Identifier
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[2,1]=>[2,1]=>1 [1,0,1,0]=>[3,1,2]=>[3,1,2]=>01 [1,1,0,0]=>[2,3,1]=>[3,2,1]=>11 [1,0,1,0,1,0]=>[4,1,2,3]=>[4,1,2,3]=>001 [1,0,1,1,0,0]=>[3,1,4,2]=>[4,3,1,2]=>011 [1,1,0,0,1,0]=>[2,4,1,3]=>[4,2,1,3]=>101 [1,1,0,1,0,0]=>[4,3,1,2]=>[3,1,4,2]=>011 [1,1,1,0,0,0]=>[2,3,4,1]=>[4,3,2,1]=>111 [1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>0001 [1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[5,4,1,2,3]=>0011 [1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[5,3,1,2,4]=>0101 [1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>[4,1,2,5,3]=>0011 [1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[5,4,3,1,2]=>0111 [1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[5,2,1,3,4]=>1001 [1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[5,4,2,1,3]=>1011 [1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,1,5,2,4]=>0101 [1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>[4,1,5,2,3]=>0011 [1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>[3,1,5,4,2]=>0111 [1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[5,3,2,1,4]=>1101 [1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>[4,2,1,5,3]=>1011 [1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>[4,3,1,5,2]=>0111 [1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,4,3,2,1]=>1111 [1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>00001 [1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[6,5,1,2,3,4]=>00011 [1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[6,4,1,2,3,5]=>00101 [1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>[5,1,2,3,6,4]=>00011 [1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[6,5,4,1,2,3]=>00111 [1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[6,3,1,2,4,5]=>01001 [1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6,5,3,1,2,4]=>01011 [1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>[4,1,2,6,3,5]=>00101 [1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>[5,1,2,6,3,4]=>00011 [1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>[4,1,2,6,5,3]=>00111 [1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[6,4,3,1,2,5]=>01101 [1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>[5,3,1,2,6,4]=>01011 [1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>[5,4,1,2,6,3]=>00111 [1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[6,5,4,3,1,2]=>01111 [1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>10001 [1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[6,5,2,1,3,4]=>10011 [1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[6,4,2,1,3,5]=>10101 [1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>[5,2,1,3,6,4]=>10011 [1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6,5,4,2,1,3]=>10111 [1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>01001 [1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>[3,1,6,5,2,4]=>01011 [1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[4,1,6,2,3,5]=>00101 [1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>[6,1,5,2,3,4]=>00011 [1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>[4,1,6,5,2,3]=>00111 [1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>[3,1,6,4,2,5]=>01101 [1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>[3,1,5,2,6,4]=>01011 [1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>[5,4,1,6,2,3]=>00111 [1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>[3,1,6,5,4,2]=>01111 [1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[6,3,2,1,4,5]=>11001 [1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[6,5,3,2,1,4]=>11011 [1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>[4,2,1,6,3,5]=>10101 [1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>[5,2,1,6,3,4]=>10011 [1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>[4,2,1,6,5,3]=>10111 [1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,3,1,6,2,5]=>01101 [1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>[5,3,1,6,2,4]=>01011 [1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>[4,1,5,2,6,3]=>00111 [1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>[4,3,1,6,5,2]=>01111 [1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[6,4,3,2,1,5]=>11101 [1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>[5,3,2,1,6,4]=>11011 [1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>[5,4,2,1,6,3]=>10111 [1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>[5,4,3,1,6,2]=>01111 [1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,5,4,3,2,1]=>11111 [1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>000001 [1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[7,6,1,2,3,4,5]=>000011 [1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[7,5,1,2,3,4,6]=>000101 [1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>[6,1,2,3,4,7,5]=>000011 [1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[7,6,5,1,2,3,4]=>000111 [1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[7,4,1,2,3,5,6]=>001001 [1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7,6,4,1,2,3,5]=>001011 [1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>[5,1,2,3,7,4,6]=>000101 [1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>[6,1,2,3,7,4,5]=>000011 [1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>[5,1,2,3,7,6,4]=>000111 [1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[7,5,4,1,2,3,6]=>001101 [1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>[6,4,1,2,3,7,5]=>001011 [1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>[6,5,1,2,3,7,4]=>000111 [1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[7,6,5,4,1,2,3]=>001111 [1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[7,3,1,2,4,5,6]=>010001 [1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[7,6,3,1,2,4,5]=>010011 [1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7,5,3,1,2,4,6]=>010101 [1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>[6,3,1,2,4,7,5]=>010011 [1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7,6,5,3,1,2,4]=>010111 [1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>[4,1,2,7,3,5,6]=>001001 [1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>[4,1,2,7,6,3,5]=>001011 [1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>[5,1,2,7,3,4,6]=>000101 [1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>[7,1,2,6,3,4,5]=>000011 [1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>[5,1,2,7,6,3,4]=>000111 [1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>[4,1,2,7,5,3,6]=>001101 [1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>[4,1,2,6,3,7,5]=>001011 [1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>[6,5,1,2,7,3,4]=>000111 [1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>[4,1,2,7,6,5,3]=>001111 [1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[7,4,3,1,2,5,6]=>011001 [1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7,6,4,3,1,2,5]=>011011 [1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>[5,3,1,2,7,4,6]=>010101 [1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>[6,3,1,2,7,4,5]=>010011 [1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>[5,3,1,2,7,6,4]=>010111 [1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>[5,4,1,2,7,3,6]=>001101 [1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>[6,4,1,2,7,3,5]=>001011 [1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>[5,1,2,6,3,7,4]=>000111 [1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>[5,4,1,2,7,6,3]=>001111 [1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7,5,4,3,1,2,6]=>011101 [1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>[6,4,3,1,2,7,5]=>011011 [1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>[6,5,3,1,2,7,4]=>010111 [1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>[6,5,4,1,2,7,3]=>001111 [1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7,6,5,4,3,1,2]=>011111 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>100001 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[7,6,2,1,3,4,5]=>100011 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[7,5,2,1,3,4,6]=>100101 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>[6,2,1,3,4,7,5]=>100011 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[7,6,5,2,1,3,4]=>100111 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[7,4,2,1,3,5,6]=>101001 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7,6,4,2,1,3,5]=>101011 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>[5,2,1,3,7,4,6]=>100101 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>[6,2,1,3,7,4,5]=>100011 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>[5,2,1,3,7,6,4]=>100111 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7,5,4,2,1,3,6]=>101101 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>[6,4,2,1,3,7,5]=>101011 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>[6,5,2,1,3,7,4]=>100111 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7,6,5,4,2,1,3]=>101111 [1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>010001 [1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>[3,1,7,6,2,4,5]=>010011 [1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>[3,1,7,5,2,4,6]=>010101 [1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>[3,1,6,2,4,7,5]=>010011 [1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>[3,1,7,6,5,2,4]=>010111 [1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>[4,1,7,2,3,5,6]=>001001 [1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>[4,1,7,6,2,3,5]=>001011 [1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>[7,1,5,2,3,4,6]=>000101 [1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>[6,1,7,2,3,4,5]=>000011 [1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>[7,6,1,5,2,3,4]=>000111 [1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>[4,1,7,5,2,3,6]=>001101 [1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>[4,1,6,2,3,7,5]=>001011 [1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>[6,1,7,5,2,3,4]=>000111 [1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>[4,1,7,6,5,2,3]=>001111 [1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>[3,1,7,4,2,5,6]=>011001 [1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>[3,1,7,6,4,2,5]=>011011 [1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>[3,1,5,2,7,4,6]=>010101 [1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>[3,1,6,2,7,4,5]=>010011 [1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>[3,1,5,2,7,6,4]=>010111 [1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>[5,4,1,7,2,3,6]=>001101 [1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>[6,4,1,7,2,3,5]=>001011 [1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>[5,1,7,2,3,6,4]=>000111 [1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>[5,4,1,7,6,2,3]=>001111 [1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>[3,1,7,5,4,2,6]=>011101 [1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>[3,1,6,4,2,7,5]=>011011 [1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>[3,1,6,5,2,7,4]=>010111 [1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>[6,5,4,1,7,2,3]=>001111 [1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>[3,1,7,6,5,4,2]=>011111 [1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>110001 [1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[7,6,3,2,1,4,5]=>110011 [1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[7,5,3,2,1,4,6]=>110101 [1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>[6,3,2,1,4,7,5]=>110011 [1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7,6,5,3,2,1,4]=>110111 [1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>[4,2,1,7,3,5,6]=>101001 [1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>[4,2,1,7,6,3,5]=>101011 [1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>[5,2,1,7,3,4,6]=>100101 [1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>[7,2,1,6,3,4,5]=>100011 [1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>[5,2,1,7,6,3,4]=>100111 [1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>[4,2,1,7,5,3,6]=>101101 [1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>[4,2,1,6,3,7,5]=>101011 [1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>[6,5,2,1,7,3,4]=>100111 [1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>[4,2,1,7,6,5,3]=>101111 [1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>[4,3,1,7,2,5,6]=>011001 [1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>[4,3,1,7,6,2,5]=>011011 [1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>[5,3,1,7,2,4,6]=>010101 [1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>[7,3,1,6,2,4,5]=>010011 [1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>[5,3,1,7,6,2,4]=>010111 [1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,1,5,2,7,3,6]=>001101 [1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>[4,1,7,2,6,3,5]=>001011 [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>[5,1,7,2,6,3,4]=>000111 [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>[4,1,5,2,7,6,3]=>001111 [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>[4,3,1,7,5,2,6]=>011101 [1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>[4,3,1,6,2,7,5]=>011011 [1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>[6,5,3,1,7,2,4]=>010111 [1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>[4,1,6,5,2,7,3]=>001111 [1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>[4,3,1,7,6,5,2]=>011111 [1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[7,4,3,2,1,5,6]=>111001 [1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7,6,4,3,2,1,5]=>111011 [1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>[5,3,2,1,7,4,6]=>110101 [1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>[6,3,2,1,7,4,5]=>110011 [1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>[5,3,2,1,7,6,4]=>110111 [1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>[5,4,2,1,7,3,6]=>101101 [1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>[6,4,2,1,7,3,5]=>101011 [1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>[5,2,1,6,3,7,4]=>100111 [1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>[5,4,2,1,7,6,3]=>101111 [1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[5,4,3,1,7,2,6]=>011101 [1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>[6,4,3,1,7,2,5]=>011011 [1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>[5,3,1,6,2,7,4]=>010111 [1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>[5,4,1,6,2,7,3]=>001111 [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>[5,4,3,1,7,6,2]=>011111 [1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[7,5,4,3,2,1,6]=>111101 [1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>[6,4,3,2,1,7,5]=>111011 [1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>[6,5,3,2,1,7,4]=>110111 [1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>[6,5,4,2,1,7,3]=>101111 [1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>[6,5,4,3,1,7,2]=>011111 [1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,6,5,4,3,2,1]=>111111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0000001 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]=>[8,7,1,2,3,4,5,6]=>0000011 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[8,6,1,2,3,4,5,7]=>0000101 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,1,2,3,4,7,5,6]=>[7,1,2,3,4,5,8,6]=>0000011 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[8,7,6,1,2,3,4,5]=>0000111 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,8,4,6,7]=>[8,5,1,2,3,4,6,7]=>0001001 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[8,7,5,1,2,3,4,6]=>0001011 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,1,2,3,6,4,5,7]=>[6,1,2,3,4,8,5,7]=>0000101 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,1,2,3,7,4,5,6]=>[7,1,2,3,4,8,5,6]=>0000011 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[7,1,2,3,6,4,8,5]=>[6,1,2,3,4,8,7,5]=>0000111 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[8,6,5,1,2,3,4,7]=>0001101 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,2,3,8,7,4,6]=>[7,5,1,2,3,4,8,6]=>0001011 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,1,2,3,6,7,4,5]=>[7,6,1,2,3,4,8,5]=>0000111 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[8,7,6,5,1,2,3,4]=>0001111 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>0010001 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[8,7,4,1,2,3,5,6]=>0010011 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[4,1,2,8,3,7,5,6]=>[7,4,1,2,3,5,8,6]=>0010011 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[8,7,6,4,1,2,3,5]=>0010111 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,1,2,5,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>0001001 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,1,2,5,3,4,8,6]=>[5,1,2,3,8,7,4,6]=>0001011 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,1,2,6,3,4,5,7]=>[6,1,2,3,8,4,5,7]=>0000101 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>[8,1,2,3,7,4,5,6]=>0000011 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[7,1,2,6,3,4,8,5]=>[6,1,2,3,8,7,4,5]=>0000111 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,1,2,5,3,8,4,7]=>[5,1,2,3,8,6,4,7]=>0001101 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[8,1,2,5,3,7,4,6]=>[5,1,2,3,7,4,8,6]=>0001011 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[8,1,2,6,3,7,4,5]=>[7,6,1,2,3,8,4,5]=>0000111 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[6,1,2,5,3,7,8,4]=>[5,1,2,3,8,7,6,4]=>0001111 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>[8,5,4,1,2,3,6,7]=>0011001 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[8,7,5,4,1,2,3,6]=>0011011 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[4,1,2,8,6,3,5,7]=>[6,4,1,2,3,8,5,7]=>0010101 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>[7,4,1,2,3,8,5,6]=>0010011 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,1,2,7,6,3,8,5]=>[6,4,1,2,3,8,7,5]=>0010111 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]=>[6,5,1,2,3,8,4,7]=>0001101 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[8,1,2,5,7,3,4,6]=>[7,5,1,2,3,8,4,6]=>0001011 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[8,1,2,7,6,3,4,5]=>[6,1,2,3,7,4,8,5]=>0000111 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[7,1,2,5,6,3,8,4]=>[6,5,1,2,3,8,7,4]=>0001111 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[8,6,5,4,1,2,3,7]=>0011101 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,8,7,3,6]=>[7,5,4,1,2,3,8,6]=>0011011 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,1,2,8,6,7,3,5]=>[7,6,4,1,2,3,8,5]=>0010111 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[8,1,2,5,6,7,3,4]=>[7,6,5,1,2,3,8,4]=>0001111 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[8,7,6,5,4,1,2,3]=>0011111 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>0100001 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,8,2,4,7,5,6]=>[7,3,1,2,4,5,8,6]=>0100011 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[8,7,6,3,1,2,4,5]=>0100111 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[8,5,3,1,2,4,6,7]=>0101001 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[8,7,5,3,1,2,4,6]=>0101011 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,8,2,6,4,5,7]=>[6,3,1,2,4,8,5,7]=>0100101 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>[6,3,1,2,4,8,7,5]=>0100111 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,5,2,8,7,4,6]=>[7,5,3,1,2,4,8,6]=>0101011 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,8,2,6,7,4,5]=>[7,6,3,1,2,4,8,5]=>0100111 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[8,7,6,5,3,1,2,4]=>0101111 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,1,4,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>0010001 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,1,4,2,3,5,8,6]=>[4,1,2,8,7,3,5,6]=>0010011 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>[4,1,2,8,6,3,5,7]=>0010101 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[8,1,4,2,3,7,5,6]=>[4,1,2,7,3,5,8,6]=>0010011 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,5,2,3,4,6,7]=>[5,1,2,8,3,4,6,7]=>0001001 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]=>[8,1,2,6,3,4,5,7]=>0000101 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,1,7,2,3,4,5,6]=>[7,1,2,8,3,4,5,6]=>0000011 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,1,7,2,3,4,8,5]=>[8,7,1,2,6,3,4,5]=>0000111 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>[5,1,2,8,6,3,4,7]=>0001101 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[8,1,5,2,3,7,4,6]=>[5,1,2,7,3,4,8,6]=>0001011 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,1,5,2,3,7,8,4]=>[5,1,2,8,7,6,3,4]=>0001111 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,4,2,8,3,6,7]=>[4,1,2,8,5,3,6,7]=>0011001 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>[4,1,2,8,7,5,3,6]=>0011011 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,1,4,2,6,3,5,7]=>[4,1,2,6,3,8,5,7]=>0010101 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>[4,1,2,6,3,8,7,5]=>0010111 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,1,5,2,6,3,4,7]=>[6,5,1,2,8,3,4,7]=>0001101 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>[7,5,1,2,8,3,4,6]=>0001011 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[7,1,8,2,6,3,4,5]=>[6,1,2,8,3,4,7,5]=>0000111 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>[6,5,1,2,8,7,3,4]=>0001111 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[8,1,4,2,6,7,3,5]=>[4,1,2,7,6,3,8,5]=>0010111 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[8,1,5,2,6,7,3,4]=>[7,6,5,1,2,8,3,4]=>0001111 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[5,1,4,2,6,7,8,3]=>[4,1,2,8,7,6,5,3]=>0011111 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[8,6,4,3,1,2,5,7]=>0110101 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>[8,7,6,4,3,1,2,5]=>0110111 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,8,5,2,4,6,7]=>[5,3,1,2,8,4,6,7]=>0101001 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,7,5,2,4,8,6]=>[5,3,1,2,8,7,4,6]=>0101011 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>[6,3,1,2,8,4,5,7]=>0100101 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>[8,3,1,2,7,4,5,6]=>0100011 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,7,6,2,4,8,5]=>[6,3,1,2,8,7,4,5]=>0100111 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,6,5,2,8,4,7]=>[5,3,1,2,8,6,4,7]=>0101101 