Identifier
-
Mp00254:
Permutations
—Inverse fireworks map⟶
Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
St000297: Binary words ⟶ ℤ
Values
=>
[1,2]=>[1,2]=>0=>0=>0
[2,1]=>[2,1]=>1=>1=>1
[1,2,3]=>[1,2,3]=>00=>00=>0
[1,3,2]=>[1,3,2]=>01=>10=>1
[2,1,3]=>[2,1,3]=>10=>01=>0
[2,3,1]=>[1,3,2]=>01=>10=>1
[3,1,2]=>[3,1,2]=>01=>10=>1
[3,2,1]=>[3,2,1]=>11=>11=>2
[1,2,3,4]=>[1,2,3,4]=>000=>000=>0
[1,2,4,3]=>[1,2,4,3]=>001=>100=>1
[1,3,2,4]=>[1,3,2,4]=>010=>010=>0
[1,3,4,2]=>[1,2,4,3]=>001=>100=>1
[1,4,2,3]=>[1,4,2,3]=>001=>100=>1
[1,4,3,2]=>[1,4,3,2]=>011=>110=>2
[2,1,3,4]=>[2,1,3,4]=>100=>001=>0
[2,1,4,3]=>[2,1,4,3]=>101=>101=>1
[2,3,1,4]=>[1,3,2,4]=>010=>010=>0
[2,3,4,1]=>[1,2,4,3]=>001=>100=>1
[2,4,1,3]=>[2,4,1,3]=>001=>100=>1
[2,4,3,1]=>[1,4,3,2]=>011=>110=>2
[3,1,2,4]=>[3,1,2,4]=>010=>010=>0
[3,1,4,2]=>[2,1,4,3]=>101=>101=>1
[3,2,1,4]=>[3,2,1,4]=>110=>011=>0
[3,2,4,1]=>[2,1,4,3]=>101=>101=>1
[3,4,1,2]=>[2,4,1,3]=>001=>100=>1
[3,4,2,1]=>[1,4,3,2]=>011=>110=>2
[4,1,2,3]=>[4,1,2,3]=>001=>100=>1
[4,1,3,2]=>[4,1,3,2]=>011=>110=>2
[4,2,1,3]=>[4,2,1,3]=>101=>101=>1
[4,2,3,1]=>[4,1,3,2]=>011=>110=>2
[4,3,1,2]=>[4,3,1,2]=>011=>110=>2
[4,3,2,1]=>[4,3,2,1]=>111=>111=>3
[1,2,3,4,5]=>[1,2,3,4,5]=>0000=>0000=>0
[1,2,3,5,4]=>[1,2,3,5,4]=>0001=>1000=>1
[1,2,4,3,5]=>[1,2,4,3,5]=>0010=>0100=>0
[1,2,4,5,3]=>[1,2,3,5,4]=>0001=>1000=>1
[1,2,5,3,4]=>[1,2,5,3,4]=>0001=>1000=>1
[1,2,5,4,3]=>[1,2,5,4,3]=>0011=>1100=>2
[1,3,2,4,5]=>[1,3,2,4,5]=>0100=>0010=>0
[1,3,2,5,4]=>[1,3,2,5,4]=>0101=>1010=>1
[1,3,4,2,5]=>[1,2,4,3,5]=>0010=>0100=>0
[1,3,4,5,2]=>[1,2,3,5,4]=>0001=>1000=>1
[1,3,5,2,4]=>[1,3,5,2,4]=>0001=>1000=>1
[1,3,5,4,2]=>[1,2,5,4,3]=>0011=>1100=>2
[1,4,2,3,5]=>[1,4,2,3,5]=>0010=>0100=>0
[1,4,2,5,3]=>[1,3,2,5,4]=>0101=>1010=>1
[1,4,3,2,5]=>[1,4,3,2,5]=>0110=>0110=>0
[1,4,3,5,2]=>[1,3,2,5,4]=>0101=>1010=>1
[1,4,5,2,3]=>[1,3,5,2,4]=>0001=>1000=>1
[1,4,5,3,2]=>[1,2,5,4,3]=>0011=>1100=>2
[1,5,2,3,4]=>[1,5,2,3,4]=>0001=>1000=>1
[1,5,2,4,3]=>[1,5,2,4,3]=>0011=>1100=>2
[1,5,3,2,4]=>[1,5,3,2,4]=>0101=>1010=>1
[1,5,3,4,2]=>[1,5,2,4,3]=>0011=>1100=>2
[1,5,4,2,3]=>[1,5,4,2,3]=>0011=>1100=>2
[1,5,4,3,2]=>[1,5,4,3,2]=>0111=>1110=>3
[2,1,3,4,5]=>[2,1,3,4,5]=>1000=>0001=>0
[2,1,3,5,4]=>[2,1,3,5,4]=>1001=>1001=>1
[2,1,4,3,5]=>[2,1,4,3,5]=>1010=>0101=>0
[2,1,4,5,3]=>[2,1,3,5,4]=>1001=>1001=>1
[2,1,5,3,4]=>[2,1,5,3,4]=>1001=>1001=>1
[2,1,5,4,3]=>[2,1,5,4,3]=>1011=>1101=>2
[2,3,1,4,5]=>[1,3,2,4,5]=>0100=>0010=>0
[2,3,1,5,4]=>[1,3,2,5,4]=>0101=>1010=>1
[2,3,4,1,5]=>[1,2,4,3,5]=>0010=>0100=>0
[2,3,4,5,1]=>[1,2,3,5,4]=>0001=>1000=>1
[2,3,5,1,4]=>[1,3,5,2,4]=>0001=>1000=>1
[2,3,5,4,1]=>[1,2,5,4,3]=>0011=>1100=>2
[2,4,1,3,5]=>[2,4,1,3,5]=>0010=>0100=>0
[2,4,1,5,3]=>[1,3,2,5,4]=>0101=>1010=>1
[2,4,3,1,5]=>[1,4,3,2,5]=>0110=>0110=>0
[2,4,3,5,1]=>[1,3,2,5,4]=>0101=>1010=>1
[2,4,5,1,3]=>[1,3,5,2,4]=>0001=>1000=>1
[2,4,5,3,1]=>[1,2,5,4,3]=>0011=>1100=>2
[2,5,1,3,4]=>[2,5,1,3,4]=>0001=>1000=>1
[2,5,1,4,3]=>[2,5,1,4,3]=>0011=>1100=>2
[2,5,3,1,4]=>[1,5,3,2,4]=>0101=>1010=>1
[2,5,3,4,1]=>[1,5,2,4,3]=>0011=>1100=>2
[2,5,4,1,3]=>[2,5,4,1,3]=>0011=>1100=>2
[2,5,4,3,1]=>[1,5,4,3,2]=>0111=>1110=>3
[3,1,2,4,5]=>[3,1,2,4,5]=>0100=>0010=>0
[3,1,2,5,4]=>[3,1,2,5,4]=>0101=>1010=>1
[3,1,4,2,5]=>[2,1,4,3,5]=>1010=>0101=>0
[3,1,4,5,2]=>[2,1,3,5,4]=>1001=>1001=>1
[3,1,5,2,4]=>[3,1,5,2,4]=>0101=>1010=>1
[3,1,5,4,2]=>[2,1,5,4,3]=>1011=>1101=>2
[3,2,1,4,5]=>[3,2,1,4,5]=>1100=>0011=>0
[3,2,1,5,4]=>[3,2,1,5,4]=>1101=>1011=>1
[3,2,4,1,5]=>[2,1,4,3,5]=>1010=>0101=>0
[3,2,4,5,1]=>[2,1,3,5,4]=>1001=>1001=>1
[3,2,5,1,4]=>[3,2,5,1,4]=>0101=>1010=>1
[3,2,5,4,1]=>[2,1,5,4,3]=>1011=>1101=>2
[3,4,1,2,5]=>[2,4,1,3,5]=>0010=>0100=>0
[3,4,1,5,2]=>[1,3,2,5,4]=>0101=>1010=>1
[3,4,2,1,5]=>[1,4,3,2,5]=>0110=>0110=>0
[3,4,2,5,1]=>[1,3,2,5,4]=>0101=>1010=>1
[3,4,5,1,2]=>[1,3,5,2,4]=>0001=>1000=>1
[3,4,5,2,1]=>[1,2,5,4,3]=>0011=>1100=>2
[3,5,1,2,4]=>[3,5,1,2,4]=>0001=>1000=>1
[3,5,1,4,2]=>[2,5,1,4,3]=>0011=>1100=>2
[3,5,2,1,4]=>[3,5,2,1,4]=>1001=>1001=>1
[3,5,2,4,1]=>[2,5,1,4,3]=>0011=>1100=>2
[3,5,4,1,2]=>[2,5,4,1,3]=>0011=>1100=>2
[3,5,4,2,1]=>[1,5,4,3,2]=>0111=>1110=>3
[4,1,2,3,5]=>[4,1,2,3,5]=>0010=>0100=>0
[4,1,2,5,3]=>[3,1,2,5,4]=>0101=>1010=>1
[4,1,3,2,5]=>[4,1,3,2,5]=>0110=>0110=>0
[4,1,3,5,2]=>[3,1,2,5,4]=>0101=>1010=>1
[4,1,5,2,3]=>[3,1,5,2,4]=>0101=>1010=>1
[4,1,5,3,2]=>[2,1,5,4,3]=>1011=>1101=>2
[4,2,1,3,5]=>[4,2,1,3,5]=>1010=>0101=>0
[4,2,1,5,3]=>[3,2,1,5,4]=>1101=>1011=>1
[4,2,3,1,5]=>[4,1,3,2,5]=>0110=>0110=>0
[4,2,3,5,1]=>[3,1,2,5,4]=>0101=>1010=>1
[4,2,5,1,3]=>[3,2,5,1,4]=>0101=>1010=>1
[4,2,5,3,1]=>[2,1,5,4,3]=>1011=>1101=>2
[4,3,1,2,5]=>[4,3,1,2,5]=>0110=>0110=>0
[4,3,1,5,2]=>[3,2,1,5,4]=>1101=>1011=>1
[4,3,2,1,5]=>[4,3,2,1,5]=>1110=>0111=>0
[4,3,2,5,1]=>[3,2,1,5,4]=>1101=>1011=>1
[4,3,5,1,2]=>[3,2,5,1,4]=>0101=>1010=>1
[4,3,5,2,1]=>[2,1,5,4,3]=>1011=>1101=>2
[4,5,1,2,3]=>[3,5,1,2,4]=>0001=>1000=>1
[4,5,1,3,2]=>[2,5,1,4,3]=>0011=>1100=>2
[4,5,2,1,3]=>[3,5,2,1,4]=>1001=>1001=>1
[4,5,2,3,1]=>[2,5,1,4,3]=>0011=>1100=>2
[4,5,3,1,2]=>[2,5,4,1,3]=>0011=>1100=>2
[4,5,3,2,1]=>[1,5,4,3,2]=>0111=>1110=>3
[5,1,2,3,4]=>[5,1,2,3,4]=>0001=>1000=>1
[5,1,2,4,3]=>[5,1,2,4,3]=>0011=>1100=>2
[5,1,3,2,4]=>[5,1,3,2,4]=>0101=>1010=>1
[5,1,3,4,2]=>[5,1,2,4,3]=>0011=>1100=>2
[5,1,4,2,3]=>[5,1,4,2,3]=>0011=>1100=>2
[5,1,4,3,2]=>[5,1,4,3,2]=>0111=>1110=>3
[5,2,1,3,4]=>[5,2,1,3,4]=>1001=>1001=>1
[5,2,1,4,3]=>[5,2,1,4,3]=>1011=>1101=>2
[5,2,3,1,4]=>[5,1,3,2,4]=>0101=>1010=>1
[5,2,3,4,1]=>[5,1,2,4,3]=>0011=>1100=>2
[5,2,4,1,3]=>[5,2,4,1,3]=>0011=>1100=>2
[5,2,4,3,1]=>[5,1,4,3,2]=>0111=>1110=>3
[5,3,1,2,4]=>[5,3,1,2,4]=>0101=>1010=>1
[5,3,1,4,2]=>[5,2,1,4,3]=>1011=>1101=>2
[5,3,2,1,4]=>[5,3,2,1,4]=>1101=>1011=>1
[5,3,2,4,1]=>[5,2,1,4,3]=>1011=>1101=>2
[5,3,4,1,2]=>[5,2,4,1,3]=>0011=>1100=>2
[5,3,4,2,1]=>[5,1,4,3,2]=>0111=>1110=>3
[5,4,1,2,3]=>[5,4,1,2,3]=>0011=>1100=>2
[5,4,1,3,2]=>[5,4,1,3,2]=>0111=>1110=>3
[5,4,2,1,3]=>[5,4,2,1,3]=>1011=>1101=>2
[5,4,2,3,1]=>[5,4,1,3,2]=>0111=>1110=>3
[5,4,3,1,2]=>[5,4,3,1,2]=>0111=>1110=>3
[5,4,3,2,1]=>[5,4,3,2,1]=>1111=>1111=>4
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000=>00000=>0
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>00001=>10000=>1
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>00010=>01000=>0
[1,2,3,5,6,4]=>[1,2,3,4,6,5]=>00001=>10000=>1
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>00001=>10000=>1
[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>00011=>11000=>2
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>00100=>00100=>0
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,2,4,5,3,6]=>[1,2,3,5,4,6]=>00010=>01000=>0
[1,2,4,5,6,3]=>[1,2,3,4,6,5]=>00001=>10000=>1
[1,2,4,6,3,5]=>[1,2,4,6,3,5]=>00001=>10000=>1
[1,2,4,6,5,3]=>[1,2,3,6,5,4]=>00011=>11000=>2
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>00010=>01000=>0
[1,2,5,3,6,4]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>00110=>01100=>0
[1,2,5,4,6,3]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,2,5,6,3,4]=>[1,2,4,6,3,5]=>00001=>10000=>1
[1,2,5,6,4,3]=>[1,2,3,6,5,4]=>00011=>11000=>2
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>00001=>10000=>1
[1,2,6,3,5,4]=>[1,2,6,3,5,4]=>00011=>11000=>2
[1,2,6,4,3,5]=>[1,2,6,4,3,5]=>00101=>10100=>1
[1,2,6,4,5,3]=>[1,2,6,3,5,4]=>00011=>11000=>2
[1,2,6,5,3,4]=>[1,2,6,5,3,4]=>00011=>11000=>2
[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>00111=>11100=>3
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>01000=>00010=>0
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>01001=>10010=>1
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[1,3,2,5,6,4]=>[1,3,2,4,6,5]=>01001=>10010=>1
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>01001=>10010=>1
[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>01011=>11010=>2
[1,3,4,2,5,6]=>[1,2,4,3,5,6]=>00100=>00100=>0
[1,3,4,2,6,5]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,3,4,5,2,6]=>[1,2,3,5,4,6]=>00010=>01000=>0
[1,3,4,5,6,2]=>[1,2,3,4,6,5]=>00001=>10000=>1
[1,3,4,6,2,5]=>[1,2,4,6,3,5]=>00001=>10000=>1
[1,3,4,6,5,2]=>[1,2,3,6,5,4]=>00011=>11000=>2
[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>00010=>01000=>0
[1,3,5,2,6,4]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,3,5,4,2,6]=>[1,2,5,4,3,6]=>00110=>01100=>0
[1,3,5,4,6,2]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,3,5,6,2,4]=>[1,2,4,6,3,5]=>00001=>10000=>1
[1,3,5,6,4,2]=>[1,2,3,6,5,4]=>00011=>11000=>2
[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>00001=>10000=>1
[1,3,6,2,5,4]=>[1,3,6,2,5,4]=>00011=>11000=>2
[1,3,6,4,2,5]=>[1,2,6,4,3,5]=>00101=>10100=>1
[1,3,6,4,5,2]=>[1,2,6,3,5,4]=>00011=>11000=>2
[1,3,6,5,2,4]=>[1,3,6,5,2,4]=>00011=>11000=>2
[1,3,6,5,4,2]=>[1,2,6,5,4,3]=>00111=>11100=>3
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>00100=>00100=>0
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>00101=>10100=>1
[1,4,2,5,3,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[1,4,2,5,6,3]=>[1,3,2,4,6,5]=>01001=>10010=>1
[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>00101=>10100=>1
[1,4,2,6,5,3]=>[1,3,2,6,5,4]=>01011=>11010=>2
[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>01100=>00110=>0
[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>01101=>10110=>1
[1,4,3,5,2,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[1,4,3,5,6,2]=>[1,3,2,4,6,5]=>01001=>10010=>1
[1,4,3,6,2,5]=>[1,4,3,6,2,5]=>00101=>10100=>1
[1,4,3,6,5,2]=>[1,3,2,6,5,4]=>01011=>11010=>2
[1,4,5,2,3,6]=>[1,3,5,2,4,6]=>00010=>01000=>0
[1,4,5,2,6,3]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,4,5,3,2,6]=>[1,2,5,4,3,6]=>00110=>01100=>0
[1,4,5,3,6,2]=>[1,2,4,3,6,5]=>00101=>10100=>1
[1,4,5,6,2,3]=>[1,2,4,6,3,5]=>00001=>10000=>1
[1,4,5,6,3,2]=>[1,2,3,6,5,4]=>00011=>11000=>2
[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>00001=>10000=>1
[1,4,6,2,5,3]=>[1,3,6,2,5,4]=>00011=>11000=>2
[1,4,6,3,2,5]=>[1,4,6,3,2,5]=>01001=>10010=>1
[1,4,6,3,5,2]=>[1,3,6,2,5,4]=>00011=>11000=>2
[1,4,6,5,2,3]=>[1,3,6,5,2,4]=>00011=>11000=>2
[1,4,6,5,3,2]=>[1,2,6,5,4,3]=>00111=>11100=>3
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>00010=>01000=>0
[1,5,2,3,6,4]=>[1,4,2,3,6,5]=>00101=>10100=>1
[1,5,2,4,3,6]=>[1,5,2,4,3,6]=>00110=>01100=>0
[1,5,2,4,6,3]=>[1,4,2,3,6,5]=>00101=>10100=>1
[1,5,2,6,3,4]=>[1,4,2,6,3,5]=>00101=>10100=>1
[1,5,2,6,4,3]=>[1,3,2,6,5,4]=>01011=>11010=>2
[1,5,3,2,4,6]=>[1,5,3,2,4,6]=>01010=>01010=>0
[1,5,3,2,6,4]=>[1,4,3,2,6,5]=>01101=>10110=>1
[1,5,3,4,2,6]=>[1,5,2,4,3,6]=>00110=>01100=>0
[1,5,3,4,6,2]=>[1,4,2,3,6,5]=>00101=>10100=>1
[1,5,3,6,2,4]=>[1,4,3,6,2,5]=>00101=>10100=>1
[1,5,3,6,4,2]=>[1,3,2,6,5,4]=>01011=>11010=>2
[1,5,4,2,3,6]=>[1,5,4,2,3,6]=>00110=>01100=>0
[1,5,4,2,6,3]=>[1,4,3,2,6,5]=>01101=>10110=>1
[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>01110=>01110=>0
[1,5,4,3,6,2]=>[1,4,3,2,6,5]=>01101=>10110=>1
[1,5,4,6,2,3]=>[1,4,3,6,2,5]=>00101=>10100=>1
[1,5,4,6,3,2]=>[1,3,2,6,5,4]=>01011=>11010=>2
[1,5,6,2,3,4]=>[1,4,6,2,3,5]=>00001=>10000=>1
[1,5,6,2,4,3]=>[1,3,6,2,5,4]=>00011=>11000=>2
[1,5,6,3,2,4]=>[1,4,6,3,2,5]=>01001=>10010=>1
[1,5,6,3,4,2]=>[1,3,6,2,5,4]=>00011=>11000=>2
[1,5,6,4,2,3]=>[1,3,6,5,2,4]=>00011=>11000=>2
[1,5,6,4,3,2]=>[1,2,6,5,4,3]=>00111=>11100=>3
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>00001=>10000=>1
[1,6,2,3,5,4]=>[1,6,2,3,5,4]=>00011=>11000=>2
[1,6,2,4,3,5]=>[1,6,2,4,3,5]=>00101=>10100=>1
[1,6,2,4,5,3]=>[1,6,2,3,5,4]=>00011=>11000=>2
[1,6,2,5,3,4]=>[1,6,2,5,3,4]=>00011=>11000=>2
[1,6,2,5,4,3]=>[1,6,2,5,4,3]=>00111=>11100=>3
[1,6,3,2,4,5]=>[1,6,3,2,4,5]=>01001=>10010=>1
[1,6,3,2,5,4]=>[1,6,3,2,5,4]=>01011=>11010=>2
[1,6,3,4,2,5]=>[1,6,2,4,3,5]=>00101=>10100=>1
[1,6,3,4,5,2]=>[1,6,2,3,5,4]=>00011=>11000=>2
[1,6,3,5,2,4]=>[1,6,3,5,2,4]=>00011=>11000=>2
[1,6,3,5,4,2]=>[1,6,2,5,4,3]=>00111=>11100=>3
[1,6,4,2,3,5]=>[1,6,4,2,3,5]=>00101=>10100=>1
[1,6,4,2,5,3]=>[1,6,3,2,5,4]=>01011=>11010=>2
[1,6,4,3,2,5]=>[1,6,4,3,2,5]=>01101=>10110=>1
[1,6,4,3,5,2]=>[1,6,3,2,5,4]=>01011=>11010=>2
[1,6,4,5,2,3]=>[1,6,3,5,2,4]=>00011=>11000=>2
[1,6,4,5,3,2]=>[1,6,2,5,4,3]=>00111=>11100=>3
[1,6,5,2,3,4]=>[1,6,5,2,3,4]=>00011=>11000=>2
[1,6,5,2,4,3]=>[1,6,5,2,4,3]=>00111=>11100=>3
[1,6,5,3,2,4]=>[1,6,5,3,2,4]=>01011=>11010=>2
[1,6,5,3,4,2]=>[1,6,5,2,4,3]=>00111=>11100=>3
[1,6,5,4,2,3]=>[1,6,5,4,2,3]=>00111=>11100=>3
[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>01111=>11110=>4
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000=>00001=>0
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>10001=>10001=>1
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>10010=>01001=>0
[2,1,3,5,6,4]=>[2,1,3,4,6,5]=>10001=>10001=>1
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>10001=>10001=>1
[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>10011=>11001=>2
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>10100=>00101=>0
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>10101=>10101=>1
[2,1,4,5,3,6]=>[2,1,3,5,4,6]=>10010=>01001=>0
[2,1,4,5,6,3]=>[2,1,3,4,6,5]=>10001=>10001=>1
[2,1,4,6,3,5]=>[2,1,4,6,3,5]=>10001=>10001=>1
[2,1,4,6,5,3]=>[2,1,3,6,5,4]=>10011=>11001=>2
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>10010=>01001=>0
[2,1,5,3,6,4]=>[2,1,4,3,6,5]=>10101=>10101=>1
[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>10110=>01101=>0
[2,1,5,4,6,3]=>[2,1,4,3,6,5]=>10101=>10101=>1
[2,1,5,6,3,4]=>[2,1,4,6,3,5]=>10001=>10001=>1
[2,1,5,6,4,3]=>[2,1,3,6,5,4]=>10011=>11001=>2
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>10001=>10001=>1
[2,1,6,3,5,4]=>[2,1,6,3,5,4]=>10011=>11001=>2
[2,1,6,4,3,5]=>[2,1,6,4,3,5]=>10101=>10101=>1
[2,1,6,4,5,3]=>[2,1,6,3,5,4]=>10011=>11001=>2
[2,1,6,5,3,4]=>[2,1,6,5,3,4]=>10011=>11001=>2
[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>10111=>11101=>3
[2,3,1,4,5,6]=>[1,3,2,4,5,6]=>01000=>00010=>0
[2,3,1,4,6,5]=>[1,3,2,4,6,5]=>01001=>10010=>1
[2,3,1,5,4,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[2,3,1,5,6,4]=>[1,3,2,4,6,5]=>01001=>10010=>1
[2,3,1,6,4,5]=>[1,3,2,6,4,5]=>01001=>10010=>1
[2,3,1,6,5,4]=>[1,3,2,6,5,4]=>01011=>11010=>2
[2,3,4,1,5,6]=>[1,2,4,3,5,6]=>00100=>00100=>0
[2,3,4,1,6,5]=>[1,2,4,3,6,5]=>00101=>10100=>1
[2,3,4,5,1,6]=>[1,2,3,5,4,6]=>00010=>01000=>0
[2,3,4,5,6,1]=>[1,2,3,4,6,5]=>00001=>10000=>1
[2,3,4,6,1,5]=>[1,2,4,6,3,5]=>00001=>10000=>1
[2,3,4,6,5,1]=>[1,2,3,6,5,4]=>00011=>11000=>2
[2,3,5,1,4,6]=>[1,3,5,2,4,6]=>00010=>01000=>0
[2,3,5,1,6,4]=>[1,2,4,3,6,5]=>00101=>10100=>1
[2,3,5,4,1,6]=>[1,2,5,4,3,6]=>00110=>01100=>0
[2,3,5,4,6,1]=>[1,2,4,3,6,5]=>00101=>10100=>1
[2,3,5,6,1,4]=>[1,2,4,6,3,5]=>00001=>10000=>1
[2,3,5,6,4,1]=>[1,2,3,6,5,4]=>00011=>11000=>2
[2,3,6,1,4,5]=>[1,3,6,2,4,5]=>00001=>10000=>1
[2,3,6,1,5,4]=>[1,3,6,2,5,4]=>00011=>11000=>2
[2,3,6,4,1,5]=>[1,2,6,4,3,5]=>00101=>10100=>1
[2,3,6,4,5,1]=>[1,2,6,3,5,4]=>00011=>11000=>2
[2,3,6,5,1,4]=>[1,3,6,5,2,4]=>00011=>11000=>2
[2,3,6,5,4,1]=>[1,2,6,5,4,3]=>00111=>11100=>3
[2,4,1,3,5,6]=>[2,4,1,3,5,6]=>00100=>00100=>0
[2,4,1,3,6,5]=>[2,4,1,3,6,5]=>00101=>10100=>1
[2,4,1,5,3,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[2,4,1,5,6,3]=>[1,3,2,4,6,5]=>01001=>10010=>1
[2,4,1,6,3,5]=>[2,4,1,6,3,5]=>00101=>10100=>1
[2,4,1,6,5,3]=>[1,3,2,6,5,4]=>01011=>11010=>2
[2,4,3,1,5,6]=>[1,4,3,2,5,6]=>01100=>00110=>0
[2,4,3,1,6,5]=>[1,4,3,2,6,5]=>01101=>10110=>1
[2,4,3,5,1,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[2,4,3,5,6,1]=>[1,3,2,4,6,5]=>01001=>10010=>1
[2,4,3,6,1,5]=>[1,4,3,6,2,5]=>00101=>10100=>1
[2,4,3,6,5,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[2,4,5,1,3,6]=>[1,3,5,2,4,6]=>00010=>01000=>0
