5,3,2]=>[1,4,6,7,2,3,5]=>100000=>000001 [7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>110000=>000011 [7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>110000=>000011 [7,6,4,2,3,1,5]=>[2,4,6,7,5,1,3]=>000000=>000000 [7,6,4,2,3,5,1]=>[2,4,6,7,3,1,5]=>000000=>000000 [7,6,4,2,5,1,3]=>[2,4,6,7,1,5,3]=>000000=>000000 [7,6,4,2,5,3,1]=>[2,4,6,7,1,3,5]=>000000=>000000 [7,6,4,3,1,2,5]=>[1,3,4,6,7,5,2]=>100000=>000001 [7,6,4,3,1,5,2]=>[1,3,4,6,7,2,5]=>100000=>000001 [7,6,4,3,2,1,5]=>[1,2,3,4,6,7,5]=>111100=>001111 [7,6,4,3,2,5,1]=>[2,3,4,6,7,1,5]=>000000=>000000 [7,6,4,3,5,1,2]=>[3,4,6,7,1,5,2]=>000000=>000000 [7,6,4,3,5,2,1]=>[3,4,6,7,1,2,5]=>000000=>000000 [7,6,4,5,1,2,3]=>[4,6,7,1,5,3,2]=>000000=>000000 [7,6,4,5,1,3,2]=>[4,6,7,1,5,2,3]=>000000=>000000 [7,6,4,5,2,1,3]=>[4,6,7,1,2,5,3]=>000000=>000000 [7,6,4,5,2,3,1]=>[4,6,7,2,5,1,3]=>000000=>000000 [7,6,4,5,3,1,2]=>[4,6,7,1,3,5,2]=>000000=>000000 [7,6,4,5,3,2,1]=>[4,6,7,1,2,3,5]=>000000=>000000 [7,6,5,1,2,3,4]=>[1,5,6,7,4,3,2]=>100000=>000001 [7,6,5,1,2,4,3]=>[1,5,6,7,3,4,2]=>100000=>000001 [7,6,5,1,3,2,4]=>[1,5,6,7,4,2,3]=>100000=>000001 [7,6,5,1,3,4,2]=>[1,5,6,7,3,2,4]=>100000=>000001 [7,6,5,1,4,2,3]=>[1,5,6,7,2,4,3]=>100000=>000001 [7,6,5,1,4,3,2]=>[1,5,6,7,2,3,4]=>100000=>000001 [7,6,5,2,1,3,4]=>[1,2,5,6,7,4,3]=>110000=>000011 [7,6,5,2,1,4,3]=>[1,2,5,6,7,3,4]=>110000=>000011 [7,6,5,2,3,1,4]=>[2,5,6,7,4,1,3]=>000000=>000000 [7,6,5,2,3,4,1]=>[2,5,6,7,3,1,4]=>000000=>000000 [7,6,5,2,4,1,3]=>[2,5,6,7,1,4,3]=>000000=>000000 [7,6,5,2,4,3,1]=>[2,5,6,7,1,3,4]=>000000=>000000 [7,6,5,3,1,2,4]=>[1,3,5,6,7,4,2]=>100000=>000001 [7,6,5,3,1,4,2]=>[1,3,5,6,7,2,4]=>100000=>000001 [7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>111000=>000111 [7,6,5,3,2,4,1]=>[2,3,5,6,7,1,4]=>000000=>000000 [7,6,5,3,4,1,2]=>[3,5,6,7,1,4,2]=>000000=>000000 [7,6,5,3,4,2,1]=>[3,5,6,7,1,2,4]=>000000=>000000 [7,6,5,4,1,2,3]=>[1,4,5,6,7,3,2]=>100000=>000001 [7,6,5,4,1,3,2]=>[1,4,5,6,7,2,3]=>100000=>000001 [7,6,5,4,2,1,3]=>[1,2,4,5,6,7,3]=>110000=>000011 [7,6,5,4,2,3,1]=>[2,4,5,6,7,1,3]=>000000=>000000 [7,6,5,4,3,1,2]=>[1,3,4,5,6,7,2]=>100000=>000001 [7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>111111=>111111
Map
weak order rowmotion
Description
Return the reversal of the permutation obtained by inverting the corresponding Laguerre heap.
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
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.