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,8,5,2,7,4,6]=>[5,3,1,2,7,4,8,6]=>0101011 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,8,6,2,7,4,5]=>[7,6,3,1,2,8,4,5]=>0100111 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]=>[5,4,1,2,8,3,6,7]=>0011001 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,1,4,5,2,3,8,6]=>[5,4,1,2,8,7,3,6]=>0011011 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,1,4,6,2,3,5,7]=>[6,4,1,2,8,3,5,7]=>0010101 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,1,4,8,2,3,5,6]=>[8,4,1,2,7,3,5,6]=>0010011 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[7,1,4,6,2,3,8,5]=>[6,4,1,2,8,7,3,5]=>0010111 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,1,6,5,2,3,4,7]=>[5,1,2,6,3,8,4,7]=>0001101 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>[6,1,2,8,3,7,4,5]=>0000111 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[7,1,6,5,2,3,8,4]=>[5,1,2,6,3,8,7,4]=>0001111 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[8,1,4,5,2,7,3,6]=>[5,4,1,2,7,3,8,6]=>0011011 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[6,1,4,5,2,7,8,3]=>[5,4,1,2,8,7,6,3]=>0011111 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>[8,7,5,4,3,1,2,6]=>0111011 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,8,6,2,5,7]=>[6,4,3,1,2,8,5,7]=>0110101 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,4,8,7,2,5,6]=>[7,4,3,1,2,8,5,6]=>0110011 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,4,7,6,2,8,5]=>[6,4,3,1,2,8,7,5]=>0110111 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,8,5,6,2,4,7]=>[6,5,3,1,2,8,4,7]=>0101101 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,8,5,7,2,4,6]=>[7,5,3,1,2,8,4,6]=>0101011 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,8,7,6,2,4,5]=>[6,3,1,2,7,4,8,5]=>0100111 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,1,4,5,6,2,3,7]=>[6,5,4,1,2,8,3,7]=>0011101 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[8,1,4,5,7,2,3,6]=>[7,5,4,1,2,8,3,6]=>0011011 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[8,1,4,7,6,2,3,5]=>[6,4,1,2,7,3,8,5]=>0010111 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[8,1,7,5,6,2,3,4]=>[6,5,1,2,7,3,8,4]=>0001111 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[8,6,5,4,3,1,2,7]=>0111101 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,4,8,6,7,2,5]=>[7,6,4,3,1,2,8,5]=>0110111 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,8,5,6,7,2,4]=>[7,6,5,3,1,2,8,4]=>0101111 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>[7,6,5,4,1,2,8,3]=>0011111 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8,7,6,5,4,3,1,2]=>0111111 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>1000001 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[8,7,2,1,3,4,5,6]=>1000011 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,8,1,3,4,7,5,6]=>[7,2,1,3,4,5,8,6]=>1000011 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,6,1,3,4,7,8,5]=>[8,7,6,2,1,3,4,5]=>1000111 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>[8,5,2,1,3,4,6,7]=>1001001 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[8,7,5,2,1,3,4,6]=>1001011 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,8,1,3,7,4,5,6]=>[7,2,1,3,4,8,5,6]=>1000011 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,7,1,3,6,4,8,5]=>[6,2,1,3,4,8,7,5]=>1000111 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[8,6,5,2,1,3,4,7]=>1001101 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[8,7,6,5,2,1,3,4]=>1001111 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[8,4,2,1,3,5,6,7]=>1010001 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>[8,7,4,2,1,3,5,6]=>1010011 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[8,6,4,2,1,3,5,7]=>1010101 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[8,7,6,4,2,1,3,5]=>1010111 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,8,1,5,3,4,6,7]=>[5,2,1,3,8,4,6,7]=>1001001 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,7,1,5,3,4,8,6]=>[5,2,1,3,8,7,4,6]=>1001011 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,8,1,6,3,4,5,7]=>[6,2,1,3,8,4,5,7]=>1000101 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,6,1,5,3,7,8,4]=>[5,2,1,3,8,7,6,4]=>1001111 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[8,5,4,2,1,3,6,7]=>1011001 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1,8,6,3,5,7]=>[6,4,2,1,3,8,5,7]=>1010101 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,8,7,3,5,6]=>[7,4,2,1,3,8,5,6]=>1010011 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,1,7,6,3,8,5]=>[6,4,2,1,3,8,7,5]=>1010111 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,8,1,5,6,3,4,7]=>[6,5,2,1,3,8,4,7]=>1001101 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,8,1,5,7,3,4,6]=>[7,5,2,1,3,8,4,6]=>1001011 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,8,1,7,6,3,4,5]=>[6,2,1,3,7,4,8,5]=>1000111 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,7,1,5,6,3,8,4]=>[6,5,2,1,3,8,7,4]=>1001111 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>[8,6,5,4,2,1,3,7]=>1011101 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1,8,6,7,3,5]=>[7,6,4,2,1,3,8,5]=>1010111 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8,7,6,5,4,2,1,3]=>1011111 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>0100001 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,3,1,2,4,5,8,6]=>[3,1,8,7,2,4,5,6]=>0100011 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,3,1,2,4,8,5,7]=>[3,1,8,6,2,4,5,7]=>0100101 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[8,3,1,2,4,7,5,6]=>[3,1,7,2,4,5,8,6]=>0100011 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,3,1,2,4,7,8,5]=>[3,1,8,7,6,2,4,5]=>0100111 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,3,1,2,8,4,6,7]=>[3,1,8,5,2,4,6,7]=>0101001 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,3,1,2,7,4,8,6]=>[3,1,8,7,5,2,4,6]=>0101011 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,3,1,2,6,4,5,7]=>[3,1,6,2,4,8,5,7]=>0100101 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[7,3,1,2,6,4,8,5]=>[3,1,6,2,4,8,7,5]=>0100111 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,1,2,8,7,4,6]=>[3,1,7,5,2,4,8,6]=>0101011 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[8,3,1,2,6,7,4,5]=>[3,1,7,6,2,4,8,5]=>0100111 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,3,1,2,6,7,8,4]=>[3,1,8,7,6,5,2,4]=>0101111 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,4,1,2,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>0010001 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,4,1,2,3,5,8,6]=>[4,1,8,7,2,3,5,6]=>0010011 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,1,2,3,8,5,7]=>[4,1,8,6,2,3,5,7]=>0010101 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[8,4,1,2,3,7,5,6]=>[4,1,7,2,3,5,8,6]=>0010011 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,4,1,2,3,7,8,5]=>[4,1,8,7,6,2,3,5]=>0010111 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,8,1,2,3,4,6,7]=>[8,1,5,2,3,4,6,7]=>0001001 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]=>[8,7,1,5,2,3,4,6]=>0001011 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[6,1,8,2,3,4,5,7]=>0000101 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6]=>[7,1,8,2,3,4,5,6]=>0000011 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,6,1,2,3,4,8,5]=>[6,1,8,7,2,3,4,5]=>0000111 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>[8,6,1,5,2,3,4,7]=>0001101 