[2,4,5,1,6,3]=>[1,2,4,3,6,5]=>00101=>10100=>1
[2,4,5,3,1,6]=>[1,2,5,4,3,6]=>00110=>01100=>0
[2,4,5,3,6,1]=>[1,2,4,3,6,5]=>00101=>10100=>1
[2,4,5,6,1,3]=>[1,2,4,6,3,5]=>00001=>10000=>1
[2,4,5,6,3,1]=>[1,2,3,6,5,4]=>00011=>11000=>2
[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>00001=>10000=>1
[2,4,6,1,5,3]=>[1,3,6,2,5,4]=>00011=>11000=>2
[2,4,6,3,1,5]=>[1,4,6,3,2,5]=>01001=>10010=>1
[2,4,6,3,5,1]=>[1,3,6,2,5,4]=>00011=>11000=>2
[2,4,6,5,1,3]=>[1,3,6,5,2,4]=>00011=>11000=>2
[2,4,6,5,3,1]=>[1,2,6,5,4,3]=>00111=>11100=>3
[2,5,1,3,4,6]=>[2,5,1,3,4,6]=>00010=>01000=>0
[2,5,1,3,6,4]=>[2,4,1,3,6,5]=>00101=>10100=>1
[2,5,1,4,3,6]=>[2,5,1,4,3,6]=>00110=>01100=>0
[2,5,1,4,6,3]=>[2,4,1,3,6,5]=>00101=>10100=>1
[2,5,1,6,3,4]=>[2,4,1,6,3,5]=>00101=>10100=>1
[2,5,1,6,4,3]=>[1,3,2,6,5,4]=>01011=>11010=>2
[2,5,3,1,4,6]=>[1,5,3,2,4,6]=>01010=>01010=>0
[2,5,3,1,6,4]=>[1,4,3,2,6,5]=>01101=>10110=>1
[2,5,3,4,1,6]=>[1,5,2,4,3,6]=>00110=>01100=>0
[2,5,3,4,6,1]=>[1,4,2,3,6,5]=>00101=>10100=>1
[2,5,3,6,1,4]=>[1,4,3,6,2,5]=>00101=>10100=>1
[2,5,3,6,4,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[2,5,4,1,3,6]=>[2,5,4,1,3,6]=>00110=>01100=>0
[2,5,4,1,6,3]=>[1,4,3,2,6,5]=>01101=>10110=>1
[2,5,4,3,1,6]=>[1,5,4,3,2,6]=>01110=>01110=>0
[2,5,4,3,6,1]=>[1,4,3,2,6,5]=>01101=>10110=>1
[2,5,4,6,1,3]=>[1,4,3,6,2,5]=>00101=>10100=>1
[2,5,4,6,3,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[2,5,6,1,3,4]=>[2,4,6,1,3,5]=>00001=>10000=>1
[2,5,6,1,4,3]=>[1,3,6,2,5,4]=>00011=>11000=>2
[2,5,6,3,1,4]=>[1,4,6,3,2,5]=>01001=>10010=>1
[2,5,6,3,4,1]=>[1,3,6,2,5,4]=>00011=>11000=>2
[2,5,6,4,1,3]=>[1,3,6,5,2,4]=>00011=>11000=>2
[2,5,6,4,3,1]=>[1,2,6,5,4,3]=>00111=>11100=>3
[2,6,1,3,4,5]=>[2,6,1,3,4,5]=>00001=>10000=>1
[2,6,1,3,5,4]=>[2,6,1,3,5,4]=>00011=>11000=>2
[2,6,1,4,3,5]=>[2,6,1,4,3,5]=>00101=>10100=>1
[2,6,1,4,5,3]=>[2,6,1,3,5,4]=>00011=>11000=>2
[2,6,1,5,3,4]=>[2,6,1,5,3,4]=>00011=>11000=>2
[2,6,1,5,4,3]=>[2,6,1,5,4,3]=>00111=>11100=>3
[2,6,3,1,4,5]=>[1,6,3,2,4,5]=>01001=>10010=>1
[2,6,3,1,5,4]=>[1,6,3,2,5,4]=>01011=>11010=>2
[2,6,3,4,1,5]=>[1,6,2,4,3,5]=>00101=>10100=>1
[2,6,3,4,5,1]=>[1,6,2,3,5,4]=>00011=>11000=>2
[2,6,3,5,1,4]=>[1,6,3,5,2,4]=>00011=>11000=>2
[2,6,3,5,4,1]=>[1,6,2,5,4,3]=>00111=>11100=>3
[2,6,4,1,3,5]=>[2,6,4,1,3,5]=>00101=>10100=>1
[2,6,4,1,5,3]=>[1,6,3,2,5,4]=>01011=>11010=>2
[2,6,4,3,1,5]=>[1,6,4,3,2,5]=>01101=>10110=>1
[2,6,4,3,5,1]=>[1,6,3,2,5,4]=>01011=>11010=>2
[2,6,4,5,1,3]=>[1,6,3,5,2,4]=>00011=>11000=>2
[2,6,4,5,3,1]=>[1,6,2,5,4,3]=>00111=>11100=>3
[2,6,5,1,3,4]=>[2,6,5,1,3,4]=>00011=>11000=>2
[2,6,5,1,4,3]=>[2,6,5,1,4,3]=>00111=>11100=>3
[2,6,5,3,1,4]=>[1,6,5,3,2,4]=>01011=>11010=>2
[2,6,5,3,4,1]=>[1,6,5,2,4,3]=>00111=>11100=>3
[2,6,5,4,1,3]=>[2,6,5,4,1,3]=>00111=>11100=>3
[2,6,5,4,3,1]=>[1,6,5,4,3,2]=>01111=>11110=>4
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>01000=>00010=>0
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>01001=>10010=>1
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>01010=>01010=>0
[3,1,2,5,6,4]=>[3,1,2,4,6,5]=>01001=>10010=>1
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>01001=>10010=>1
[3,1,2,6,5,4]=>[3,1,2,6,5,4]=>01011=>11010=>2
[3,1,4,2,5,6]=>[2,1,4,3,5,6]=>10100=>00101=>0
[3,1,4,2,6,5]=>[2,1,4,3,6,5]=>10101=>10101=>1
[3,1,4,5,2,6]=>[2,1,3,5,4,6]=>10010=>01001=>0
[3,1,4,5,6,2]=>[2,1,3,4,6,5]=>10001=>10001=>1
[3,1,4,6,2,5]=>[2,1,4,6,3,5]=>10001=>10001=>1
[3,1,4,6,5,2]=>[2,1,3,6,5,4]=>10011=>11001=>2
[3,1,5,2,4,6]=>[3,1,5,2,4,6]=>01010=>01010=>0
[3,1,5,2,6,4]=>[2,1,4,3,6,5]=>10101=>10101=>1
[3,1,5,4,2,6]=>[2,1,5,4,3,6]=>10110=>01101=>0
[3,1,5,4,6,2]=>[2,1,4,3,6,5]=>10101=>10101=>1
[3,1,5,6,2,4]=>[2,1,4,6,3,5]=>10001=>10001=>1
[3,1,5,6,4,2]=>[2,1,3,6,5,4]=>10011=>11001=>2
[3,1,6,2,4,5]=>[3,1,6,2,4,5]=>01001=>10010=>1
[3,1,6,2,5,4]=>[3,1,6,2,5,4]=>01011=>11010=>2
[3,1,6,4,2,5]=>[2,1,6,4,3,5]=>10101=>10101=>1
[3,1,6,4,5,2]=>[2,1,6,3,5,4]=>10011=>11001=>2
[3,1,6,5,2,4]=>[3,1,6,5,2,4]=>01011=>11010=>2
[3,1,6,5,4,2]=>[2,1,6,5,4,3]=>10111=>11101=>3
[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000=>00011=>0
[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>11001=>10011=>1
[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>11010=>01011=>0
[3,2,1,5,6,4]=>[3,2,1,4,6,5]=>11001=>10011=>1
[3,2,1,6,4,5]=>[3,2,1,6,4,5]=>11001=>10011=>1
[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>11011=>11011=>2
[3,2,4,1,5,6]=>[2,1,4,3,5,6]=>10100=>00101=>0
[3,2,4,1,6,5]=>[2,1,4,3,6,5]=>10101=>10101=>1
[3,2,4,5,1,6]=>[2,1,3,5,4,6]=>10010=>01001=>0
[3,2,4,5,6,1]=>[2,1,3,4,6,5]=>10001=>10001=>1
[3,2,4,6,1,5]=>[2,1,4,6,3,5]=>10001=>10001=>1
[3,2,4,6,5,1]=>[2,1,3,6,5,4]=>10011=>11001=>2
[3,2,5,1,4,6]=>[3,2,5,1,4,6]=>01010=>01010=>0
[3,2,5,1,6,4]=>[2,1,4,3,6,5]=>10101=>10101=>1
[3,2,5,4,1,6]=>[2,1,5,4,3,6]=>10110=>01101=>0
[3,2,5,4,6,1]=>[2,1,4,3,6,5]=>10101=>10101=>1
[3,2,5,6,1,4]=>[2,1,4,6,3,5]=>10001=>10001=>1
[3,2,5,6,4,1]=>[2,1,3,6,5,4]=>10011=>11001=>2
[3,2,6,1,4,5]=>[3,2,6,1,4,5]=>01001=>10010=>1
[3,2,6,1,5,4]=>[3,2,6,1,5,4]=>01011=>11010=>2
[3,2,6,4,1,5]=>[2,1,6,4,3,5]=>10101=>10101=>1
[3,2,6,4,5,1]=>[2,1,6,3,5,4]=>10011=>11001=>2
[3,2,6,5,1,4]=>[3,2,6,5,1,4]=>01011=>11010=>2
[3,2,6,5,4,1]=>[2,1,6,5,4,3]=>10111=>11101=>3
[3,4,1,2,5,6]=>[2,4,1,3,5,6]=>00100=>00100=>0
[3,4,1,2,6,5]=>[2,4,1,3,6,5]=>00101=>10100=>1
[3,4,1,5,2,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[3,4,1,5,6,2]=>[1,3,2,4,6,5]=>01001=>10010=>1
[3,4,1,6,2,5]=>[2,4,1,6,3,5]=>00101=>10100=>1
[3,4,1,6,5,2]=>[1,3,2,6,5,4]=>01011=>11010=>2
[3,4,2,1,5,6]=>[1,4,3,2,5,6]=>01100=>00110=>0
[3,4,2,1,6,5]=>[1,4,3,2,6,5]=>01101=>10110=>1
[3,4,2,5,1,6]=>[1,3,2,5,4,6]=>01010=>01010=>0
[3,4,2,5,6,1]=>[1,3,2,4,6,5]=>01001=>10010=>1
[3,4,2,6,1,5]=>[1,4,3,6,2,5]=>00101=>10100=>1
[3,4,2,6,5,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[3,4,5,1,2,6]=>[1,3,5,2,4,6]=>00010=>01000=>0
[3,4,5,1,6,2]=>[1,2,4,3,6,5]=>00101=>10100=>1
[3,4,5,2,1,6]=>[1,2,5,4,3,6]=>00110=>01100=>0
[3,4,5,2,6,1]=>[1,2,4,3,6,5]=>00101=>10100=>1
[3,4,5,6,1,2]=>[1,2,4,6,3,5]=>00001=>10000=>1
[3,4,5,6,2,1]=>[1,2,3,6,5,4]=>00011=>11000=>2
[3,4,6,1,2,5]=>[2,4,6,1,3,5]=>00001=>10000=>1
[3,4,6,1,5,2]=>[1,3,6,2,5,4]=>00011=>11000=>2
[3,4,6,2,1,5]=>[1,4,6,3,2,5]=>01001=>10010=>1
[3,4,6,2,5,1]=>[1,3,6,2,5,4]=>00011=>11000=>2
[3,4,6,5,1,2]=>[1,3,6,5,2,4]=>00011=>11000=>2
[3,4,6,5,2,1]=>[1,2,6,5,4,3]=>00111=>11100=>3
[3,5,1,2,4,6]=>[3,5,1,2,4,6]=>00010=>01000=>0
[3,5,1,2,6,4]=>[2,4,1,3,6,5]=>00101=>10100=>1
[3,5,1,4,2,6]=>[2,5,1,4,3,6]=>00110=>01100=>0
[3,5,1,4,6,2]=>[2,4,1,3,6,5]=>00101=>10100=>1
[3,5,1,6,2,4]=>[2,4,1,6,3,5]=>00101=>10100=>1
[3,5,1,6,4,2]=>[1,3,2,6,5,4]=>01011=>11010=>2
[3,5,2,1,4,6]=>[3,5,2,1,4,6]=>10010=>01001=>0
[3,5,2,1,6,4]=>[1,4,3,2,6,5]=>01101=>10110=>1
[3,5,2,4,1,6]=>[2,5,1,4,3,6]=>00110=>01100=>0
[3,5,2,4,6,1]=>[2,4,1,3,6,5]=>00101=>10100=>1
[3,5,2,6,1,4]=>[1,4,3,6,2,5]=>00101=>10100=>1
[3,5,2,6,4,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[3,5,4,1,2,6]=>[2,5,4,1,3,6]=>00110=>01100=>0
[3,5,4,1,6,2]=>[1,4,3,2,6,5]=>01101=>10110=>1
[3,5,4,2,1,6]=>[1,5,4,3,2,6]=>01110=>01110=>0
[3,5,4,2,6,1]=>[1,4,3,2,6,5]=>01101=>10110=>1
[3,5,4,6,1,2]=>[1,4,3,6,2,5]=>00101=>10100=>1
[3,5,4,6,2,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[3,5,6,1,2,4]=>[2,4,6,1,3,5]=>00001=>10000=>1
[3,5,6,1,4,2]=>[1,3,6,2,5,4]=>00011=>11000=>2
[3,5,6,2,1,4]=>[1,4,6,3,2,5]=>01001=>10010=>1
[3,5,6,2,4,1]=>[1,3,6,2,5,4]=>00011=>11000=>2
[3,5,6,4,1,2]=>[1,3,6,5,2,4]=>00011=>11000=>2
[3,5,6,4,2,1]=>[1,2,6,5,4,3]=>00111=>11100=>3
[3,6,1,2,4,5]=>[3,6,1,2,4,5]=>00001=>10000=>1
[3,6,1,2,5,4]=>[3,6,1,2,5,4]=>00011=>11000=>2
[3,6,1,4,2,5]=>[2,6,1,4,3,5]=>00101=>10100=>1
[3,6,1,4,5,2]=>[2,6,1,3,5,4]=>00011=>11000=>2
[3,6,1,5,2,4]=>[3,6,1,5,2,4]=>00011=>11000=>2
[3,6,1,5,4,2]=>[2,6,1,5,4,3]=>00111=>11100=>3
[3,6,2,1,4,5]=>[3,6,2,1,4,5]=>10001=>10001=>1
[3,6,2,1,5,4]=>[3,6,2,1,5,4]=>10011=>11001=>2
[3,6,2,4,1,5]=>[2,6,1,4,3,5]=>00101=>10100=>1
[3,6,2,4,5,1]=>[2,6,1,3,5,4]=>00011=>11000=>2
[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>00011=>11000=>2
[3,6,2,5,4,1]=>[2,6,1,5,4,3]=>00111=>11100=>3
[3,6,4,1,2,5]=>[2,6,4,1,3,5]=>00101=>10100=>1
[3,6,4,1,5,2]=>[1,6,3,2,5,4]=>01011=>11010=>2
[3,6,4,2,1,5]=>[1,6,4,3,2,5]=>01101=>10110=>1
[3,6,4,2,5,1]=>[1,6,3,2,5,4]=>01011=>11010=>2
[3,6,4,5,1,2]=>[1,6,3,5,2,4]=>00011=>11000=>2
[3,6,4,5,2,1]=>[1,6,2,5,4,3]=>00111=>11100=>3
[3,6,5,1,2,4]=>[3,6,5,1,2,4]=>00011=>11000=>2
[3,6,5,1,4,2]=>[2,6,5,1,4,3]=>00111=>11100=>3
[3,6,5,2,1,4]=>[3,6,5,2,1,4]=>10011=>11001=>2
[3,6,5,2,4,1]=>[2,6,5,1,4,3]=>00111=>11100=>3
[3,6,5,4,1,2]=>[2,6,5,4,1,3]=>00111=>11100=>3
[3,6,5,4,2,1]=>[1,6,5,4,3,2]=>01111=>11110=>4
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>00100=>00100=>0
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>00101=>10100=>1
[4,1,2,5,3,6]=>[3,1,2,5,4,6]=>01010=>01010=>0
[4,1,2,5,6,3]=>[3,1,2,4,6,5]=>01001=>10010=>1
[4,1,2,6,3,5]=>[4,1,2,6,3,5]=>00101=>10100=>1
[4,1,2,6,5,3]=>[3,1,2,6,5,4]=>01011=>11010=>2
[4,1,3,2,5,6]=>[4,1,3,2,5,6]=>01100=>00110=>0
[4,1,3,2,6,5]=>[4,1,3,2,6,5]=>01101=>10110=>1
[4,1,3,5,2,6]=>[3,1,2,5,4,6]=>01010=>01010=>0
[4,1,3,5,6,2]=>[3,1,2,4,6,5]=>01001=>10010=>1
[4,1,3,6,2,5]=>[4,1,3,6,2,5]=>00101=>10100=>1
[4,1,3,6,5,2]=>[3,1,2,6,5,4]=>01011=>11010=>2
[4,1,5,2,3,6]=>[3,1,5,2,4,6]=>01010=>01010=>0
[4,1,5,2,6,3]=>[2,1,4,3,6,5]=>10101=>10101=>1
[4,1,5,3,2,6]=>[2,1,5,4,3,6]=>10110=>01101=>0
[4,1,5,3,6,2]=>[2,1,4,3,6,5]=>10101=>10101=>1
[4,1,5,6,2,3]=>[2,1,4,6,3,5]=>10001=>10001=>1
[4,1,5,6,3,2]=>[2,1,3,6,5,4]=>10011=>11001=>2
[4,1,6,2,3,5]=>[4,1,6,2,3,5]=>00101=>10100=>1
[4,1,6,2,5,3]=>[3,1,6,2,5,4]=>01011=>11010=>2
[4,1,6,3,2,5]=>[4,1,6,3,2,5]=>01101=>10110=>1
[4,1,6,3,5,2]=>[3,1,6,2,5,4]=>01011=>11010=>2
[4,1,6,5,2,3]=>[3,1,6,5,2,4]=>01011=>11010=>2
[4,1,6,5,3,2]=>[2,1,6,5,4,3]=>10111=>11101=>3
[4,2,1,3,5,6]=>[4,2,1,3,5,6]=>10100=>00101=>0
[4,2,1,3,6,5]=>[4,2,1,3,6,5]=>10101=>10101=>1
[4,2,1,5,3,6]=>[3,2,1,5,4,6]=>11010=>01011=>0
[4,2,1,5,6,3]=>[3,2,1,4,6,5]=>11001=>10011=>1
[4,2,1,6,3,5]=>[4,2,1,6,3,5]=>10101=>10101=>1
[4,2,1,6,5,3]=>[3,2,1,6,5,4]=>11011=>11011=>2
[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>01100=>00110=>0
[4,2,3,1,6,5]=>[4,1,3,2,6,5]=>01101=>10110=>1
[4,2,3,5,1,6]=>[3,1,2,5,4,6]=>01010=>01010=>0
[4,2,3,5,6,1]=>[3,1,2,4,6,5]=>01001=>10010=>1
[4,2,3,6,1,5]=>[4,1,3,6,2,5]=>00101=>10100=>1
[4,2,3,6,5,1]=>[3,1,2,6,5,4]=>01011=>11010=>2
[4,2,5,1,3,6]=>[3,2,5,1,4,6]=>01010=>01010=>0
[4,2,5,1,6,3]=>[2,1,4,3,6,5]=>10101=>10101=>1
[4,2,5,3,1,6]=>[2,1,5,4,3,6]=>10110=>01101=>0
[4,2,5,3,6,1]=>[2,1,4,3,6,5]=>10101=>10101=>1
[4,2,5,6,1,3]=>[2,1,4,6,3,5]=>10001=>10001=>1
[4,2,5,6,3,1]=>[2,1,3,6,5,4]=>10011=>11001=>2
[4,2,6,1,3,5]=>[4,2,6,1,3,5]=>00101=>10100=>1
[4,2,6,1,5,3]=>[3,2,6,1,5,4]=>01011=>11010=>2
[4,2,6,3,1,5]=>[4,1,6,3,2,5]=>01101=>10110=>1
[4,2,6,3,5,1]=>[3,1,6,2,5,4]=>01011=>11010=>2
[4,2,6,5,1,3]=>[3,2,6,5,1,4]=>01011=>11010=>2
[4,2,6,5,3,1]=>[2,1,6,5,4,3]=>10111=>11101=>3
[4,3,1,2,5,6]=>[4,3,1,2,5,6]=>01100=>00110=>0
[4,3,1,2,6,5]=>[4,3,1,2,6,5]=>01101=>10110=>1
[4,3,1,5,2,6]=>[3,2,1,5,4,6]=>11010=>01011=>0
[4,3,1,5,6,2]=>[3,2,1,4,6,5]=>11001=>10011=>1
[4,3,1,6,2,5]=>[4,3,1,6,2,5]=>01101=>10110=>1
[4,3,1,6,5,2]=>[3,2,1,6,5,4]=>11011=>11011=>2
[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100=>00111=>0
[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>11101=>10111=>1
[4,3,2,5,1,6]=>[3,2,1,5,4,6]=>11010=>01011=>0
[4,3,2,5,6,1]=>[3,2,1,4,6,5]=>11001=>10011=>1
[4,3,2,6,1,5]=>[4,3,2,6,1,5]=>01101=>10110=>1
[4,3,2,6,5,1]=>[3,2,1,6,5,4]=>11011=>11011=>2
[4,3,5,1,2,6]=>[3,2,5,1,4,6]=>01010=>01010=>0
[4,3,5,1,6,2]=>[2,1,4,3,6,5]=>10101=>10101=>1
[4,3,5,2,1,6]=>[2,1,5,4,3,6]=>10110=>01101=>0
[4,3,5,2,6,1]=>[2,1,4,3,6,5]=>10101=>10101=>1
[4,3,5,6,1,2]=>[2,1,4,6,3,5]=>10001=>10001=>1
[4,3,5,6,2,1]=>[2,1,3,6,5,4]=>10011=>11001=>2
[4,3,6,1,2,5]=>[4,3,6,1,2,5]=>00101=>10100=>1
[4,3,6,1,5,2]=>[3,2,6,1,5,4]=>01011=>11010=>2
[4,3,6,2,1,5]=>[4,3,6,2,1,5]=>10101=>10101=>1
[4,3,6,2,5,1]=>[3,2,6,1,5,4]=>01011=>11010=>2
[4,3,6,5,1,2]=>[3,2,6,5,1,4]=>01011=>11010=>2
[4,3,6,5,2,1]=>[2,1,6,5,4,3]=>10111=>11101=>3
[4,5,1,2,3,6]=>[3,5,1,2,4,6]=>00010=>01000=>0
[4,5,1,2,6,3]=>[2,4,1,3,6,5]=>00101=>10100=>1
[4,5,1,3,2,6]=>[2,5,1,4,3,6]=>00110=>01100=>0
[4,5,1,3,6,2]=>[2,4,1,3,6,5]=>00101=>10100=>1
[4,5,1,6,2,3]=>[2,4,1,6,3,5]=>00101=>10100=>1
[4,5,1,6,3,2]=>[1,3,2,6,5,4]=>01011=>11010=>2
[4,5,2,1,3,6]=>[3,5,2,1,4,6]=>10010=>01001=>0
[4,5,2,1,6,3]=>[1,4,3,2,6,5]=>01101=>10110=>1
[4,5,2,3,1,6]=>[2,5,1,4,3,6]=>00110=>01100=>0
[4,5,2,3,6,1]=>[2,4,1,3,6,5]=>00101=>10100=>1
[4,5,2,6,1,3]=>[1,4,3,6,2,5]=>00101=>10100=>1
[4,5,2,6,3,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[4,5,3,1,2,6]=>[2,5,4,1,3,6]=>00110=>01100=>0
[4,5,3,1,6,2]=>[1,4,3,2,6,5]=>01101=>10110=>1
[4,5,3,2,1,6]=>[1,5,4,3,2,6]=>01110=>01110=>0
[4,5,3,2,6,1]=>[1,4,3,2,6,5]=>01101=>10110=>1
[4,5,3,6,1,2]=>[1,4,3,6,2,5]=>00101=>10100=>1
[4,5,3,6,2,1]=>[1,3,2,6,5,4]=>01011=>11010=>2
[4,5,6,1,2,3]=>[2,4,6,1,3,5]=>00001=>10000=>1
[4,5,6,1,3,2]=>[1,3,6,2,5,4]=>00011=>11000=>2
[4,5,6,2,1,3]=>[1,4,6,3,2,5]=>01001=>10010=>1
[4,5,6,2,3,1]=>[1,3,6,2,5,4]=>00011=>11000=>2
[4,5,6,3,1,2]=>[1,3,6,5,2,4]=>00011=>11000=>2
[4,5,6,3,2,1]=>[1,2,6,5,4,3]=>00111=>11100=>3
[4,6,1,2,3,5]=>[4,6,1,2,3,5]=>00001=>10000=>1
[4,6,1,2,5,3]=>[3,6,1,2,5,4]=>00011=>11000=>2
[4,6,1,3,2,5]=>[4,6,1,3,2,5]=>01001=>10010=>1
[4,6,1,3,5,2]=>[3,6,1,2,5,4]=>00011=>11000=>2
[4,6,1,5,2,3]=>[3,6,1,5,2,4]=>00011=>11000=>2
[4,6,1,5,3,2]=>[2,6,1,5,4,3]=>00111=>11100=>3
[4,6,2,1,3,5]=>[4,6,2,1,3,5]=>10001=>10001=>1
[4,6,2,1,5,3]=>[3,6,2,1,5,4]=>10011=>11001=>2
[4,6,2,3,1,5]=>[4,6,1,3,2,5]=>01001=>10010=>1
[4,6,2,3,5,1]=>[3,6,1,2,5,4]=>00011=>11000=>2
[4,6,2,5,1,3]=>[3,6,2,5,1,4]=>00011=>11000=>2
[4,6,2,5,3,1]=>[2,6,1,5,4,3]=>00111=>11100=>3
[4,6,3,1,2,5]=>[4,6,3,1,2,5]=>01001=>10010=>1
[4,6,3,1,5,2]=>[3,6,2,1,5,4]=>10011=>11001=>2
[4,6,3,2,1,5]=>[4,6,3,2,1,5]=>11001=>10011=>1
[4,6,3,2,5,1]=>[3,6,2,1,5,4]=>10011=>11001=>2
[4,6,3,5,1,2]=>[3,6,2,5,1,4]=>00011=>11000=>2
[4,6,3,5,2,1]=>[2,6,1,5,4,3]=>00111=>11100=>3
[4,6,5,1,2,3]=>[3,6,5,1,2,4]=>00011=>11000=>2
[4,6,5,1,3,2]=>[2,6,5,1,4,3]=>00111=>11100=>3
[4,6,5,2,1,3]=>[3,6,5,2,1,4]=>10011=>11001=>2
[4,6,5,2,3,1]=>[2,6,5,1,4,3]=>00111=>11100=>3
[4,6,5,3,1,2]=>[2,6,5,4,1,3]=>00111=>11100=>3
[4,6,5,3,2,1]=>[1,6,5,4,3,2]=>01111=>11110=>4
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>00010=>01000=>0
[5,1,2,3,6,4]=>[4,1,2,3,6,5]=>00101=>10100=>1
[5,1,2,4,3,6]=>[5,1,2,4,3,6]=>00110=>01100=>0
[5,1,2,4,6,3]=>[4,1,2,3,6,5]=>00101=>10100=>1
[5,1,2,6,3,4]=>[4,1,2,6,3,5]=>00101=>10100=>1
[5,1,2,6,4,3]=>[3,1,2,6,5,4]=>01011=>11010=>2
[5,1,3,2,4,6]=>[5,1,3,2,4,6]=>01010=>01010=>0
[5,1,3,2,6,4]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,1,3,4,2,6]=>[5,1,2,4,3,6]=>00110=>01100=>0
[5,1,3,4,6,2]=>[4,1,2,3,6,5]=>00101=>10100=>1
[5,1,3,6,2,4]=>[4,1,3,6,2,5]=>00101=>10100=>1
[5,1,3,6,4,2]=>[3,1,2,6,5,4]=>01011=>11010=>2
[5,1,4,2,3,6]=>[5,1,4,2,3,6]=>00110=>01100=>0
[5,1,4,2,6,3]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,1,4,3,2,6]=>[5,1,4,3,2,6]=>01110=>01110=>0
[5,1,4,3,6,2]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,1,4,6,2,3]=>[4,1,3,6,2,5]=>00101=>10100=>1
[5,1,4,6,3,2]=>[3,1,2,6,5,4]=>01011=>11010=>2
[5,1,6,2,3,4]=>[4,1,6,2,3,5]=>00101=>10100=>1
[5,1,6,2,4,3]=>[3,1,6,2,5,4]=>01011=>11010=>2
[5,1,6,3,2,4]=>[4,1,6,3,2,5]=>01101=>10110=>1
[5,1,6,3,4,2]=>[3,1,6,2,5,4]=>01011=>11010=>2