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,8,1,2,3,7,4,6]=>[7,1,5,2,3,4,8,6]=>0001011 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,6,1,2,3,7,4,5]=>[7,6,1,8,2,3,4,5]=>0000111 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]=>[8,7,6,1,5,2,3,4]=>0001111 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>[4,1,8,5,2,3,6,7]=>0011001 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,4,1,2,7,3,8,6]=>[4,1,8,7,5,2,3,6]=>0011011 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,4,1,2,6,3,5,7]=>[4,1,6,2,3,8,5,7]=>0010101 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8,4,1,2,7,3,5,6]=>[4,1,7,2,3,8,5,6]=>0010011 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7,4,1,2,6,3,8,5]=>[4,1,6,2,3,8,7,5]=>0010111 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[5,8,1,2,6,3,4,7]=>[6,1,8,5,2,3,4,7]=>0001101 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>[7,1,8,5,2,3,4,6]=>0001011 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,1,2,6,3,4,5]=>[6,1,7,2,3,4,8,5]=>0000111 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,7,1,2,6,3,8,4]=>[6,1,8,7,5,2,3,4]=>0001111 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,4,1,2,8,7,3,6]=>[4,1,7,5,2,3,8,6]=>0011011 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8,4,1,2,6,7,3,5]=>[4,1,7,6,2,3,8,5]=>0010111 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,8,1,2,6,7,3,4]=>[7,6,1,8,5,2,3,4]=>0001111 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,1,2,6,7,8,3]=>[4,1,8,7,6,5,2,3]=>0011111 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,3,1,8,2,5,6,7]=>[3,1,8,4,2,5,6,7]=>0110001 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,1,8,2,7,5,6]=>[3,1,7,4,2,5,8,6]=>0110011 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,1,6,2,7,8,5]=>[3,1,8,7,6,4,2,5]=>0110111 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,3,1,5,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>0101001 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,3,1,5,2,4,8,6]=>[3,1,5,2,8,7,4,6]=>0101011 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,3,1,6,2,4,5,7]=>[3,1,6,2,8,4,5,7]=>0100101 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,3,1,8,2,4,5,6]=>[3,1,8,2,7,4,5,6]=>0100011 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7,3,1,6,2,4,8,5]=>[3,1,6,2,8,7,4,5]=>0100111 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>[3,1,5,2,7,4,8,6]=>0101011 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[6,3,1,5,2,7,8,4]=>[3,1,5,2,8,7,6,4]=>0101111 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,4,1,5,2,3,6,7]=>[5,4,1,8,2,3,6,7]=>0011001 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>[5,4,1,8,7,2,3,6]=>0011011 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>[6,4,1,8,2,3,5,7]=>0010101 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>[8,4,1,7,2,3,5,6]=>0010011 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8,7,1,5,2,3,4,6]=>[5,1,7,2,3,8,4,6]=>0001011 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>[6,1,7,2,3,8,4,5]=>0000111 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[6,7,1,5,2,3,8,4]=>[5,1,8,7,2,3,6,4]=>0001111 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8,4,1,6,2,7,3,5]=>[7,6,4,1,8,2,3,5]=>0010111 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,8,1,5,2,7,3,4]=>[5,1,7,2,3,8,6,4]=>0001111 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[6,4,1,5,2,7,8,3]=>[5,4,1,8,7,6,2,3]=>0011111 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,1,5,8,2,6,7]=>[3,1,8,5,4,2,6,7]=>0111001 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,1,5,7,2,8,6]=>[3,1,8,7,5,4,2,6]=>0111011 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,1,8,6,2,5,7]=>[3,1,6,4,2,8,5,7]=>0110101 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>[3,1,6,5,2,8,4,7]=>0101101 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>[3,1,7,5,2,8,4,6]=>0101011 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>[3,1,6,2,7,4,8,5]=>0100111 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]=>[3,1,6,5,2,8,7,4]=>0101111 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8,4,1,5,7,2,3,6]=>[7,5,4,1,8,2,3,6]=>0011011 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[8,4,1,7,6,2,3,5]=>[6,4,1,7,2,3,8,5]=>0010111 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7,4,1,5,6,2,8,3]=>[6,5,4,1,8,7,2,3]=>0011111 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,3,1,5,6,8,2,7]=>[3,1,8,6,5,4,2,7]=>0111101 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,3,1,5,8,7,2,6]=>[3,1,7,5,4,2,8,6]=>0111011 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,3,1,8,6,7,2,5]=>[3,1,7,6,4,2,8,5]=>0110111 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[8,3,1,5,6,7,2,4]=>[3,1,7,6,5,2,8,4]=>0101111 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8,4,1,5,6,7,2,3]=>[7,6,5,4,1,8,2,3]=>0011111 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,2]=>[3,1,8,7,6,5,4,2]=>0111111 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>1100001 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>[8,7,3,2,1,4,5,6]=>1100011 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>[8,6,3,2,1,4,5,7]=>1100101 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,3,8,1,4,7,5,6]=>[7,3,2,1,4,5,8,6]=>1100011 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[8,7,6,3,2,1,4,5]=>1100111 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>[8,5,3,2,1,4,6,7]=>1101001 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[8,7,5,3,2,1,4,6]=>1101011 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,3,8,1,6,4,5,7]=>[6,3,2,1,4,8,5,7]=>1100101 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,3,7,1,6,4,8,5]=>[6,3,2,1,4,8,7,5]=>1100111 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>[8,6,5,3,2,1,4,7]=>1101101 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8,7,6,5,3,2,1,4]=>1101111 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,8,4,1,3,5,6,7]=>[4,2,1,8,3,5,6,7]=>1010001 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,7,4,1,3,5,8,6]=>[4,2,1,8,7,3,5,6]=>1010011 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>[4,2,1,8,6,3,5,7]=>1010101 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,8,4,1,3,7,5,6]=>[4,2,1,7,3,5,8,6]=>1010011 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>[4,2,1,8,7,6,3,5]=>1010111 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,8,5,1,3,4,6,7]=>[5,2,1,8,3,4,6,7]=>1001001 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,7,5,1,3,4,8,6]=>[5,2,1,8,7,3,4,6]=>1001011 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,6,8,1,3,4,5,7]=>[8,2,1,6,3,4,5,7]=>1000101 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,8,7,1,3,4,5,6]=>[7,2,1,8,3,4,5,6]=>1000011 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[8,7,2,1,6,3,4,5]=>1000111 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,8,5,1,3,7,4,6]=>[5,2,1,7,3,4,8,6]=>1001011 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,6,8,1,3,7,4,5]=>[7,2,1,8,6,3,4,5]=>1000111 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>[5,2,1,8,7,6,3,4]=>1001111 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,5,4,1,8,3,6,7]=>[4,2,1,8,5,3,6,7]=>1011001 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,8,4,1,6,3,5,7]=>[4,2,1,6,3,8,5,7]=>1010101 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,8,4,1,7,3,5,6]=>[4,2,1,7,3,8,5,6]=>1010011 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,7,4,1,6,3,8,5]=>[4,2,1,6,3,8,7,5]=>1010111 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,8,5,1,6,3,4,7]=>[6,5,2,1,8,3,4,7]=>1001101 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,8,5,1,7,3,4,6]=>[7,5,2,1,8,3,4,6]=>1001011 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,7,8,1,6,3,4,5]=>[6,2,1,8,3,4,7,5]=>1000111 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,7,5,1,6,3,8,4]=>[6,5,2,1,8,7,3,4]=>1001111 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,1,6,8,3,7]=>[4,2,1,8,6,5,3,7]=>1011101 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,5,4,1,6,7,8,3]=>[4,2,1,8,7,6,5,3]=>1011111 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,3,4,1,2,5,6,7]=>[4,3,1,8,2,5,6,7]=>0110001 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,3,4,1,2,5,8,6]=>[4,3,1,8,7,2,5,6]=>0110011 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,3,4,1,2,8,5,7]=>[4,3,1,8,6,2,5,7]=>0110101 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[8,3,4,1,2,7,5,6]=>[4,3,1,7,2,5,8,6]=>0110011 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,3,5,1,2,4,6,7]=>[5,3,1,8,2,4,6,7]=>0101001 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>[5,3,1,8,7,2,4,6]=>0101011 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,3,8,1,2,4,5,7]=>[8,3,1,6,2,4,5,7]=>0100101 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,3,7,1,2,4,5,6]=>[7,3,1,8,2,4,5,6]=>0100011 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,3,7,1,2,4,8,5]=>[8,7,3,1,6,2,4,5]=>0100111 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,5,1,2,8,4,7]=>[5,3,1,8,6,2,4,7]=>0101101 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>[7,3,1,8,6,2,4,5]=>0100111 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,5,4,1,2,3,6,7]=>[4,1,5,2,8,3,6,7]=>0011001 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,5,4,1,2,3,8,6]=>[4,1,5,2,8,7,3,6]=>0011011 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,8,4,1,2,3,5,7]=>[4,1,8,2,6,3,5,7]=>0010101 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,4,1,2,3,5,6]=>[4,1,7,2,8,3,5,6]=>0010011 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,1,2,3,8,5]=>[4,1,8,7,2,6,3,5]=>0010111 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>[5,1,8,2,6,3,4,7]=>0001101 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>[5,1,7,2,8,3,4,6]=>0001011 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[8,1,7,2,6,3,4,5]=>0000111 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,1,2,3,8,4]=>[5,1,8,7,2,6,3,4]=>0001111 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>[4,1,5,2,7,3,8,6]=>0011011 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]=>[5,1,7,2,8,6,3,4]=>0001111 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[6,5,4,1,2,7,8,3]=>[4,1,5,2,8,7,6,3]=>0011111 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,3,4,1,8,2,6,7]=>[4,3,1,8,5,2,6,7]=>0111001 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,3,4,1,7,2,8,6]=>[4,3,1,8,7,5,2,6]=>0111011 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,3,4,1,6,2,5,7]=>[4,3,1,6,2,8,5,7]=>0110101 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8,3,4,1,7,2,5,6]=>[4,3,1,7,2,8,5,6]=>0110011 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,3,5,1,6,2,4,7]=>[6,5,3,1,8,2,4,7]=>0101101 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8,3,5,1,7,2,4,6]=>[7,5,3,1,8,2,4,6]=>0101011 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,3,8,1,6,2,4,5]=>[6,3,1,8,2,4,7,5]=>0100111 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>[4,1,6,2,8,3,7,5]=>0010111 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]=>[6,5,1,8,2,7,3,4]=>0001111 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,3,4,1,8,7,2,6]=>[4,3,1,7,5,2,8,6]=>0111011 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8,3,4,1,6,7,2,5]=>[4,3,1,7,6,2,8,5]=>0110111 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[8,3,5,1,6,7,2,4]=>[7,6,5,3,1,8,2,4]=>0101111 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8,5,4,1,6,7,2,3]=>[4,1,7,6,5,2,8,3]=>0011111 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[5,3,4,1,6,7,8,2]=>[4,3,1,8,7,6,5,2]=>0111111 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[8,4,3,2,1,5,6,7]=>1110001 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>[8,7,4,3,2,1,5,6]=>1110011 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[8,6,4,3,2,1,5,7]=>1110101 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,8,1,7,5,6]=>[7,4,3,2,1,5,8,6]=>1110011 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>[8,7,6,4,3,2,1,5]=>1110111 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,8,5,1,4,6,7]=>[5,3,2,1,8,4,6,7]=>1101001 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,8,6,1,4,5,7]=>[6,3,2,1,8,4,5,7]=>1100101 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,7,8,1,4,5,6]=>[8,3,2,1,7,4,5,6]=>1100011 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,6,1,4,8,5]=>[6,3,2,1,8,7,4,5]=>1100111 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,6,5,1,8,4,7]=>[5,3,2,1,8,6,4,7]=>1101101 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,8,5,1,7,4,6]=>[5,3,2,1,7,4,8,6]=>1101011 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,8,6,1,7,4,5]=>[7,6,3,2,1,8,4,5]=>1100111 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,6,5,1,7,8,4]=>[5,3,2,1,8,7,6,4]=>1101111 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,8,4,5,1,3,6,7]=>[5,4,2,1,8,3,6,7]=>1011001 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,4,5,1,3,8,6]=>[5,4,2,1,8,7,3,6]=>1011011 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,8,4,6,1,3,5,7]=>[6,4,2,1,8,3,5,7]=>1010101 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]=>[8,4,2,1,7,3,5,6]=>1010011 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,8,6,5,1,3,4,7]=>[5,2,1,6,3,8,4,7]=>1001101 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,7,8,6,1,3,4,5]=>[6,2,1,8,3,7,4,5]=>1000111 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]=>[5,2,1,6,3,8,7,4]=>1001111 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]=>[7,6,4,2,1,8,3,5]=>1010111 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,8,6,5,1,7,3,4]=>[5,2,1,7,6,3,8,4]=>1001111 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,6,4,5,1,7,8,3]=>[5,4,2,1,8,7,6,3]=>1011111 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,3,4,5,1,2,8,6]=>[5,4,3,1,8,7,2,6]=>0111011 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,3,4,6,1,2,5,7]=>[6,4,3,1,8,2,5,7]=>0110101 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,3,6,5,1,2,4,7]=>[5,3,1,6,2,8,4,7]=>0101101 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]=>[5,3,1,8,2,7,4,6]=>0101011 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,8,6,1,2,4,5]=>[6,3,1,8,2,7,4,5]=>0100111 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[5,4,1,6,2,8,3,7]=>0011101 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>[5,1,6,2,8,3,7,4]=>0001111 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[8,3,4,5,1,7,2,6]=>[5,4,3,1,7,2,8,6]=>0111011 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[8,3,4,6,1,7,2,5]=>[7,6,4,3,1,8,2,5]=>0110111 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8,6,4,5,1,7,2,3]=>[5,4,1,7,6,2,8,3]=>0011111 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[6,3,4,5,1,7,8,2]=>[5,4,3,1,8,7,6,2]=>0111111 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>[8,5,4,3,2,1,6,7]=>1111001 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>[8,7,5,4,3,2,1,6]=>1111011 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,3,4,8,6,1,5,7]=>[6,4,3,2,1,8,5,7]=>1110101 