[5,1,6,4,2,3]=>[3,1,6,5,2,4]=>01011=>11010=>2
[5,1,6,4,3,2]=>[2,1,6,5,4,3]=>10111=>11101=>3
[5,2,1,3,4,6]=>[5,2,1,3,4,6]=>10010=>01001=>0
[5,2,1,3,6,4]=>[4,2,1,3,6,5]=>10101=>10101=>1
[5,2,1,4,3,6]=>[5,2,1,4,3,6]=>10110=>01101=>0
[5,2,1,4,6,3]=>[4,2,1,3,6,5]=>10101=>10101=>1
[5,2,1,6,3,4]=>[4,2,1,6,3,5]=>10101=>10101=>1
[5,2,1,6,4,3]=>[3,2,1,6,5,4]=>11011=>11011=>2
[5,2,3,1,4,6]=>[5,1,3,2,4,6]=>01010=>01010=>0
[5,2,3,1,6,4]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>00110=>01100=>0
[5,2,3,4,6,1]=>[4,1,2,3,6,5]=>00101=>10100=>1
[5,2,3,6,1,4]=>[4,1,3,6,2,5]=>00101=>10100=>1
[5,2,3,6,4,1]=>[3,1,2,6,5,4]=>01011=>11010=>2
[5,2,4,1,3,6]=>[5,2,4,1,3,6]=>00110=>01100=>0
[5,2,4,1,6,3]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,2,4,3,1,6]=>[5,1,4,3,2,6]=>01110=>01110=>0
[5,2,4,3,6,1]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,2,4,6,1,3]=>[4,1,3,6,2,5]=>00101=>10100=>1
[5,2,4,6,3,1]=>[3,1,2,6,5,4]=>01011=>11010=>2
[5,2,6,1,3,4]=>[4,2,6,1,3,5]=>00101=>10100=>1
[5,2,6,1,4,3]=>[3,2,6,1,5,4]=>01011=>11010=>2
[5,2,6,3,1,4]=>[4,1,6,3,2,5]=>01101=>10110=>1
[5,2,6,3,4,1]=>[3,1,6,2,5,4]=>01011=>11010=>2
[5,2,6,4,1,3]=>[3,2,6,5,1,4]=>01011=>11010=>2
[5,2,6,4,3,1]=>[2,1,6,5,4,3]=>10111=>11101=>3
[5,3,1,2,4,6]=>[5,3,1,2,4,6]=>01010=>01010=>0
[5,3,1,2,6,4]=>[4,3,1,2,6,5]=>01101=>10110=>1
[5,3,1,4,2,6]=>[5,2,1,4,3,6]=>10110=>01101=>0
[5,3,1,4,6,2]=>[4,2,1,3,6,5]=>10101=>10101=>1
[5,3,1,6,2,4]=>[4,3,1,6,2,5]=>01101=>10110=>1
[5,3,1,6,4,2]=>[3,2,1,6,5,4]=>11011=>11011=>2
[5,3,2,1,4,6]=>[5,3,2,1,4,6]=>11010=>01011=>0
[5,3,2,1,6,4]=>[4,3,2,1,6,5]=>11101=>10111=>1
[5,3,2,4,1,6]=>[5,2,1,4,3,6]=>10110=>01101=>0
[5,3,2,4,6,1]=>[4,2,1,3,6,5]=>10101=>10101=>1
[5,3,2,6,1,4]=>[4,3,2,6,1,5]=>01101=>10110=>1
[5,3,2,6,4,1]=>[3,2,1,6,5,4]=>11011=>11011=>2
[5,3,4,1,2,6]=>[5,2,4,1,3,6]=>00110=>01100=>0
[5,3,4,1,6,2]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,3,4,2,1,6]=>[5,1,4,3,2,6]=>01110=>01110=>0
[5,3,4,2,6,1]=>[4,1,3,2,6,5]=>01101=>10110=>1
[5,3,4,6,1,2]=>[4,1,3,6,2,5]=>00101=>10100=>1
[5,3,4,6,2,1]=>[3,1,2,6,5,4]=>01011=>11010=>2
[5,3,6,1,2,4]=>[4,3,6,1,2,5]=>00101=>10100=>1
[5,3,6,1,4,2]=>[3,2,6,1,5,4]=>01011=>11010=>2
[5,3,6,2,1,4]=>[4,3,6,2,1,5]=>10101=>10101=>1
[5,3,6,2,4,1]=>[3,2,6,1,5,4]=>01011=>11010=>2
[5,3,6,4,1,2]=>[3,2,6,5,1,4]=>01011=>11010=>2
[5,3,6,4,2,1]=>[2,1,6,5,4,3]=>10111=>11101=>3
[5,4,1,2,3,6]=>[5,4,1,2,3,6]=>00110=>01100=>0
[5,4,1,2,6,3]=>[4,3,1,2,6,5]=>01101=>10110=>1
[5,4,1,3,2,6]=>[5,4,1,3,2,6]=>01110=>01110=>0
[5,4,1,3,6,2]=>[4,3,1,2,6,5]=>01101=>10110=>1
[5,4,1,6,2,3]=>[4,3,1,6,2,5]=>01101=>10110=>1
[5,4,1,6,3,2]=>[3,2,1,6,5,4]=>11011=>11011=>2
[5,4,2,1,3,6]=>[5,4,2,1,3,6]=>10110=>01101=>0
[5,4,2,1,6,3]=>[4,3,2,1,6,5]=>11101=>10111=>1
[5,4,2,3,1,6]=>[5,4,1,3,2,6]=>01110=>01110=>0
[5,4,2,3,6,1]=>[4,3,1,2,6,5]=>01101=>10110=>1
[5,4,2,6,1,3]=>[4,3,2,6,1,5]=>01101=>10110=>1
[5,4,2,6,3,1]=>[3,2,1,6,5,4]=>11011=>11011=>2
[5,4,3,1,2,6]=>[5,4,3,1,2,6]=>01110=>01110=>0
[5,4,3,1,6,2]=>[4,3,2,1,6,5]=>11101=>10111=>1
[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110=>01111=>0
[5,4,3,2,6,1]=>[4,3,2,1,6,5]=>11101=>10111=>1
[5,4,3,6,1,2]=>[4,3,2,6,1,5]=>01101=>10110=>1
[5,4,3,6,2,1]=>[3,2,1,6,5,4]=>11011=>11011=>2
[5,4,6,1,2,3]=>[4,3,6,1,2,5]=>00101=>10100=>1
[5,4,6,1,3,2]=>[3,2,6,1,5,4]=>01011=>11010=>2
[5,4,6,2,1,3]=>[4,3,6,2,1,5]=>10101=>10101=>1
[5,4,6,2,3,1]=>[3,2,6,1,5,4]=>01011=>11010=>2
[5,4,6,3,1,2]=>[3,2,6,5,1,4]=>01011=>11010=>2
[5,4,6,3,2,1]=>[2,1,6,5,4,3]=>10111=>11101=>3
[5,6,1,2,3,4]=>[4,6,1,2,3,5]=>00001=>10000=>1
[5,6,1,2,4,3]=>[3,6,1,2,5,4]=>00011=>11000=>2
[5,6,1,3,2,4]=>[4,6,1,3,2,5]=>01001=>10010=>1
[5,6,1,3,4,2]=>[3,6,1,2,5,4]=>00011=>11000=>2
[5,6,1,4,2,3]=>[3,6,1,5,2,4]=>00011=>11000=>2
[5,6,1,4,3,2]=>[2,6,1,5,4,3]=>00111=>11100=>3
[5,6,2,1,3,4]=>[4,6,2,1,3,5]=>10001=>10001=>1
[5,6,2,1,4,3]=>[3,6,2,1,5,4]=>10011=>11001=>2
[5,6,2,3,1,4]=>[4,6,1,3,2,5]=>01001=>10010=>1
[5,6,2,3,4,1]=>[3,6,1,2,5,4]=>00011=>11000=>2
[5,6,2,4,1,3]=>[3,6,2,5,1,4]=>00011=>11000=>2
[5,6,2,4,3,1]=>[2,6,1,5,4,3]=>00111=>11100=>3
[5,6,3,1,2,4]=>[4,6,3,1,2,5]=>01001=>10010=>1
[5,6,3,1,4,2]=>[3,6,2,1,5,4]=>10011=>11001=>2
[5,6,3,2,1,4]=>[4,6,3,2,1,5]=>11001=>10011=>1
[5,6,3,2,4,1]=>[3,6,2,1,5,4]=>10011=>11001=>2
[5,6,3,4,1,2]=>[3,6,2,5,1,4]=>00011=>11000=>2
[5,6,3,4,2,1]=>[2,6,1,5,4,3]=>00111=>11100=>3
[5,6,4,1,2,3]=>[3,6,5,1,2,4]=>00011=>11000=>2
[5,6,4,1,3,2]=>[2,6,5,1,4,3]=>00111=>11100=>3
[5,6,4,2,1,3]=>[3,6,5,2,1,4]=>10011=>11001=>2
[5,6,4,2,3,1]=>[2,6,5,1,4,3]=>00111=>11100=>3
[5,6,4,3,1,2]=>[2,6,5,4,1,3]=>00111=>11100=>3
[5,6,4,3,2,1]=>[1,6,5,4,3,2]=>01111=>11110=>4
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>00001=>10000=>1
[6,1,2,3,5,4]=>[6,1,2,3,5,4]=>00011=>11000=>2
[6,1,2,4,3,5]=>[6,1,2,4,3,5]=>00101=>10100=>1
[6,1,2,4,5,3]=>[6,1,2,3,5,4]=>00011=>11000=>2
[6,1,2,5,3,4]=>[6,1,2,5,3,4]=>00011=>11000=>2
[6,1,2,5,4,3]=>[6,1,2,5,4,3]=>00111=>11100=>3
[6,1,3,2,4,5]=>[6,1,3,2,4,5]=>01001=>10010=>1
[6,1,3,2,5,4]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,1,3,4,2,5]=>[6,1,2,4,3,5]=>00101=>10100=>1
[6,1,3,4,5,2]=>[6,1,2,3,5,4]=>00011=>11000=>2
[6,1,3,5,2,4]=>[6,1,3,5,2,4]=>00011=>11000=>2
[6,1,3,5,4,2]=>[6,1,2,5,4,3]=>00111=>11100=>3
[6,1,4,2,3,5]=>[6,1,4,2,3,5]=>00101=>10100=>1
[6,1,4,2,5,3]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,1,4,3,2,5]=>[6,1,4,3,2,5]=>01101=>10110=>1
[6,1,4,3,5,2]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,1,4,5,2,3]=>[6,1,3,5,2,4]=>00011=>11000=>2
[6,1,4,5,3,2]=>[6,1,2,5,4,3]=>00111=>11100=>3
[6,1,5,2,3,4]=>[6,1,5,2,3,4]=>00011=>11000=>2
[6,1,5,2,4,3]=>[6,1,5,2,4,3]=>00111=>11100=>3
[6,1,5,3,2,4]=>[6,1,5,3,2,4]=>01011=>11010=>2
[6,1,5,3,4,2]=>[6,1,5,2,4,3]=>00111=>11100=>3
[6,1,5,4,2,3]=>[6,1,5,4,2,3]=>00111=>11100=>3
[6,1,5,4,3,2]=>[6,1,5,4,3,2]=>01111=>11110=>4
[6,2,1,3,4,5]=>[6,2,1,3,4,5]=>10001=>10001=>1
[6,2,1,3,5,4]=>[6,2,1,3,5,4]=>10011=>11001=>2
[6,2,1,4,3,5]=>[6,2,1,4,3,5]=>10101=>10101=>1
[6,2,1,4,5,3]=>[6,2,1,3,5,4]=>10011=>11001=>2
[6,2,1,5,3,4]=>[6,2,1,5,3,4]=>10011=>11001=>2
[6,2,1,5,4,3]=>[6,2,1,5,4,3]=>10111=>11101=>3
[6,2,3,1,4,5]=>[6,1,3,2,4,5]=>01001=>10010=>1
[6,2,3,1,5,4]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,2,3,4,1,5]=>[6,1,2,4,3,5]=>00101=>10100=>1
[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>00011=>11000=>2
[6,2,3,5,1,4]=>[6,1,3,5,2,4]=>00011=>11000=>2
[6,2,3,5,4,1]=>[6,1,2,5,4,3]=>00111=>11100=>3
[6,2,4,1,3,5]=>[6,2,4,1,3,5]=>00101=>10100=>1
[6,2,4,1,5,3]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,2,4,3,1,5]=>[6,1,4,3,2,5]=>01101=>10110=>1
[6,2,4,3,5,1]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,2,4,5,1,3]=>[6,1,3,5,2,4]=>00011=>11000=>2
[6,2,4,5,3,1]=>[6,1,2,5,4,3]=>00111=>11100=>3
[6,2,5,1,3,4]=>[6,2,5,1,3,4]=>00011=>11000=>2
[6,2,5,1,4,3]=>[6,2,5,1,4,3]=>00111=>11100=>3
[6,2,5,3,1,4]=>[6,1,5,3,2,4]=>01011=>11010=>2
[6,2,5,3,4,1]=>[6,1,5,2,4,3]=>00111=>11100=>3
[6,2,5,4,1,3]=>[6,2,5,4,1,3]=>00111=>11100=>3
[6,2,5,4,3,1]=>[6,1,5,4,3,2]=>01111=>11110=>4
[6,3,1,2,4,5]=>[6,3,1,2,4,5]=>01001=>10010=>1
[6,3,1,2,5,4]=>[6,3,1,2,5,4]=>01011=>11010=>2
[6,3,1,4,2,5]=>[6,2,1,4,3,5]=>10101=>10101=>1
[6,3,1,4,5,2]=>[6,2,1,3,5,4]=>10011=>11001=>2
[6,3,1,5,2,4]=>[6,3,1,5,2,4]=>01011=>11010=>2
[6,3,1,5,4,2]=>[6,2,1,5,4,3]=>10111=>11101=>3
[6,3,2,1,4,5]=>[6,3,2,1,4,5]=>11001=>10011=>1
[6,3,2,1,5,4]=>[6,3,2,1,5,4]=>11011=>11011=>2
[6,3,2,4,1,5]=>[6,2,1,4,3,5]=>10101=>10101=>1
[6,3,2,4,5,1]=>[6,2,1,3,5,4]=>10011=>11001=>2
[6,3,2,5,1,4]=>[6,3,2,5,1,4]=>01011=>11010=>2
[6,3,2,5,4,1]=>[6,2,1,5,4,3]=>10111=>11101=>3
[6,3,4,1,2,5]=>[6,2,4,1,3,5]=>00101=>10100=>1
[6,3,4,1,5,2]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,3,4,2,1,5]=>[6,1,4,3,2,5]=>01101=>10110=>1
[6,3,4,2,5,1]=>[6,1,3,2,5,4]=>01011=>11010=>2
[6,3,4,5,1,2]=>[6,1,3,5,2,4]=>00011=>11000=>2
[6,3,4,5,2,1]=>[6,1,2,5,4,3]=>00111=>11100=>3
[6,3,5,1,2,4]=>[6,3,5,1,2,4]=>00011=>11000=>2
[6,3,5,1,4,2]=>[6,2,5,1,4,3]=>00111=>11100=>3
[6,3,5,2,1,4]=>[6,3,5,2,1,4]=>10011=>11001=>2
[6,3,5,2,4,1]=>[6,2,5,1,4,3]=>00111=>11100=>3
[6,3,5,4,1,2]=>[6,2,5,4,1,3]=>00111=>11100=>3
[6,3,5,4,2,1]=>[6,1,5,4,3,2]=>01111=>11110=>4
[6,4,1,2,3,5]=>[6,4,1,2,3,5]=>00101=>10100=>1
[6,4,1,2,5,3]=>[6,3,1,2,5,4]=>01011=>11010=>2
[6,4,1,3,2,5]=>[6,4,1,3,2,5]=>01101=>10110=>1
[6,4,1,3,5,2]=>[6,3,1,2,5,4]=>01011=>11010=>2
[6,4,1,5,2,3]=>[6,3,1,5,2,4]=>01011=>11010=>2
[6,4,1,5,3,2]=>[6,2,1,5,4,3]=>10111=>11101=>3
[6,4,2,1,3,5]=>[6,4,2,1,3,5]=>10101=>10101=>1
[6,4,2,1,5,3]=>[6,3,2,1,5,4]=>11011=>11011=>2
[6,4,2,3,1,5]=>[6,4,1,3,2,5]=>01101=>10110=>1
[6,4,2,3,5,1]=>[6,3,1,2,5,4]=>01011=>11010=>2
[6,4,2,5,1,3]=>[6,3,2,5,1,4]=>01011=>11010=>2
[6,4,2,5,3,1]=>[6,2,1,5,4,3]=>10111=>11101=>3
[6,4,3,1,2,5]=>[6,4,3,1,2,5]=>01101=>10110=>1
[6,4,3,1,5,2]=>[6,3,2,1,5,4]=>11011=>11011=>2
[6,4,3,2,1,5]=>[6,4,3,2,1,5]=>11101=>10111=>1
[6,4,3,2,5,1]=>[6,3,2,1,5,4]=>11011=>11011=>2
[6,4,3,5,1,2]=>[6,3,2,5,1,4]=>01011=>11010=>2
[6,4,3,5,2,1]=>[6,2,1,5,4,3]=>10111=>11101=>3
[6,4,5,1,2,3]=>[6,3,5,1,2,4]=>00011=>11000=>2
[6,4,5,1,3,2]=>[6,2,5,1,4,3]=>00111=>11100=>3
[6,4,5,2,1,3]=>[6,3,5,2,1,4]=>10011=>11001=>2
[6,4,5,2,3,1]=>[6,2,5,1,4,3]=>00111=>11100=>3
[6,4,5,3,1,2]=>[6,2,5,4,1,3]=>00111=>11100=>3
[6,4,5,3,2,1]=>[6,1,5,4,3,2]=>01111=>11110=>4
[6,5,1,2,3,4]=>[6,5,1,2,3,4]=>00011=>11000=>2
[6,5,1,2,4,3]=>[6,5,1,2,4,3]=>00111=>11100=>3
[6,5,1,3,2,4]=>[6,5,1,3,2,4]=>01011=>11010=>2
[6,5,1,3,4,2]=>[6,5,1,2,4,3]=>00111=>11100=>3
[6,5,1,4,2,3]=>[6,5,1,4,2,3]=>00111=>11100=>3
[6,5,1,4,3,2]=>[6,5,1,4,3,2]=>01111=>11110=>4
[6,5,2,1,3,4]=>[6,5,2,1,3,4]=>10011=>11001=>2
[6,5,2,1,4,3]=>[6,5,2,1,4,3]=>10111=>11101=>3
[6,5,2,3,1,4]=>[6,5,1,3,2,4]=>01011=>11010=>2
[6,5,2,3,4,1]=>[6,5,1,2,4,3]=>00111=>11100=>3
[6,5,2,4,1,3]=>[6,5,2,4,1,3]=>00111=>11100=>3
[6,5,2,4,3,1]=>[6,5,1,4,3,2]=>01111=>11110=>4
[6,5,3,1,2,4]=>[6,5,3,1,2,4]=>01011=>11010=>2
[6,5,3,1,4,2]=>[6,5,2,1,4,3]=>10111=>11101=>3
[6,5,3,2,1,4]=>[6,5,3,2,1,4]=>11011=>11011=>2
[6,5,3,2,4,1]=>[6,5,2,1,4,3]=>10111=>11101=>3
[6,5,3,4,1,2]=>[6,5,2,4,1,3]=>00111=>11100=>3
[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>01111=>11110=>4
[6,5,4,1,2,3]=>[6,5,4,1,2,3]=>00111=>11100=>3
[6,5,4,1,3,2]=>[6,5,4,1,3,2]=>01111=>11110=>4
[6,5,4,2,1,3]=>[6,5,4,2,1,3]=>10111=>11101=>3
[6,5,4,2,3,1]=>[6,5,4,1,3,2]=>01111=>11110=>4
[6,5,4,3,1,2]=>[6,5,4,3,1,2]=>01111=>11110=>4
[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111=>11111=>5
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000=>000000=>0
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>000001=>100000=>1
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>000010=>010000=>0
[1,2,3,4,6,7,5]=>[1,2,3,4,5,7,6]=>000001=>100000=>1
[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>000001=>100000=>1
[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>000100=>001000=>0
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,3,5,6,4,7]=>[1,2,3,4,6,5,7]=>000010=>010000=>0
[1,2,3,5,6,7,4]=>[1,2,3,4,5,7,6]=>000001=>100000=>1
[1,2,3,5,7,4,6]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,2,3,5,7,6,4]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>000010=>010000=>0
[1,2,3,6,4,7,5]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[1,2,3,6,5,7,4]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,3,6,7,4,5]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,2,3,6,7,5,4]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>000001=>100000=>1
[1,2,3,7,4,6,5]=>[1,2,3,7,4,6,5]=>000011=>110000=>2
[1,2,3,7,5,4,6]=>[1,2,3,7,5,4,6]=>000101=>101000=>1
[1,2,3,7,5,6,4]=>[1,2,3,7,4,6,5]=>000011=>110000=>2
[1,2,3,7,6,4,5]=>[1,2,3,7,6,4,5]=>000011=>110000=>2
[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000=>000100=>0
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,2,4,3,6,7,5]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>001001=>100100=>1
[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,2,4,5,3,6,7]=>[1,2,3,5,4,6,7]=>000100=>001000=>0
[1,2,4,5,3,7,6]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,4,5,6,3,7]=>[1,2,3,4,6,5,7]=>000010=>010000=>0
[1,2,4,5,6,7,3]=>[1,2,3,4,5,7,6]=>000001=>100000=>1
[1,2,4,5,7,3,6]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,2,4,5,7,6,3]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,2,4,6,3,5,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[1,2,4,6,3,7,5]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,4,6,5,3,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[1,2,4,6,5,7,3]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,4,6,7,3,5]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,2,4,6,7,5,3]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,2,4,7,3,5,6]=>[1,2,4,7,3,5,6]=>000001=>100000=>1
[1,2,4,7,3,6,5]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,2,4,7,5,3,6]=>[1,2,3,7,5,4,6]=>000101=>101000=>1
[1,2,4,7,5,6,3]=>[1,2,3,7,4,6,5]=>000011=>110000=>2
[1,2,4,7,6,3,5]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,2,4,7,6,5,3]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>000100=>001000=>0
[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>000101=>101000=>1
[1,2,5,3,6,4,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,2,5,3,6,7,4]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,2,5,3,7,4,6]=>[1,2,5,3,7,4,6]=>000101=>101000=>1
[1,2,5,3,7,6,4]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>001100=>001100=>0
[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,2,5,4,6,3,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,2,5,4,6,7,3]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,2,5,4,7,3,6]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,2,5,4,7,6,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,2,5,6,3,4,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[1,2,5,6,3,7,4]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,5,6,4,3,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[1,2,5,6,4,7,3]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,2,5,6,7,3,4]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,2,5,6,7,4,3]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,2,5,7,3,4,6]=>[1,2,5,7,3,4,6]=>000001=>100000=>1
[1,2,5,7,3,6,4]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,2,5,7,4,3,6]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[1,2,5,7,4,6,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,2,5,7,6,3,4]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,2,5,7,6,4,3]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>000010=>010000=>0
[1,2,6,3,4,7,5]=>[1,2,5,3,4,7,6]=>000101=>101000=>1
[1,2,6,3,5,4,7]=>[1,2,6,3,5,4,7]=>000110=>011000=>0
[1,2,6,3,5,7,4]=>[1,2,5,3,4,7,6]=>000101=>101000=>1
[1,2,6,3,7,4,5]=>[1,2,5,3,7,4,6]=>000101=>101000=>1
[1,2,6,3,7,5,4]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,2,6,4,3,5,7]=>[1,2,6,4,3,5,7]=>001010=>010100=>0
[1,2,6,4,3,7,5]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,2,6,4,5,3,7]=>[1,2,6,3,5,4,7]=>000110=>011000=>0
[1,2,6,4,5,7,3]=>[1,2,5,3,4,7,6]=>000101=>101000=>1
[1,2,6,4,7,3,5]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,2,6,4,7,5,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,2,6,5,3,4,7]=>[1,2,6,5,3,4,7]=>000110=>011000=>0
[1,2,6,5,3,7,4]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[1,2,6,5,4,7,3]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,2,6,5,7,3,4]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,2,6,5,7,4,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,2,6,7,3,4,5]=>[1,2,5,7,3,4,6]=>000001=>100000=>1