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,4,8,7,1,5,6]=>[7,4,3,2,1,8,5,6]=>1110011 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,4,7,6,1,8,5]=>[6,4,3,2,1,8,7,5]=>1110111 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,8,5,7,1,4,6]=>[7,5,3,2,1,8,4,6]=>1101011 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,8,7,6,1,4,5]=>[6,3,2,1,7,4,8,5]=>1100111 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,5,6,1,8,4]=>[6,5,3,2,1,8,7,4]=>1101111 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,8,4,5,7,1,3,6]=>[7,5,4,2,1,8,3,6]=>1011011 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,8,4,7,6,1,3,5]=>[6,4,2,1,7,3,8,5]=>1010111 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,8,7,5,6,1,3,4]=>[6,5,2,1,7,3,8,4]=>1001111 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[6,5,4,3,1,8,2,7]=>0111101 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8,3,4,5,7,1,2,6]=>[7,5,4,3,1,8,2,6]=>0111011 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8,3,4,7,6,1,2,5]=>[6,4,3,1,7,2,8,5]=>0110111 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,3,7,5,6,1,2,4]=>[6,5,3,1,7,2,8,4]=>0101111 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,7,4,5,6,1,2,3]=>[6,5,4,1,7,2,8,3]=>0011111 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,2]=>[6,5,4,3,1,8,7,2]=>0111111 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>[8,6,5,4,3,2,1,7]=>1111101 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,4,5,8,7,1,6]=>[7,5,4,3,2,1,8,6]=>1111011 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,8,6,7,1,5]=>[7,6,4,3,2,1,8,5]=>1110111 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,8,5,6,7,1,4]=>[7,6,5,3,2,1,8,4]=>1101111 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,8,4,5,6,7,1,3]=>[7,6,5,4,2,1,8,3]=>1011111 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[8,3,4,5,6,7,1,2]=>[7,6,5,4,3,1,8,2]=>0111111 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,7,6,5,4,3,2,1]=>1111111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>00000001 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,1,2,3,4,5,6,9,7]=>[9,8,1,2,3,4,5,6,7]=>00000011 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>[9,7,1,2,3,4,5,6,8]=>00000101 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,1,2,3,4,5,8,6,7]=>[8,1,2,3,4,5,6,9,7]=>00000011 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,8,9,6]=>[9,8,7,1,2,3,4,5,6]=>00000111 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,1,2,3,4,9,5,7,8]=>[9,6,1,2,3,4,5,7,8]=>00001001 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]=>[9,8,6,1,2,3,4,5,7]=>00001011 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,1,2,3,4,7,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>00000101 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,1,2,3,4,8,5,6,7]=>[8,1,2,3,4,5,9,6,7]=>00000011 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,1,2,3,4,9,8,5,7]=>[8,6,1,2,3,4,5,9,7]=>00001011 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[9,1,2,3,4,7,8,5,6]=>[8,7,1,2,3,4,5,9,6]=>00000111 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,7,8,9,5]=>[9,8,7,6,1,2,3,4,5]=>00001111 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[9,1,2,3,6,4,5,7,8]=>[6,1,2,3,4,9,5,7,8]=>00001001 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,1,2,3,9,4,5,6,7]=>[9,1,2,3,4,8,5,6,7]=>00000011 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,4]=>[9,8,7,6,5,1,2,3,4]=>00011111 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,8,3,5,6,9,7]=>[9,8,4,1,2,3,5,6,7]=>00100011 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,1,2,5,3,4,6,7,8]=>[5,1,2,3,9,4,6,7,8]=>00010001 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,2,8,3,4,5,6,7]=>[8,1,2,3,9,4,5,6,7]=>00000011 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[7,1,2,8,3,4,5,9,6]=>[9,8,1,2,3,7,4,5,6]=>00000111 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]=>[9,5,4,1,2,3,6,7,8]=>00110001 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,3]=>[9,8,7,6,5,4,1,2,3]=>00111111 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,9,2,4,5,6,7,8]=>[9,3,1,2,4,5,6,7,8]=>01000001 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,9,2,4,5,8,6,7]=>[8,3,1,2,4,5,6,9,7]=>01000011 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>[9,7,5,3,1,2,4,6,8]=>01010101 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[9,1,4,2,3,5,8,6,7]=>[4,1,2,8,3,5,6,9,7]=>00100011 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,8,2,3,4,5,6,7]=>[8,1,2,9,3,4,5,6,7]=>00000011 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,1,4,5,2,3,6,7,8]=>[5,4,1,2,9,3,6,7,8]=>00110001 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,1,4,8,2,3,5,6,7]=>[8,4,1,2,9,3,5,6,7]=>00100011 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>[9,7,6,5,4,3,1,2,8]=>01111101 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,2]=>[9,8,7,6,5,4,3,1,2]=>01111111 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>10000001 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,9,1,3,4,5,8,6,7]=>[8,2,1,3,4,5,6,9,7]=>10000011 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,4]=>[9,8,7,6,5,2,1,3,4]=>10011111 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>[9,8,7,6,5,4,2,1,3]=>10111111 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[3,1,9,2,4,5,6,7,8]=>01000001 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[8,3,1,2,4,5,6,9,7]=>[3,1,9,8,2,4,5,6,7]=>01000011 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[9,3,1,2,4,5,8,6,7]=>[3,1,8,2,4,5,6,9,7]=>01000011 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[7,1,9,2,3,4,5,6,8]=>00000101 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[9,1,8,2,3,4,5,6,7]=>00000011 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,7,1,2,3,4,8,5,6]=>[8,7,1,9,2,3,4,5,6]=>00000111 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,8,1,2,3,7,4,5,6]=>[7,1,8,2,3,4,5,9,6]=>00000111 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,2]=>[3,1,9,8,7,6,5,4,2]=>01111111 [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>[9,8,7,6,5,3,2,1,4]=>11011111 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,3,4,1,2,5,6,7,8]=>[4,3,1,9,2,5,6,7,8]=>01100001 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>11101111 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[7,3,4,5,1,2,8,9,6]=>[5,4,3,1,9,8,7,2,6]=>01110111 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>[9,5,4,3,2,1,6,7,8]=>11110001 [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>[9,8,5,4,3,2,1,6,7]=>11110011 [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>[9,8,7,5,4,3,2,1,6]=>11110111 [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>[9,6,5,4,3,2,1,7,8]=>11111001 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>[9,8,6,5,4,3,2,1,7]=>11111011 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>[9,7,6,5,4,3,2,1,8]=>11111101 [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,9,8,1,7]=>[8,6,5,4,3,2,1,9,7]=>11111011 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,9,7,8,1,6]=>[8,7,5,4,3,2,1,9,6]=>11110111 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,9,6,7,8,1,5]=>[8,7,6,4,3,2,1,9,5]=>11101111 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,9,5,6,7,8,1,4]=>[8,7,6,5,3,2,1,9,4]=>11011111 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,9,4,5,6,7,8,1,3]=>[8,7,6,5,4,2,1,9,3]=>10111111 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,2]=>[8,7,6,5,4,3,1,9,2]=>01111111 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>[10,8,7,6,5,4,3,2,1,9]=>111111101 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,2]=>[10,9,8,7,6,5,4,3,1,2]=>011111111 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[11,9,8,7,6,5,4,3,2,1,10]=>1111111101 [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[11,10,9,8,7,6,5,4,3,1,2]=>0111111111 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>11111111101 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[10,9,7,6,5,4,3,2,1,8]=>111111011 [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>[10,9,8,7,6,5,4,2,1,3]=>101111111 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>[10,7,6,5,4,3,2,1,8,9]=>111111001 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>[10,8,7,6,5,4,3,1,2,9]=>011111101 [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,3]=>[10,9,8,7,6,5,4,1,2,3]=>001111111 []=>[1]=>[1]=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,10,2,3,4,5,6,7,8]=>000000011 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,3,1,5,2,7,4,9,6,8]=>[3,1,5,2,7,4,9,6,10,8]=>010101011 [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,3,1,5,6,7,8,9,10,2]=>[3,1,10,9,8,7,6,5,4,2]=>011111111 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,3,10,1,2,4,5,6,7,8]=>[10,3,1,9,2,4,5,6,7,8]=>010000011 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10,9,8,1,2,3,4,5,6,7]=>[8,1,9,2,10,3,4,5,6,7]=>000000111 [1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[10,5,4,1,2,9,8,3,6,7]=>[4,1,5,2,8,3,9,6,10,7]=>001100111 [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[7,3,4,5,6,1,8,9,10,2]=>[6,5,4,3,1,10,9,8,7,2]=>011111111 [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[9,3,4,5,6,7,8,1,10,2]=>[8,7,6,5,4,3,1,10,9,2]=>011111111 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,4,5,6,7,10,9,1,8]=>[9,7,6,5,4,3,2,1,10,8]=>111111011 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,10,8,9,1,7]=>[9,8,6,5,4,3,2,1,10,7]=>111110111 [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,10,7,8,9,1,6]=>[9,8,7,5,4,3,2,1,10,6]=>111101111 [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[2,3,4,10,6,7,8,9,1,5]=>[9,8,7,6,4,3,2,1,10,5]=>111011111 [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,3,10,5,6,7,8,9,1,4]=>[9,8,7,6,5,3,2,1,10,4]=>110111111 [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,10,4,5,6,7,8,9,1,3]=>[9,8,7,6,5,4,2,1,10,3]=>101111111 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10,3,4,5,6,7,8,9,1,2]=>[9,8,7,6,5,4,3,1,10,2]=>011111111 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>000000001 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,1,2,3,4,5,6,7,10,8]=>[10,9,1,2,3,4,5,6,7,8]=>000000011 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,1,2,3,4,5,6,9,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>000000011 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,9,6,7,8]=>[9,1,2,3,4,5,6,10,7,8]=>000000011 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,1,2,3,4,10,5,6,7,8]=>[10,1,2,3,4,5,9,6,7,8]=>000000011 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,9,4,5,6,7,8]=>[9,1,2,3,4,10,5,6,7,8]=>000000011 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,9,3,4,5,6,7,8]=>[9,1,2,3,10,4,5,6,7,8]=>000000011 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[10,1,2,9,3,4,5,6,7,8]=>000000011 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>0000000001 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[11,10,1,2,3,4,5,6,7,8,9]=>0000000011 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,1,2,3,4,5,6,9,10,7]=>[10,9,8,1,2,3,4,5,6,7]=>000000111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[11,1,2,3,4,5,6,7,10,8,9]=>[10,1,2,3,4,5,6,7,8,11,9]=>0000000011 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,1,2,3,4,5,10,9,6,8]=>[9,7,1,2,3,4,5,6,10,8]=>000001011 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[11,1,2,3,4,5,6,10,7,8,9]=>[10,1,2,3,4,5,6,7,11,8,9]=>0000000011 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[10,1,2,3,4,5,11,6,7,8,9]=>[11,1,2,3,4,5,6,10,7,8,9]=>0000000011 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,2,3,4,10,5,6,7,8,9]=>[10,1,2,3,4,5,11,6,7,8,9]=>0000000011 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,1,2,11,3,4,5,6,7,8,9]=>[11,1,2,3,10,4,5,6,7,8,9]=>0000000011 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,1,10,2,3,4,5,6,7,8,9]=>[10,1,2,11,3,4,5,6,7,8,9]=>0000000011 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[10,1,11,2,3,4,5,6,7,8,9]=>0000000011 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>00000000001 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>[12,11,1,2,3,4,5,6,7,8,9,10]=>00000000011 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[12,1,2,3,4,5,6,7,8,11,9,10]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>00000000011 [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,6]=>[10,9,8,7,1,2,3,4,5,6]=>000001111 [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,5]=>[10,9,8,7,6,1,2,3,4,5]=>000011111 [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,4]=>[10,9,8,7,6,5,1,2,3,4]=>000111111 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,10,3,5,6,7,8,9]=>[10,4,1,2,3,5,6,7,8,9]=>001000001 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>[10,9,7,5,3,1,2,4,6,8]=>010101011 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>100000001 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>[10,8,6,4,2,1,3,5,7,9]=>101010101 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,8,10,3,9]=>[10,8,7,6,5,4,2,1,3,9]=>101111101 [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,4]=>[10,9,8,7,6,5,3,2,1,4]=>110111111 [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>[10,9,8,7,6,4,3,2,1,5]=>111011111 [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>[10,9,8,7,5,4,3,2,1,6]=>111101111 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>[10,9,8,6,5,4,3,2,1,7]=>111110111 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,11,6,8,9,10]=>[11,7,1,2,3,4,5,6,8,9,10]=>0000010001 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[11,2,1,3,4,5,6,7,8,9,10]=>1000000001 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,10,1,2,3,4,6,7,8,9]=>[10,1,5,2,3,4,6,7,8,9]=>000100001 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[12,2,1,3,4,5,6,7,8,9,10,11]=>10000000001 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,3,1,2,4,5,6,9,7,8]=>[3,1,9,2,4,5,6,7,10,8]=>010000011 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,10,2,4,5,6,9,7,8]=>[9,3,1,2,4,5,6,7,10,8]=>010000011 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,3,1,2,4,5,6,7,10,8]=>[3,1,10,9,2,4,5,6,7,8]=>010000011 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,3,4,1,2,5,6,7,8,9]=>[4,3,1,10,2,5,6,7,8,9]=>011000001 [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11,3,4,5,6,7,8,9,10,1,2]=>[10,9,8,7,6,5,4,3,1,11,2]=>0111111111 [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[12,3,4,5,6,7,8,9,10,11,1,2]=>[11,10,9,8,7,6,5,4,3,1,12,2]=>01111111111 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,1,2,5,3,4,6,7,8,9]=>[5,1,2,3,10,4,6,7,8,9]=>000100001 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,7,1,2,3,4,5,6,10,8]=>[7,1,10,9,2,3,4,5,6,8]=>000001011 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[2,3,4,5,6,7,11,9,10,1,8]=>[10,9,7,6,5,4,3,2,1,11,8]=>1111110111 [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[2,3,4,11,6,7,8,9,10,1,5]=>[10,9,8,7,6,4,3,2,1,11,5]=>1110111111 [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.