[1,2,6,7,3,5,4]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,2,6,7,4,3,5]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[1,2,6,7,4,5,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,2,6,7,5,3,4]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,2,6,7,5,4,3]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>000001=>100000=>1
[1,2,7,3,4,6,5]=>[1,2,7,3,4,6,5]=>000011=>110000=>2
[1,2,7,3,5,4,6]=>[1,2,7,3,5,4,6]=>000101=>101000=>1
[1,2,7,3,5,6,4]=>[1,2,7,3,4,6,5]=>000011=>110000=>2
[1,2,7,3,6,4,5]=>[1,2,7,3,6,4,5]=>000011=>110000=>2
[1,2,7,3,6,5,4]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[1,2,7,4,3,5,6]=>[1,2,7,4,3,5,6]=>001001=>100100=>1
[1,2,7,4,3,6,5]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,2,7,4,5,3,6]=>[1,2,7,3,5,4,6]=>000101=>101000=>1
[1,2,7,4,5,6,3]=>[1,2,7,3,4,6,5]=>000011=>110000=>2
[1,2,7,4,6,3,5]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[1,2,7,4,6,5,3]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[1,2,7,5,3,4,6]=>[1,2,7,5,3,4,6]=>000101=>101000=>1
[1,2,7,5,3,6,4]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,2,7,5,4,3,6]=>[1,2,7,5,4,3,6]=>001101=>101100=>1
[1,2,7,5,4,6,3]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,2,7,5,6,3,4]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[1,2,7,5,6,4,3]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[1,2,7,6,3,4,5]=>[1,2,7,6,3,4,5]=>000011=>110000=>2
[1,2,7,6,3,5,4]=>[1,2,7,6,3,5,4]=>000111=>111000=>3
[1,2,7,6,4,3,5]=>[1,2,7,6,4,3,5]=>001011=>110100=>2
[1,2,7,6,4,5,3]=>[1,2,7,6,3,5,4]=>000111=>111000=>3
[1,2,7,6,5,3,4]=>[1,2,7,6,5,3,4]=>000111=>111000=>3
[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000=>000010=>0
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[1,3,2,4,6,7,5]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>010001=>100010=>1
[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,3,2,5,6,4,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[1,3,2,5,6,7,4]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[1,3,2,5,7,4,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,3,2,5,7,6,4]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>010010=>010010=>0
[1,3,2,6,4,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[1,3,2,6,5,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,3,2,6,7,4,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,3,2,6,7,5,4]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>010001=>100010=>1
[1,3,2,7,4,6,5]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[1,3,2,7,5,4,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[1,3,2,7,5,6,4]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[1,3,2,7,6,4,5]=>[1,3,2,7,6,4,5]=>010011=>110010=>2
[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,3,4,2,5,6,7]=>[1,2,4,3,5,6,7]=>001000=>000100=>0
[1,3,4,2,5,7,6]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,3,4,2,6,5,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,3,4,2,6,7,5]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,3,4,2,7,5,6]=>[1,2,4,3,7,5,6]=>001001=>100100=>1
[1,3,4,2,7,6,5]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,3,4,5,2,6,7]=>[1,2,3,5,4,6,7]=>000100=>001000=>0
[1,3,4,5,2,7,6]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,3,4,5,6,2,7]=>[1,2,3,4,6,5,7]=>000010=>010000=>0
[1,3,4,5,6,7,2]=>[1,2,3,4,5,7,6]=>000001=>100000=>1
[1,3,4,5,7,2,6]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,3,4,5,7,6,2]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,3,4,6,2,5,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[1,3,4,6,2,7,5]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,3,4,6,5,2,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[1,3,4,6,5,7,2]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,3,4,6,7,2,5]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,3,4,6,7,5,2]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,3,4,7,2,5,6]=>[1,2,4,7,3,5,6]=>000001=>100000=>1
[1,3,4,7,2,6,5]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,3,4,7,5,2,6]=>[1,2,3,7,5,4,6]=>000101=>101000=>1
[1,3,4,7,5,6,2]=>[1,2,3,7,4,6,5]=>000011=>110000=>2
[1,3,4,7,6,2,5]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,3,4,7,6,5,2]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,3,5,2,4,6,7]=>[1,3,5,2,4,6,7]=>000100=>001000=>0
[1,3,5,2,4,7,6]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,3,5,2,6,4,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,3,5,2,6,7,4]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,3,5,2,7,4,6]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[1,3,5,2,7,6,4]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,3,5,4,2,6,7]=>[1,2,5,4,3,6,7]=>001100=>001100=>0
[1,3,5,4,2,7,6]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,3,5,4,6,2,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,3,5,4,6,7,2]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,3,5,4,7,2,6]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,3,5,4,7,6,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,3,5,6,2,4,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[1,3,5,6,2,7,4]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,3,5,6,4,2,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[1,3,5,6,4,7,2]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,3,5,6,7,2,4]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,3,5,6,7,4,2]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,3,5,7,2,4,6]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[1,3,5,7,2,6,4]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,3,5,7,4,2,6]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[1,3,5,7,4,6,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,3,5,7,6,2,4]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,3,5,7,6,4,2]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,3,6,2,4,5,7]=>[1,3,6,2,4,5,7]=>000010=>010000=>0
[1,3,6,2,4,7,5]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,3,6,2,5,4,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[1,3,6,2,5,7,4]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,3,6,2,7,4,5]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[1,3,6,2,7,5,4]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,3,6,4,2,5,7]=>[1,2,6,4,3,5,7]=>001010=>010100=>0
[1,3,6,4,2,7,5]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,3,6,4,5,2,7]=>[1,2,6,3,5,4,7]=>000110=>011000=>0
[1,3,6,4,5,7,2]=>[1,2,5,3,4,7,6]=>000101=>101000=>1
[1,3,6,4,7,2,5]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,3,6,4,7,5,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,3,6,5,2,4,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[1,3,6,5,2,7,4]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,3,6,5,4,2,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[1,3,6,5,4,7,2]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,3,6,5,7,2,4]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,3,6,5,7,4,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,3,6,7,2,4,5]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[1,3,6,7,2,5,4]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,3,6,7,4,2,5]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[1,3,6,7,4,5,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,3,6,7,5,2,4]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,3,6,7,5,4,2]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,3,7,2,4,5,6]=>[1,3,7,2,4,5,6]=>000001=>100000=>1
[1,3,7,2,4,6,5]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[1,3,7,2,5,4,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[1,3,7,2,5,6,4]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[1,3,7,2,6,4,5]=>[1,3,7,2,6,4,5]=>000011=>110000=>2
[1,3,7,2,6,5,4]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,3,7,4,2,5,6]=>[1,2,7,4,3,5,6]=>001001=>100100=>1
[1,3,7,4,2,6,5]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,3,7,4,5,2,6]=>[1,2,7,3,5,4,6]=>000101=>101000=>1
[1,3,7,4,5,6,2]=>[1,2,7,3,4,6,5]=>000011=>110000=>2
[1,3,7,4,6,2,5]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[1,3,7,4,6,5,2]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[1,3,7,5,2,4,6]=>[1,3,7,5,2,4,6]=>000101=>101000=>1
[1,3,7,5,2,6,4]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,3,7,5,4,2,6]=>[1,2,7,5,4,3,6]=>001101=>101100=>1
[1,3,7,5,4,6,2]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,3,7,5,6,2,4]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[1,3,7,5,6,4,2]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[1,3,7,6,2,4,5]=>[1,3,7,6,2,4,5]=>000011=>110000=>2
[1,3,7,6,2,5,4]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[1,3,7,6,4,2,5]=>[1,2,7,6,4,3,5]=>001011=>110100=>2
[1,3,7,6,4,5,2]=>[1,2,7,6,3,5,4]=>000111=>111000=>3
[1,3,7,6,5,2,4]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[1,3,7,6,5,4,2]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>001000=>000100=>0
[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>001001=>100100=>1
[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>001010=>010100=>0
[1,4,2,3,6,7,5]=>[1,4,2,3,5,7,6]=>001001=>100100=>1
[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>001001=>100100=>1
[1,4,2,3,7,6,5]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,4,2,5,3,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[1,4,2,5,3,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,4,2,5,6,3,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[1,4,2,5,6,7,3]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[1,4,2,5,7,3,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,4,2,5,7,6,3]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,4,2,6,3,5,7]=>[1,4,2,6,3,5,7]=>001010=>010100=>0
[1,4,2,6,3,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,4,2,6,5,3,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[1,4,2,6,5,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,4,2,6,7,3,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,4,2,6,7,5,3]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,4,2,7,3,5,6]=>[1,4,2,7,3,5,6]=>001001=>100100=>1
[1,4,2,7,3,6,5]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[1,4,2,7,5,3,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[1,4,2,7,5,6,3]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[1,4,2,7,6,3,5]=>[1,4,2,7,6,3,5]=>001011=>110100=>2
[1,4,2,7,6,5,3]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000=>000110=>0
[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[1,4,3,2,6,7,5]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[1,4,3,2,7,5,6]=>[1,4,3,2,7,5,6]=>011001=>100110=>1
[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,4,3,5,2,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[1,4,3,5,2,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,4,3,5,6,2,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[1,4,3,5,6,7,2]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[1,4,3,5,7,2,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,4,3,5,7,6,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,4,3,6,2,5,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[1,4,3,6,2,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,4,3,6,5,2,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[1,4,3,6,5,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,4,3,6,7,2,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,4,3,6,7,5,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,4,3,7,2,5,6]=>[1,4,3,7,2,5,6]=>001001=>100100=>1
[1,4,3,7,2,6,5]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,4,3,7,5,2,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[1,4,3,7,5,6,2]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[1,4,3,7,6,2,5]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[1,4,3,7,6,5,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,4,5,2,3,6,7]=>[1,3,5,2,4,6,7]=>000100=>001000=>0
[1,4,5,2,3,7,6]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,4,5,2,6,3,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,4,5,2,6,7,3]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,4,5,2,7,3,6]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[1,4,5,2,7,6,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,4,5,3,2,6,7]=>[1,2,5,4,3,6,7]=>001100=>001100=>0
[1,4,5,3,2,7,6]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,4,5,3,6,2,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[1,4,5,3,6,7,2]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[1,4,5,3,7,2,6]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,4,5,3,7,6,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,4,5,6,2,3,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[1,4,5,6,2,7,3]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,4,5,6,3,2,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[1,4,5,6,3,7,2]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[1,4,5,6,7,2,3]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[1,4,5,6,7,3,2]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[1,4,5,7,2,3,6]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[1,4,5,7,2,6,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,4,5,7,3,2,6]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[1,4,5,7,3,6,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,4,5,7,6,2,3]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,4,5,7,6,3,2]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,4,6,2,3,5,7]=>[1,4,6,2,3,5,7]=>000010=>010000=>0
[1,4,6,2,3,7,5]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,4,6,2,5,3,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[1,4,6,2,5,7,3]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,4,6,2,7,3,5]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[1,4,6,2,7,5,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,4,6,3,2,5,7]=>[1,4,6,3,2,5,7]=>010010=>010010=>0
[1,4,6,3,2,7,5]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,4,6,3,5,2,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[1,4,6,3,5,7,2]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,4,6,3,7,2,5]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,4,6,3,7,5,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,4,6,5,2,3,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[1,4,6,5,2,7,3]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,4,6,5,3,2,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[1,4,6,5,3,7,2]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,4,6,5,7,2,3]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,4,6,5,7,3,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,4,6,7,2,3,5]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[1,4,6,7,2,5,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,4,6,7,3,2,5]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[1,4,6,7,3,5,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,4,6,7,5,2,3]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,4,6,7,5,3,2]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,4,7,2,3,5,6]=>[1,4,7,2,3,5,6]=>000001=>100000=>1
[1,4,7,2,3,6,5]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[1,4,7,2,5,3,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[1,4,7,2,5,6,3]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[1,4,7,2,6,3,5]=>[1,4,7,2,6,3,5]=>000011=>110000=>2
[1,4,7,2,6,5,3]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,4,7,3,2,5,6]=>[1,4,7,3,2,5,6]=>010001=>100010=>1
[1,4,7,3,2,6,5]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[1,4,7,3,5,2,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[1,4,7,3,5,6,2]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[1,4,7,3,6,2,5]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[1,4,7,3,6,5,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,4,7,5,2,3,6]=>[1,3,7,5,2,4,6]=>000101=>101000=>1
[1,4,7,5,2,6,3]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,4,7,5,3,2,6]=>[1,2,7,5,4,3,6]=>001101=>101100=>1
[1,4,7,5,3,6,2]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[1,4,7,5,6,2,3]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[1,4,7,5,6,3,2]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[1,4,7,6,2,3,5]=>[1,4,7,6,2,3,5]=>000011=>110000=>2
[1,4,7,6,2,5,3]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[1,4,7,6,3,2,5]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[1,4,7,6,3,5,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[1,4,7,6,5,2,3]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[1,4,7,6,5,3,2]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>000100=>001000=>0
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>000101=>101000=>1
[1,5,2,3,6,4,7]=>[1,4,2,3,6,5,7]=>001010=>010100=>0
[1,5,2,3,6,7,4]=>[1,4,2,3,5,7,6]=>001001=>100100=>1
[1,5,2,3,7,4,6]=>[1,5,2,3,7,4,6]=>000101=>101000=>1
[1,5,2,3,7,6,4]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,5,2,4,3,6,7]=>[1,5,2,4,3,6,7]=>001100=>001100=>0
[1,5,2,4,3,7,6]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,5,2,4,6,3,7]=>[1,4,2,3,6,5,7]=>001010=>010100=>0
[1,5,2,4,6,7,3]=>[1,4,2,3,5,7,6]=>001001=>100100=>1
[1,5,2,4,7,3,6]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[1,5,2,4,7,6,3]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,5,2,6,3,4,7]=>[1,4,2,6,3,5,7]=>001010=>010100=>0
[1,5,2,6,3,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,5,2,6,4,3,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[1,5,2,6,4,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,5,2,6,7,3,4]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,5,2,6,7,4,3]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,5,2,7,3,4,6]=>[1,5,2,7,3,4,6]=>000101=>101000=>1
[1,5,2,7,3,6,4]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[1,5,2,7,4,3,6]=>[1,5,2,7,4,3,6]=>001101=>101100=>1
[1,5,2,7,4,6,3]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[1,5,2,7,6,3,4]=>[1,4,2,7,6,3,5]=>001011=>110100=>2
[1,5,2,7,6,4,3]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,5,3,2,4,6,7]=>[1,5,3,2,4,6,7]=>010100=>001010=>0
[1,5,3,2,4,7,6]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[1,5,3,2,6,4,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[1,5,3,2,6,7,4]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[1,5,3,2,7,4,6]=>[1,5,3,2,7,4,6]=>010101=>101010=>1
[1,5,3,2,7,6,4]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,5,3,4,2,6,7]=>[1,5,2,4,3,6,7]=>001100=>001100=>0
[1,5,3,4,2,7,6]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,5,3,4,6,2,7]=>[1,4,2,3,6,5,7]=>001010=>010100=>0
[1,5,3,4,6,7,2]=>[1,4,2,3,5,7,6]=>001001=>100100=>1
[1,5,3,4,7,2,6]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[1,5,3,4,7,6,2]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,5,3,6,2,4,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[1,5,3,6,2,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,5,3,6,4,2,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[1,5,3,6,4,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,5,3,6,7,2,4]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,5,3,6,7,4,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,5,3,7,2,4,6]=>[1,5,3,7,2,4,6]=>000101=>101000=>1
[1,5,3,7,2,6,4]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,5,3,7,4,2,6]=>[1,5,2,7,4,3,6]=>001101=>101100=>1
[1,5,3,7,4,6,2]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[1,5,3,7,6,2,4]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[1,5,3,7,6,4,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,5,4,2,3,6,7]=>[1,5,4,2,3,6,7]=>001100=>001100=>0
[1,5,4,2,3,7,6]=>[1,5,4,2,3,7,6]=>001101=>101100=>1
[1,5,4,2,6,3,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[1,5,4,2,6,7,3]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[1,5,4,2,7,3,6]=>[1,5,4,2,7,3,6]=>001101=>101100=>1
[1,5,4,2,7,6,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>011100=>001110=>0
[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[1,5,4,3,6,2,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[1,5,4,3,6,7,2]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[1,5,4,3,7,2,6]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[1,5,4,3,7,6,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,5,4,6,2,3,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[1,5,4,6,2,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,5,4,6,3,2,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[1,5,4,6,3,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[1,5,4,6,7,2,3]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[1,5,4,6,7,3,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[1,5,4,7,2,3,6]=>[1,5,4,7,2,3,6]=>000101=>101000=>1
[1,5,4,7,2,6,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,5,4,7,3,2,6]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[1,5,4,7,3,6,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,5,4,7,6,2,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[1,5,4,7,6,3,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,5,6,2,3,4,7]=>[1,4,6,2,3,5,7]=>000010=>010000=>0
[1,5,6,2,3,7,4]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,5,6,2,4,3,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[1,5,6,2,4,7,3]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,5,6,2,7,3,4]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[1,5,6,2,7,4,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,5,6,3,2,4,7]=>[1,4,6,3,2,5,7]=>010010=>010010=>0
[1,5,6,3,2,7,4]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,5,6,3,4,2,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[1,5,6,3,4,7,2]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[1,5,6,3,7,2,4]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,5,6,3,7,4,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,5,6,4,2,3,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[1,5,6,4,2,7,3]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,5,6,4,3,2,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[1,5,6,4,3,7,2]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[1,5,6,4,7,2,3]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[1,5,6,4,7,3,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[1,5,6,7,2,3,4]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[1,5,6,7,2,4,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,5,6,7,3,2,4]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[1,5,6,7,3,4,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[1,5,6,7,4,2,3]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[1,5,6,7,4,3,2]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[1,5,7,2,3,4,6]=>[1,5,7,2,3,4,6]=>000001=>100000=>1
[1,5,7,2,3,6,4]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[1,5,7,2,4,3,6]=>[1,5,7,2,4,3,6]=>001001=>100100=>1
[1,5,7,2,4,6,3]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[1,5,7,2,6,3,4]=>[1,4,7,2,6,3,5]=>000011=>110000=>2
[1,5,7,2,6,4,3]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,5,7,3,2,4,6]=>[1,5,7,3,2,4,6]=>010001=>100010=>1
[1,5,7,3,2,6,4]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[1,5,7,3,4,2,6]=>[1,5,7,2,4,3,6]=>001001=>100100=>1
[1,5,7,3,4,6,2]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[1,5,7,3,6,2,4]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[1,5,7,3,6,4,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,5,7,4,2,3,6]=>[1,5,7,4,2,3,6]=>001001=>100100=>1
[1,5,7,4,2,6,3]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[1,5,7,4,3,2,6]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[1,5,7,4,3,6,2]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[1,5,7,4,6,2,3]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[1,5,7,4,6,3,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,5,7,6,2,3,4]=>[1,4,7,6,2,3,5]=>000011=>110000=>2
[1,5,7,6,2,4,3]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[1,5,7,6,3,2,4]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[1,5,7,6,3,4,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[1,5,7,6,4,2,3]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[1,5,7,6,4,3,2]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>000010=>010000=>0
[1,6,2,3,4,7,5]=>[1,5,2,3,4,7,6]=>000101=>101000=>1
[1,6,2,3,5,4,7]=>[1,6,2,3,5,4,7]=>000110=>011000=>0
[1,6,2,3,5,7,4]=>[1,5,2,3,4,7,6]=>000101=>101000=>1
[1,6,2,3,7,4,5]=>[1,5,2,3,7,4,6]=>000101=>101000=>1
[1,6,2,3,7,5,4]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,6,2,4,3,5,7]=>[1,6,2,4,3,5,7]=>001010=>010100=>0
[1,6,2,4,3,7,5]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,2,4,5,3,7]=>[1,6,2,3,5,4,7]=>000110=>011000=>0
[1,6,2,4,5,7,3]=>[1,5,2,3,4,7,6]=>000101=>101000=>1
[1,6,2,4,7,3,5]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[1,6,2,4,7,5,3]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,6,2,5,3,4,7]=>[1,6,2,5,3,4,7]=>000110=>011000=>0
[1,6,2,5,3,7,4]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,2,5,4,3,7]=>[1,6,2,5,4,3,7]=>001110=>011100=>0
[1,6,2,5,4,7,3]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,2,5,7,3,4]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[1,6,2,5,7,4,3]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,6,2,7,3,4,5]=>[1,5,2,7,3,4,6]=>000101=>101000=>1
[1,6,2,7,3,5,4]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[1,6,2,7,4,3,5]=>[1,5,2,7,4,3,6]=>001101=>101100=>1
[1,6,2,7,4,5,3]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[1,6,2,7,5,3,4]=>[1,4,2,7,6,3,5]=>001011=>110100=>2
[1,6,2,7,5,4,3]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,6,3,2,4,5,7]=>[1,6,3,2,4,5,7]=>010010=>010010=>0
[1,6,3,2,4,7,5]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[1,6,3,2,5,4,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[1,6,3,2,5,7,4]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[1,6,3,2,7,4,5]=>[1,5,3,2,7,4,6]=>010101=>101010=>1
[1,6,3,2,7,5,4]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,6,3,4,2,5,7]=>[1,6,2,4,3,5,7]=>001010=>010100=>0
[1,6,3,4,2,7,5]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,3,4,5,2,7]=>[1,6,2,3,5,4,7]=>000110=>011000=>0
[1,6,3,4,5,7,2]=>[1,5,2,3,4,7,6]=>000101=>101000=>1
[1,6,3,4,7,2,5]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[1,6,3,4,7,5,2]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,6,3,5,2,4,7]=>[1,6,3,5,2,4,7]=>000110=>011000=>0
[1,6,3,5,2,7,4]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,3,5,4,2,7]=>[1,6,2,5,4,3,7]=>001110=>011100=>0
[1,6,3,5,4,7,2]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,3,5,7,2,4]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[1,6,3,5,7,4,2]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,6,3,7,2,4,5]=>[1,5,3,7,2,4,6]=>000101=>101000=>1
[1,6,3,7,2,5,4]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,6,3,7,4,2,5]=>[1,5,2,7,4,3,6]=>001101=>101100=>1
[1,6,3,7,4,5,2]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[1,6,3,7,5,2,4]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[1,6,3,7,5,4,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,6,4,2,3,5,7]=>[1,6,4,2,3,5,7]=>001010=>010100=>0
[1,6,4,2,3,7,5]=>[1,5,4,2,3,7,6]=>001101=>101100=>1
[1,6,4,2,5,3,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[1,6,4,2,5,7,3]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[1,6,4,2,7,3,5]=>[1,5,4,2,7,3,6]=>001101=>101100=>1
[1,6,4,2,7,5,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,6,4,3,2,5,7]=>[1,6,4,3,2,5,7]=>011010=>010110=>0
[1,6,4,3,2,7,5]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[1,6,4,3,5,2,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[1,6,4,3,5,7,2]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[1,6,4,3,7,2,5]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[1,6,4,3,7,5,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,6,4,5,2,3,7]=>[1,6,3,5,2,4,7]=>000110=>011000=>0
[1,6,4,5,2,7,3]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,4,5,3,2,7]=>[1,6,2,5,4,3,7]=>001110=>011100=>0
[1,6,4,5,3,7,2]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[1,6,4,5,7,2,3]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[1,6,4,5,7,3,2]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[1,6,4,7,2,3,5]=>[1,5,4,7,2,3,6]=>000101=>101000=>1
[1,6,4,7,2,5,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,6,4,7,3,2,5]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[1,6,4,7,3,5,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,6,4,7,5,2,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[1,6,4,7,5,3,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,6,5,2,3,4,7]=>[1,6,5,2,3,4,7]=>000110=>011000=>0
[1,6,5,2,3,7,4]=>[1,5,4,2,3,7,6]=>001101=>101100=>1
[1,6,5,2,4,3,7]=>[1,6,5,2,4,3,7]=>001110=>011100=>0
[1,6,5,2,4,7,3]=>[1,5,4,2,3,7,6]=>001101=>101100=>1
[1,6,5,2,7,3,4]=>[1,5,4,2,7,3,6]=>001101=>101100=>1
[1,6,5,2,7,4,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,6,5,3,2,4,7]=>[1,6,5,3,2,4,7]=>010110=>011010=>0
[1,6,5,3,2,7,4]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[1,6,5,3,4,2,7]=>[1,6,5,2,4,3,7]=>001110=>011100=>0
[1,6,5,3,4,7,2]=>[1,5,4,2,3,7,6]=>001101=>101100=>1
[1,6,5,3,7,2,4]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[1,6,5,3,7,4,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,6,5,4,2,3,7]=>[1,6,5,4,2,3,7]=>001110=>011100=>0
[1,6,5,4,2,7,3]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>011110=>011110=>0
[1,6,5,4,3,7,2]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[1,6,5,4,7,2,3]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[1,6,5,4,7,3,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[1,6,5,7,2,3,4]=>[1,5,4,7,2,3,6]=>000101=>101000=>1
[1,6,5,7,2,4,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,6,5,7,3,2,4]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[1,6,5,7,3,4,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[1,6,5,7,4,2,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[1,6,5,7,4,3,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[1,6,7,2,3,4,5]=>[1,5,7,2,3,4,6]=>000001=>100000=>1
[1,6,7,2,3,5,4]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[1,6,7,2,4,3,5]=>[1,5,7,2,4,3,6]=>001001=>100100=>1
[1,6,7,2,4,5,3]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[1,6,7,2,5,3,4]=>[1,4,7,2,6,3,5]=>000011=>110000=>2
[1,6,7,2,5,4,3]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,6,7,3,2,4,5]=>[1,5,7,3,2,4,6]=>010001=>100010=>1
[1,6,7,3,2,5,4]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[1,6,7,3,4,2,5]=>[1,5,7,2,4,3,6]=>001001=>100100=>1
[1,6,7,3,4,5,2]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[1,6,7,3,5,2,4]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[1,6,7,3,5,4,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,6,7,4,2,3,5]=>[1,5,7,4,2,3,6]=>001001=>100100=>1
[1,6,7,4,2,5,3]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[1,6,7,4,3,2,5]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[1,6,7,4,3,5,2]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[1,6,7,4,5,2,3]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[1,6,7,4,5,3,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[1,6,7,5,2,3,4]=>[1,4,7,6,2,3,5]=>000011=>110000=>2
[1,6,7,5,2,4,3]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[1,6,7,5,3,2,4]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[1,6,7,5,3,4,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[1,6,7,5,4,2,3]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[1,6,7,5,4,3,2]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>000001=>100000=>1
[1,7,2,3,4,6,5]=>[1,7,2,3,4,6,5]=>000011=>110000=>2
[1,7,2,3,5,4,6]=>[1,7,2,3,5,4,6]=>000101=>101000=>1
[1,7,2,3,5,6,4]=>[1,7,2,3,4,6,5]=>000011=>110000=>2
[1,7,2,3,6,4,5]=>[1,7,2,3,6,4,5]=>000011=>110000=>2
[1,7,2,3,6,5,4]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[1,7,2,4,3,5,6]=>[1,7,2,4,3,5,6]=>001001=>100100=>1
[1,7,2,4,3,6,5]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,2,4,5,3,6]=>[1,7,2,3,5,4,6]=>000101=>101000=>1
[1,7,2,4,5,6,3]=>[1,7,2,3,4,6,5]=>000011=>110000=>2
[1,7,2,4,6,3,5]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[1,7,2,4,6,5,3]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[1,7,2,5,3,4,6]=>[1,7,2,5,3,4,6]=>000101=>101000=>1
[1,7,2,5,3,6,4]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,2,5,4,3,6]=>[1,7,2,5,4,3,6]=>001101=>101100=>1
[1,7,2,5,4,6,3]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,2,5,6,3,4]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[1,7,2,5,6,4,3]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[1,7,2,6,3,4,5]=>[1,7,2,6,3,4,5]=>000011=>110000=>2
[1,7,2,6,3,5,4]=>[1,7,2,6,3,5,4]=>000111=>111000=>3
[1,7,2,6,4,3,5]=>[1,7,2,6,4,3,5]=>001011=>110100=>2
[1,7,2,6,4,5,3]=>[1,7,2,6,3,5,4]=>000111=>111000=>3
[1,7,2,6,5,3,4]=>[1,7,2,6,5,3,4]=>000111=>111000=>3
[1,7,2,6,5,4,3]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[1,7,3,2,4,5,6]=>[1,7,3,2,4,5,6]=>010001=>100010=>1
[1,7,3,2,4,6,5]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[1,7,3,2,5,4,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[1,7,3,2,5,6,4]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[1,7,3,2,6,4,5]=>[1,7,3,2,6,4,5]=>010011=>110010=>2
[1,7,3,2,6,5,4]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[1,7,3,4,2,5,6]=>[1,7,2,4,3,5,6]=>001001=>100100=>1
[1,7,3,4,2,6,5]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,3,4,5,2,6]=>[1,7,2,3,5,4,6]=>000101=>101000=>1
[1,7,3,4,5,6,2]=>[1,7,2,3,4,6,5]=>000011=>110000=>2
[1,7,3,4,6,2,5]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[1,7,3,4,6,5,2]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[1,7,3,5,2,4,6]=>[1,7,3,5,2,4,6]=>000101=>101000=>1
[1,7,3,5,2,6,4]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,3,5,4,2,6]=>[1,7,2,5,4,3,6]=>001101=>101100=>1
[1,7,3,5,4,6,2]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,3,5,6,2,4]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[1,7,3,5,6,4,2]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[1,7,3,6,2,4,5]=>[1,7,3,6,2,4,5]=>000011=>110000=>2
[1,7,3,6,2,5,4]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[1,7,3,6,4,2,5]=>[1,7,2,6,4,3,5]=>001011=>110100=>2
[1,7,3,6,4,5,2]=>[1,7,2,6,3,5,4]=>000111=>111000=>3
[1,7,3,6,5,2,4]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[1,7,3,6,5,4,2]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[1,7,4,2,3,5,6]=>[1,7,4,2,3,5,6]=>001001=>100100=>1
[1,7,4,2,3,6,5]=>[1,7,4,2,3,6,5]=>001011=>110100=>2
[1,7,4,2,5,3,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[1,7,4,2,5,6,3]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[1,7,4,2,6,3,5]=>[1,7,4,2,6,3,5]=>001011=>110100=>2
[1,7,4,2,6,5,3]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[1,7,4,3,2,5,6]=>[1,7,4,3,2,5,6]=>011001=>100110=>1
[1,7,4,3,2,6,5]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[1,7,4,3,5,2,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[1,7,4,3,5,6,2]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[1,7,4,3,6,2,5]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[1,7,4,3,6,5,2]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[1,7,4,5,2,3,6]=>[1,7,3,5,2,4,6]=>000101=>101000=>1
[1,7,4,5,2,6,3]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,4,5,3,2,6]=>[1,7,2,5,4,3,6]=>001101=>101100=>1
[1,7,4,5,3,6,2]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[1,7,4,5,6,2,3]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[1,7,4,5,6,3,2]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[1,7,4,6,2,3,5]=>[1,7,4,6,2,3,5]=>000011=>110000=>2
[1,7,4,6,2,5,3]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[1,7,4,6,3,2,5]=>[1,7,4,6,3,2,5]=>010011=>110010=>2
[1,7,4,6,3,5,2]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[1,7,4,6,5,2,3]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[1,7,4,6,5,3,2]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[1,7,5,2,3,4,6]=>[1,7,5,2,3,4,6]=>000101=>101000=>1
[1,7,5,2,3,6,4]=>[1,7,4,2,3,6,5]=>001011=>110100=>2
[1,7,5,2,4,3,6]=>[1,7,5,2,4,3,6]=>001101=>101100=>1
[1,7,5,2,4,6,3]=>[1,7,4,2,3,6,5]=>001011=>110100=>2
[1,7,5,2,6,3,4]=>[1,7,4,2,6,3,5]=>001011=>110100=>2
[1,7,5,2,6,4,3]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[1,7,5,3,2,4,6]=>[1,7,5,3,2,4,6]=>010101=>101010=>1
[1,7,5,3,2,6,4]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[1,7,5,3,4,2,6]=>[1,7,5,2,4,3,6]=>001101=>101100=>1
[1,7,5,3,4,6,2]=>[1,7,4,2,3,6,5]=>001011=>110100=>2
[1,7,5,3,6,2,4]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[1,7,5,3,6,4,2]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[1,7,5,4,2,3,6]=>[1,7,5,4,2,3,6]=>001101=>101100=>1
[1,7,5,4,2,6,3]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[1,7,5,4,3,2,6]=>[1,7,5,4,3,2,6]=>011101=>101110=>1
[1,7,5,4,3,6,2]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[1,7,5,4,6,2,3]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[1,7,5,4,6,3,2]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[1,7,5,6,2,3,4]=>[1,7,4,6,2,3,5]=>000011=>110000=>2
[1,7,5,6,2,4,3]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[1,7,5,6,3,2,4]=>[1,7,4,6,3,2,5]=>010011=>110010=>2
[1,7,5,6,3,4,2]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[1,7,5,6,4,2,3]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[1,7,5,6,4,3,2]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[1,7,6,2,3,4,5]=>[1,7,6,2,3,4,5]=>000011=>110000=>2
[1,7,6,2,3,5,4]=>[1,7,6,2,3,5,4]=>000111=>111000=>3
[1,7,6,2,4,3,5]=>[1,7,6,2,4,3,5]=>001011=>110100=>2
[1,7,6,2,4,5,3]=>[1,7,6,2,3,5,4]=>000111=>111000=>3
[1,7,6,2,5,3,4]=>[1,7,6,2,5,3,4]=>000111=>111000=>3
[1,7,6,2,5,4,3]=>[1,7,6,2,5,4,3]=>001111=>111100=>4
[1,7,6,3,2,4,5]=>[1,7,6,3,2,4,5]=>010011=>110010=>2
[1,7,6,3,2,5,4]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[1,7,6,3,4,2,5]=>[1,7,6,2,4,3,5]=>001011=>110100=>2
[1,7,6,3,4,5,2]=>[1,7,6,2,3,5,4]=>000111=>111000=>3
[1,7,6,3,5,2,4]=>[1,7,6,3,5,2,4]=>000111=>111000=>3
[1,7,6,3,5,4,2]=>[1,7,6,2,5,4,3]=>001111=>111100=>4
[1,7,6,4,2,3,5]=>[1,7,6,4,2,3,5]=>001011=>110100=>2
[1,7,6,4,2,5,3]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[1,7,6,4,3,2,5]=>[1,7,6,4,3,2,5]=>011011=>110110=>2
[1,7,6,4,3,5,2]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[1,7,6,4,5,2,3]=>[1,7,6,3,5,2,4]=>000111=>111000=>3
[1,7,6,4,5,3,2]=>[1,7,6,2,5,4,3]=>001111=>111100=>4
[1,7,6,5,2,3,4]=>[1,7,6,5,2,3,4]=>000111=>111000=>3
[1,7,6,5,2,4,3]=>[1,7,6,5,2,4,3]=>001111=>111100=>4
[1,7,6,5,3,2,4]=>[1,7,6,5,3,2,4]=>010111=>111010=>3
[1,7,6,5,3,4,2]=>[1,7,6,5,2,4,3]=>001111=>111100=>4
[1,7,6,5,4,2,3]=>[1,7,6,5,4,2,3]=>001111=>111100=>4
[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>011111=>111110=>5
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000=>000001=>0
[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>100001=>100001=>1
[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>100010=>010001=>0
[2,1,3,4,6,7,5]=>[2,1,3,4,5,7,6]=>100001=>100001=>1
[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>100001=>100001=>1
[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>100100=>001001=>0
[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,3,5,6,4,7]=>[2,1,3,4,6,5,7]=>100010=>010001=>0
[2,1,3,5,6,7,4]=>[2,1,3,4,5,7,6]=>100001=>100001=>1
[2,1,3,5,7,4,6]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[2,1,3,5,7,6,4]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>100010=>010001=>0
[2,1,3,6,4,7,5]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[2,1,3,6,5,7,4]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,3,6,7,4,5]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[2,1,3,6,7,5,4]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>100001=>100001=>1
[2,1,3,7,4,6,5]=>[2,1,3,7,4,6,5]=>100011=>110001=>2
[2,1,3,7,5,4,6]=>[2,1,3,7,5,4,6]=>100101=>101001=>1
[2,1,3,7,5,6,4]=>[2,1,3,7,4,6,5]=>100011=>110001=>2
[2,1,3,7,6,4,5]=>[2,1,3,7,6,4,5]=>100011=>110001=>2
[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>101000=>000101=>0
[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[2,1,4,3,6,7,5]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>101001=>100101=>1
[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[2,1,4,5,3,6,7]=>[2,1,3,5,4,6,7]=>100100=>001001=>0
[2,1,4,5,3,7,6]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,4,5,6,3,7]=>[2,1,3,4,6,5,7]=>100010=>010001=>0
[2,1,4,5,6,7,3]=>[2,1,3,4,5,7,6]=>100001=>100001=>1
[2,1,4,5,7,3,6]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[2,1,4,5,7,6,3]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[2,1,4,6,3,5,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[2,1,4,6,3,7,5]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,4,6,5,3,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[2,1,4,6,5,7,3]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,4,6,7,3,5]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[2,1,4,6,7,5,3]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[2,1,4,7,3,5,6]=>[2,1,4,7,3,5,6]=>100001=>100001=>1
[2,1,4,7,3,6,5]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[2,1,4,7,5,3,6]=>[2,1,3,7,5,4,6]=>100101=>101001=>1
[2,1,4,7,5,6,3]=>[2,1,3,7,4,6,5]=>100011=>110001=>2
[2,1,4,7,6,3,5]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[2,1,4,7,6,5,3]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>100100=>001001=>0
[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>100101=>101001=>1
[2,1,5,3,6,4,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[2,1,5,3,6,7,4]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[2,1,5,3,7,4,6]=>[2,1,5,3,7,4,6]=>100101=>101001=>1
[2,1,5,3,7,6,4]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>101100=>001101=>0
[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[2,1,5,4,6,3,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[2,1,5,4,6,7,3]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[2,1,5,4,7,3,6]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[2,1,5,4,7,6,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[2,1,5,6,3,4,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[2,1,5,6,3,7,4]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,5,6,4,3,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[2,1,5,6,4,7,3]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[2,1,5,6,7,3,4]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[2,1,5,6,7,4,3]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[2,1,5,7,3,4,6]=>[2,1,5,7,3,4,6]=>100001=>100001=>1
[2,1,5,7,3,6,4]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[2,1,5,7,4,3,6]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[2,1,5,7,4,6,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[2,1,5,7,6,3,4]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[2,1,5,7,6,4,3]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>100010=>010001=>0
[2,1,6,3,4,7,5]=>[2,1,5,3,4,7,6]=>100101=>101001=>1
[2,1,6,3,5,4,7]=>[2,1,6,3,5,4,7]=>100110=>011001=>0
[2,1,6,3,5,7,4]=>[2,1,5,3,4,7,6]=>100101=>101001=>1
[2,1,6,3,7,4,5]=>[2,1,5,3,7,4,6]=>100101=>101001=>1
[2,1,6,3,7,5,4]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[2,1,6,4,3,5,7]=>[2,1,6,4,3,5,7]=>101010=>010101=>0
[2,1,6,4,3,7,5]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[2,1,6,4,5,3,7]=>[2,1,6,3,5,4,7]=>100110=>011001=>0
[2,1,6,4,5,7,3]=>[2,1,5,3,4,7,6]=>100101=>101001=>1
[2,1,6,4,7,3,5]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[2,1,6,4,7,5,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[2,1,6,5,3,4,7]=>[2,1,6,5,3,4,7]=>100110=>011001=>0
[2,1,6,5,3,7,4]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[2,1,6,5,4,7,3]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[2,1,6,5,7,3,4]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[2,1,6,5,7,4,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[2,1,6,7,3,4,5]=>[2,1,5,7,3,4,6]=>100001=>100001=>1
[2,1,6,7,3,5,4]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[2,1,6,7,4,3,5]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[2,1,6,7,4,5,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[2,1,6,7,5,3,4]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[2,1,6,7,5,4,3]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>100001=>100001=>1
[2,1,7,3,4,6,5]=>[2,1,7,3,4,6,5]=>100011=>110001=>2
[2,1,7,3,5,4,6]=>[2,1,7,3,5,4,6]=>100101=>101001=>1
[2,1,7,3,5,6,4]=>[2,1,7,3,4,6,5]=>100011=>110001=>2
[2,1,7,3,6,4,5]=>[2,1,7,3,6,4,5]=>100011=>110001=>2
[2,1,7,3,6,5,4]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[2,1,7,4,3,5,6]=>[2,1,7,4,3,5,6]=>101001=>100101=>1
[2,1,7,4,3,6,5]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[2,1,7,4,5,3,6]=>[2,1,7,3,5,4,6]=>100101=>101001=>1
[2,1,7,4,5,6,3]=>[2,1,7,3,4,6,5]=>100011=>110001=>2
[2,1,7,4,6,3,5]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[2,1,7,4,6,5,3]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[2,1,7,5,3,4,6]=>[2,1,7,5,3,4,6]=>100101=>101001=>1
[2,1,7,5,3,6,4]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[2,1,7,5,4,3,6]=>[2,1,7,5,4,3,6]=>101101=>101101=>1
[2,1,7,5,4,6,3]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[2,1,7,5,6,3,4]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[2,1,7,5,6,4,3]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[2,1,7,6,3,4,5]=>[2,1,7,6,3,4,5]=>100011=>110001=>2
[2,1,7,6,3,5,4]=>[2,1,7,6,3,5,4]=>100111=>111001=>3
[2,1,7,6,4,3,5]=>[2,1,7,6,4,3,5]=>101011=>110101=>2
[2,1,7,6,4,5,3]=>[2,1,7,6,3,5,4]=>100111=>111001=>3
[2,1,7,6,5,3,4]=>[2,1,7,6,5,3,4]=>100111=>111001=>3
[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[2,3,1,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000=>000010=>0
[2,3,1,4,5,7,6]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[2,3,1,4,6,5,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[2,3,1,4,6,7,5]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[2,3,1,4,7,5,6]=>[1,3,2,4,7,5,6]=>010001=>100010=>1
[2,3,1,4,7,6,5]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,3,1,5,4,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[2,3,1,5,4,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,3,1,5,6,4,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[2,3,1,5,6,7,4]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[2,3,1,5,7,4,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,3,1,5,7,6,4]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,3,1,6,4,5,7]=>[1,3,2,6,4,5,7]=>010010=>010010=>0
[2,3,1,6,4,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,3,1,6,5,4,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[2,3,1,6,5,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,3,1,6,7,4,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,3,1,6,7,5,4]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,3,1,7,4,5,6]=>[1,3,2,7,4,5,6]=>010001=>100010=>1
[2,3,1,7,4,6,5]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[2,3,1,7,5,4,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[2,3,1,7,5,6,4]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[2,3,1,7,6,4,5]=>[1,3,2,7,6,4,5]=>010011=>110010=>2
[2,3,1,7,6,5,4]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,3,4,1,5,6,7]=>[1,2,4,3,5,6,7]=>001000=>000100=>0
[2,3,4,1,5,7,6]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[2,3,4,1,6,5,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[2,3,4,1,6,7,5]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[2,3,4,1,7,5,6]=>[1,2,4,3,7,5,6]=>001001=>100100=>1
[2,3,4,1,7,6,5]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,3,4,5,1,6,7]=>[1,2,3,5,4,6,7]=>000100=>001000=>0
[2,3,4,5,1,7,6]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[2,3,4,5,6,1,7]=>[1,2,3,4,6,5,7]=>000010=>010000=>0
[2,3,4,5,6,7,1]=>[1,2,3,4,5,7,6]=>000001=>100000=>1
[2,3,4,5,7,1,6]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[2,3,4,5,7,6,1]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[2,3,4,6,1,5,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[2,3,4,6,1,7,5]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[2,3,4,6,5,1,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[2,3,4,6,5,7,1]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[2,3,4,6,7,1,5]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[2,3,4,6,7,5,1]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[2,3,4,7,1,5,6]=>[1,2,4,7,3,5,6]=>000001=>100000=>1
[2,3,4,7,1,6,5]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,3,4,7,5,1,6]=>[1,2,3,7,5,4,6]=>000101=>101000=>1
[2,3,4,7,5,6,1]=>[1,2,3,7,4,6,5]=>000011=>110000=>2
[2,3,4,7,6,1,5]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[2,3,4,7,6,5,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[2,3,5,1,4,6,7]=>[1,3,5,2,4,6,7]=>000100=>001000=>0
[2,3,5,1,4,7,6]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,3,5,1,6,4,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[2,3,5,1,6,7,4]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[2,3,5,1,7,4,6]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[2,3,5,1,7,6,4]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,3,5,4,1,6,7]=>[1,2,5,4,3,6,7]=>001100=>001100=>0
[2,3,5,4,1,7,6]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,3,5,4,6,1,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[2,3,5,4,6,7,1]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[2,3,5,4,7,1,6]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,3,5,4,7,6,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,3,5,6,1,4,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[2,3,5,6,1,7,4]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[2,3,5,6,4,1,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[2,3,5,6,4,7,1]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[2,3,5,6,7,1,4]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[2,3,5,6,7,4,1]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[2,3,5,7,1,4,6]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[2,3,5,7,1,6,4]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,3,5,7,4,1,6]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[2,3,5,7,4,6,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,3,5,7,6,1,4]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[2,3,5,7,6,4,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[2,3,6,1,4,5,7]=>[1,3,6,2,4,5,7]=>000010=>010000=>0
[2,3,6,1,4,7,5]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,3,6,1,5,4,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[2,3,6,1,5,7,4]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,3,6,1,7,4,5]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[2,3,6,1,7,5,4]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,3,6,4,1,5,7]=>[1,2,6,4,3,5,7]=>001010=>010100=>0
[2,3,6,4,1,7,5]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,3,6,4,5,1,7]=>[1,2,6,3,5,4,7]=>000110=>011000=>0
[2,3,6,4,5,7,1]=>[1,2,5,3,4,7,6]=>000101=>101000=>1
[2,3,6,4,7,1,5]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,3,6,4,7,5,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,3,6,5,1,4,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[2,3,6,5,1,7,4]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,3,6,5,4,1,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[2,3,6,5,4,7,1]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,3,6,5,7,1,4]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,3,6,5,7,4,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,3,6,7,1,4,5]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[2,3,6,7,1,5,4]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,3,6,7,4,1,5]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[2,3,6,7,4,5,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,3,6,7,5,1,4]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[2,3,6,7,5,4,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[2,3,7,1,4,5,6]=>[1,3,7,2,4,5,6]=>000001=>100000=>1
[2,3,7,1,4,6,5]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[2,3,7,1,5,4,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[2,3,7,1,5,6,4]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[2,3,7,1,6,4,5]=>[1,3,7,2,6,4,5]=>000011=>110000=>2
[2,3,7,1,6,5,4]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,3,7,4,1,5,6]=>[1,2,7,4,3,5,6]=>001001=>100100=>1
[2,3,7,4,1,6,5]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[2,3,7,4,5,1,6]=>[1,2,7,3,5,4,6]=>000101=>101000=>1
[2,3,7,4,5,6,1]=>[1,2,7,3,4,6,5]=>000011=>110000=>2
[2,3,7,4,6,1,5]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[2,3,7,4,6,5,1]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[2,3,7,5,1,4,6]=>[1,3,7,5,2,4,6]=>000101=>101000=>1
[2,3,7,5,1,6,4]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[2,3,7,5,4,1,6]=>[1,2,7,5,4,3,6]=>001101=>101100=>1
[2,3,7,5,4,6,1]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[2,3,7,5,6,1,4]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[2,3,7,5,6,4,1]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[2,3,7,6,1,4,5]=>[1,3,7,6,2,4,5]=>000011=>110000=>2
[2,3,7,6,1,5,4]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[2,3,7,6,4,1,5]=>[1,2,7,6,4,3,5]=>001011=>110100=>2
[2,3,7,6,4,5,1]=>[1,2,7,6,3,5,4]=>000111=>111000=>3
[2,3,7,6,5,1,4]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[2,3,7,6,5,4,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[2,4,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>001000=>000100=>0
[2,4,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[2,4,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[2,4,1,3,6,7,5]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[2,4,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>001001=>100100=>1
[2,4,1,3,7,6,5]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[2,4,1,5,3,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[2,4,1,5,3,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,4,1,5,6,3,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[2,4,1,5,6,7,3]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[2,4,1,5,7,3,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,4,1,5,7,6,3]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,4,1,6,3,5,7]=>[2,4,1,6,3,5,7]=>001010=>010100=>0
[2,4,1,6,3,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,4,1,6,5,3,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[2,4,1,6,5,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,4,1,6,7,3,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,4,1,6,7,5,3]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,4,1,7,3,5,6]=>[2,4,1,7,3,5,6]=>001001=>100100=>1
[2,4,1,7,3,6,5]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[2,4,1,7,5,3,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[2,4,1,7,5,6,3]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[2,4,1,7,6,3,5]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[2,4,1,7,6,5,3]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,4,3,1,5,6,7]=>[1,4,3,2,5,6,7]=>011000=>000110=>0
[2,4,3,1,5,7,6]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[2,4,3,1,6,5,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[2,4,3,1,6,7,5]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[2,4,3,1,7,5,6]=>[1,4,3,2,7,5,6]=>011001=>100110=>1
[2,4,3,1,7,6,5]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,4,3,5,1,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[2,4,3,5,1,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,4,3,5,6,1,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[2,4,3,5,6,7,1]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[2,4,3,5,7,1,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,4,3,5,7,6,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,4,3,6,1,5,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[2,4,3,6,1,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,4,3,6,5,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[2,4,3,6,5,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,4,3,6,7,1,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,4,3,6,7,5,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,4,3,7,1,5,6]=>[1,4,3,7,2,5,6]=>001001=>100100=>1
[2,4,3,7,1,6,5]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,4,3,7,5,1,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[2,4,3,7,5,6,1]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[2,4,3,7,6,1,5]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[2,4,3,7,6,5,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,4,5,1,3,6,7]=>[1,3,5,2,4,6,7]=>000100=>001000=>0
[2,4,5,1,3,7,6]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,4,5,1,6,3,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[2,4,5,1,6,7,3]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[2,4,5,1,7,3,6]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[2,4,5,1,7,6,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,4,5,3,1,6,7]=>[1,2,5,4,3,6,7]=>001100=>001100=>0
[2,4,5,3,1,7,6]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,4,5,3,6,1,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[2,4,5,3,6,7,1]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[2,4,5,3,7,1,6]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,4,5,3,7,6,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,4,5,6,1,3,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[2,4,5,6,1,7,3]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[2,4,5,6,3,1,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[2,4,5,6,3,7,1]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[2,4,5,6,7,1,3]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[2,4,5,6,7,3,1]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[2,4,5,7,1,3,6]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[2,4,5,7,1,6,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,4,5,7,3,1,6]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[2,4,5,7,3,6,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,4,5,7,6,1,3]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[2,4,5,7,6,3,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[2,4,6,1,3,5,7]=>[2,4,6,1,3,5,7]=>000010=>010000=>0
[2,4,6,1,3,7,5]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,4,6,1,5,3,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[2,4,6,1,5,7,3]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,4,6,1,7,3,5]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[2,4,6,1,7,5,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,4,6,3,1,5,7]=>[1,4,6,3,2,5,7]=>010010=>010010=>0
[2,4,6,3,1,7,5]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,4,6,3,5,1,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[2,4,6,3,5,7,1]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,4,6,3,7,1,5]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,4,6,3,7,5,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,4,6,5,1,3,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[2,4,6,5,1,7,3]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,4,6,5,3,1,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[2,4,6,5,3,7,1]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,4,6,5,7,1,3]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,4,6,5,7,3,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,4,6,7,1,3,5]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[2,4,6,7,1,5,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,4,6,7,3,1,5]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[2,4,6,7,3,5,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,4,6,7,5,1,3]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[2,4,6,7,5,3,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[2,4,7,1,3,5,6]=>[2,4,7,1,3,5,6]=>000001=>100000=>1
[2,4,7,1,3,6,5]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[2,4,7,1,5,3,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[2,4,7,1,5,6,3]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[2,4,7,1,6,3,5]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[2,4,7,1,6,5,3]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,4,7,3,1,5,6]=>[1,4,7,3,2,5,6]=>010001=>100010=>1
[2,4,7,3,1,6,5]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[2,4,7,3,5,1,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[2,4,7,3,5,6,1]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[2,4,7,3,6,1,5]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[2,4,7,3,6,5,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,4,7,5,1,3,6]=>[1,3,7,5,2,4,6]=>000101=>101000=>1
[2,4,7,5,1,6,3]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[2,4,7,5,3,1,6]=>[1,2,7,5,4,3,6]=>001101=>101100=>1
[2,4,7,5,3,6,1]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[2,4,7,5,6,1,3]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[2,4,7,5,6,3,1]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[2,4,7,6,1,3,5]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[2,4,7,6,1,5,3]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[2,4,7,6,3,1,5]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[2,4,7,6,3,5,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[2,4,7,6,5,1,3]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[2,4,7,6,5,3,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[2,5,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>000100=>001000=>0
[2,5,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>000101=>101000=>1
[2,5,1,3,6,4,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[2,5,1,3,6,7,4]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[2,5,1,3,7,4,6]=>[2,5,1,3,7,4,6]=>000101=>101000=>1
[2,5,1,3,7,6,4]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[2,5,1,4,3,6,7]=>[2,5,1,4,3,6,7]=>001100=>001100=>0
[2,5,1,4,3,7,6]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[2,5,1,4,6,3,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[2,5,1,4,6,7,3]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[2,5,1,4,7,3,6]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[2,5,1,4,7,6,3]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[2,5,1,6,3,4,7]=>[2,4,1,6,3,5,7]=>001010=>010100=>0
[2,5,1,6,3,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,5,1,6,4,3,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[2,5,1,6,4,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,5,1,6,7,3,4]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,5,1,6,7,4,3]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,5,1,7,3,4,6]=>[2,5,1,7,3,4,6]=>000101=>101000=>1
[2,5,1,7,3,6,4]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[2,5,1,7,4,3,6]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[2,5,1,7,4,6,3]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[2,5,1,7,6,3,4]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[2,5,1,7,6,4,3]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,5,3,1,4,6,7]=>[1,5,3,2,4,6,7]=>010100=>001010=>0
[2,5,3,1,4,7,6]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[2,5,3,1,6,4,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[2,5,3,1,6,7,4]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[2,5,3,1,7,4,6]=>[1,5,3,2,7,4,6]=>010101=>101010=>1
[2,5,3,1,7,6,4]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,5,3,4,1,6,7]=>[1,5,2,4,3,6,7]=>001100=>001100=>0
[2,5,3,4,1,7,6]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[2,5,3,4,6,1,7]=>[1,4,2,3,6,5,7]=>001010=>010100=>0
[2,5,3,4,6,7,1]=>[1,4,2,3,5,7,6]=>001001=>100100=>1
[2,5,3,4,7,1,6]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[2,5,3,4,7,6,1]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[2,5,3,6,1,4,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[2,5,3,6,1,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,5,3,6,4,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[2,5,3,6,4,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,5,3,6,7,1,4]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,5,3,6,7,4,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,5,3,7,1,4,6]=>[1,5,3,7,2,4,6]=>000101=>101000=>1
[2,5,3,7,1,6,4]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,5,3,7,4,1,6]=>[1,5,2,7,4,3,6]=>001101=>101100=>1
[2,5,3,7,4,6,1]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[2,5,3,7,6,1,4]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[2,5,3,7,6,4,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,5,4,1,3,6,7]=>[2,5,4,1,3,6,7]=>001100=>001100=>0
[2,5,4,1,3,7,6]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[2,5,4,1,6,3,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[2,5,4,1,6,7,3]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[2,5,4,1,7,3,6]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[2,5,4,1,7,6,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,5,4,3,1,6,7]=>[1,5,4,3,2,6,7]=>011100=>001110=>0
[2,5,4,3,1,7,6]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[2,5,4,3,6,1,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[2,5,4,3,6,7,1]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[2,5,4,3,7,1,6]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[2,5,4,3,7,6,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,5,4,6,1,3,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[2,5,4,6,1,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,5,4,6,3,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[2,5,4,6,3,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[2,5,4,6,7,1,3]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[2,5,4,6,7,3,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[2,5,4,7,1,3,6]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[2,5,4,7,1,6,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,5,4,7,3,1,6]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[2,5,4,7,3,6,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,5,4,7,6,1,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[2,5,4,7,6,3,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,5,6,1,3,4,7]=>[2,4,6,1,3,5,7]=>000010=>010000=>0
[2,5,6,1,3,7,4]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,5,6,1,4,3,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[2,5,6,1,4,7,3]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,5,6,1,7,3,4]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[2,5,6,1,7,4,3]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,5,6,3,1,4,7]=>[1,4,6,3,2,5,7]=>010010=>010010=>0
[2,5,6,3,1,7,4]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,5,6,3,4,1,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[2,5,6,3,4,7,1]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[2,5,6,3,7,1,4]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,5,6,3,7,4,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,5,6,4,1,3,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[2,5,6,4,1,7,3]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,5,6,4,3,1,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[2,5,6,4,3,7,1]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[2,5,6,4,7,1,3]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[2,5,6,4,7,3,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[2,5,6,7,1,3,4]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[2,5,6,7,1,4,3]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,5,6,7,3,1,4]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[2,5,6,7,3,4,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[2,5,6,7,4,1,3]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[2,5,6,7,4,3,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[2,5,7,1,3,4,6]=>[2,5,7,1,3,4,6]=>000001=>100000=>1
[2,5,7,1,3,6,4]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[2,5,7,1,4,3,6]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[2,5,7,1,4,6,3]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[2,5,7,1,6,3,4]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[2,5,7,1,6,4,3]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,5,7,3,1,4,6]=>[1,5,7,3,2,4,6]=>010001=>100010=>1
[2,5,7,3,1,6,4]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[2,5,7,3,4,1,6]=>[1,5,7,2,4,3,6]=>001001=>100100=>1
[2,5,7,3,4,6,1]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[2,5,7,3,6,1,4]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[2,5,7,3,6,4,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,5,7,4,1,3,6]=>[2,5,7,4,1,3,6]=>001001=>100100=>1
[2,5,7,4,1,6,3]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[2,5,7,4,3,1,6]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[2,5,7,4,3,6,1]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[2,5,7,4,6,1,3]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[2,5,7,4,6,3,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,5,7,6,1,3,4]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[2,5,7,6,1,4,3]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[2,5,7,6,3,1,4]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[2,5,7,6,3,4,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[2,5,7,6,4,1,3]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[2,5,7,6,4,3,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[2,6,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>000010=>010000=>0
[2,6,1,3,4,7,5]=>[2,5,1,3,4,7,6]=>000101=>101000=>1
[2,6,1,3,5,4,7]=>[2,6,1,3,5,4,7]=>000110=>011000=>0
[2,6,1,3,5,7,4]=>[2,5,1,3,4,7,6]=>000101=>101000=>1
[2,6,1,3,7,4,5]=>[2,5,1,3,7,4,6]=>000101=>101000=>1
[2,6,1,3,7,5,4]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[2,6,1,4,3,5,7]=>[2,6,1,4,3,5,7]=>001010=>010100=>0
[2,6,1,4,3,7,5]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[2,6,1,4,5,3,7]=>[2,6,1,3,5,4,7]=>000110=>011000=>0
[2,6,1,4,5,7,3]=>[2,5,1,3,4,7,6]=>000101=>101000=>1
[2,6,1,4,7,3,5]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[2,6,1,4,7,5,3]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[2,6,1,5,3,4,7]=>[2,6,1,5,3,4,7]=>000110=>011000=>0
[2,6,1,5,3,7,4]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[2,6,1,5,4,3,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[2,6,1,5,4,7,3]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[2,6,1,5,7,3,4]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[2,6,1,5,7,4,3]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[2,6,1,7,3,4,5]=>[2,5,1,7,3,4,6]=>000101=>101000=>1
[2,6,1,7,3,5,4]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[2,6,1,7,4,3,5]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[2,6,1,7,4,5,3]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[2,6,1,7,5,3,4]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[2,6,1,7,5,4,3]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,6,3,1,4,5,7]=>[1,6,3,2,4,5,7]=>010010=>010010=>0
[2,6,3,1,4,7,5]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[2,6,3,1,5,4,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[2,6,3,1,5,7,4]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[2,6,3,1,7,4,5]=>[1,5,3,2,7,4,6]=>010101=>101010=>1
[2,6,3,1,7,5,4]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,6,3,4,1,5,7]=>[1,6,2,4,3,5,7]=>001010=>010100=>0
[2,6,3,4,1,7,5]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[2,6,3,4,5,1,7]=>[1,6,2,3,5,4,7]=>000110=>011000=>0
[2,6,3,4,5,7,1]=>[1,5,2,3,4,7,6]=>000101=>101000=>1
[2,6,3,4,7,1,5]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[2,6,3,4,7,5,1]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[2,6,3,5,1,4,7]=>[1,6,3,5,2,4,7]=>000110=>011000=>0
[2,6,3,5,1,7,4]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[2,6,3,5,4,1,7]=>[1,6,2,5,4,3,7]=>001110=>011100=>0
[2,6,3,5,4,7,1]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[2,6,3,5,7,1,4]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[2,6,3,5,7,4,1]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[2,6,3,7,1,4,5]=>[1,5,3,7,2,4,6]=>000101=>101000=>1
[2,6,3,7,1,5,4]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,6,3,7,4,1,5]=>[1,5,2,7,4,3,6]=>001101=>101100=>1
[2,6,3,7,4,5,1]=>[1,4,2,7,3,6,5]=>001011=>110100=>2
[2,6,3,7,5,1,4]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[2,6,3,7,5,4,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,6,4,1,3,5,7]=>[2,6,4,1,3,5,7]=>001010=>010100=>0
[2,6,4,1,3,7,5]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[2,6,4,1,5,3,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[2,6,4,1,5,7,3]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[2,6,4,1,7,3,5]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[2,6,4,1,7,5,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,6,4,3,1,5,7]=>[1,6,4,3,2,5,7]=>011010=>010110=>0
[2,6,4,3,1,7,5]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[2,6,4,3,5,1,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[2,6,4,3,5,7,1]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[2,6,4,3,7,1,5]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[2,6,4,3,7,5,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,6,4,5,1,3,7]=>[1,6,3,5,2,4,7]=>000110=>011000=>0
[2,6,4,5,1,7,3]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[2,6,4,5,3,1,7]=>[1,6,2,5,4,3,7]=>001110=>011100=>0
[2,6,4,5,3,7,1]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[2,6,4,5,7,1,3]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[2,6,4,5,7,3,1]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[2,6,4,7,1,3,5]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[2,6,4,7,1,5,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,6,4,7,3,1,5]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[2,6,4,7,3,5,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,6,4,7,5,1,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[2,6,4,7,5,3,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,6,5,1,3,4,7]=>[2,6,5,1,3,4,7]=>000110=>011000=>0
[2,6,5,1,3,7,4]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[2,6,5,1,4,3,7]=>[2,6,5,1,4,3,7]=>001110=>011100=>0
[2,6,5,1,4,7,3]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[2,6,5,1,7,3,4]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[2,6,5,1,7,4,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,6,5,3,1,4,7]=>[1,6,5,3,2,4,7]=>010110=>011010=>0
[2,6,5,3,1,7,4]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[2,6,5,3,4,1,7]=>[1,6,5,2,4,3,7]=>001110=>011100=>0
[2,6,5,3,4,7,1]=>[1,5,4,2,3,7,6]=>001101=>101100=>1
[2,6,5,3,7,1,4]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[2,6,5,3,7,4,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,6,5,4,1,3,7]=>[2,6,5,4,1,3,7]=>001110=>011100=>0
[2,6,5,4,1,7,3]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[2,6,5,4,3,1,7]=>[1,6,5,4,3,2,7]=>011110=>011110=>0
[2,6,5,4,3,7,1]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[2,6,5,4,7,1,3]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[2,6,5,4,7,3,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[2,6,5,7,1,3,4]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[2,6,5,7,1,4,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,6,5,7,3,1,4]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[2,6,5,7,3,4,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[2,6,5,7,4,1,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[2,6,5,7,4,3,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[2,6,7,1,3,4,5]=>[2,5,7,1,3,4,6]=>000001=>100000=>1
[2,6,7,1,3,5,4]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[2,6,7,1,4,3,5]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[2,6,7,1,4,5,3]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[2,6,7,1,5,3,4]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[2,6,7,1,5,4,3]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,6,7,3,1,4,5]=>[1,5,7,3,2,4,6]=>010001=>100010=>1
[2,6,7,3,1,5,4]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[2,6,7,3,4,1,5]=>[1,5,7,2,4,3,6]=>001001=>100100=>1
[2,6,7,3,4,5,1]=>[1,4,7,2,3,6,5]=>000011=>110000=>2
[2,6,7,3,5,1,4]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[2,6,7,3,5,4,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,6,7,4,1,3,5]=>[2,5,7,4,1,3,6]=>001001=>100100=>1
[2,6,7,4,1,5,3]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[2,6,7,4,3,1,5]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[2,6,7,4,3,5,1]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[2,6,7,4,5,1,3]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[2,6,7,4,5,3,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[2,6,7,5,1,3,4]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[2,6,7,5,1,4,3]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[2,6,7,5,3,1,4]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[2,6,7,5,3,4,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[2,6,7,5,4,1,3]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[2,6,7,5,4,3,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[2,7,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>000001=>100000=>1
[2,7,1,3,4,6,5]=>[2,7,1,3,4,6,5]=>000011=>110000=>2
[2,7,1,3,5,4,6]=>[2,7,1,3,5,4,6]=>000101=>101000=>1
[2,7,1,3,5,6,4]=>[2,7,1,3,4,6,5]=>000011=>110000=>2
[2,7,1,3,6,4,5]=>[2,7,1,3,6,4,5]=>000011=>110000=>2
[2,7,1,3,6,5,4]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[2,7,1,4,3,5,6]=>[2,7,1,4,3,5,6]=>001001=>100100=>1
[2,7,1,4,3,6,5]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[2,7,1,4,5,3,6]=>[2,7,1,3,5,4,6]=>000101=>101000=>1
[2,7,1,4,5,6,3]=>[2,7,1,3,4,6,5]=>000011=>110000=>2
[2,7,1,4,6,3,5]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[2,7,1,4,6,5,3]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[2,7,1,5,3,4,6]=>[2,7,1,5,3,4,6]=>000101=>101000=>1
[2,7,1,5,3,6,4]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[2,7,1,5,4,3,6]=>[2,7,1,5,4,3,6]=>001101=>101100=>1
[2,7,1,5,4,6,3]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[2,7,1,5,6,3,4]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[2,7,1,5,6,4,3]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[2,7,1,6,3,4,5]=>[2,7,1,6,3,4,5]=>000011=>110000=>2
[2,7,1,6,3,5,4]=>[2,7,1,6,3,5,4]=>000111=>111000=>3
[2,7,1,6,4,3,5]=>[2,7,1,6,4,3,5]=>001011=>110100=>2
[2,7,1,6,4,5,3]=>[2,7,1,6,3,5,4]=>000111=>111000=>3
[2,7,1,6,5,3,4]=>[2,7,1,6,5,3,4]=>000111=>111000=>3
[2,7,1,6,5,4,3]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[2,7,3,1,4,5,6]=>[1,7,3,2,4,5,6]=>010001=>100010=>1
[2,7,3,1,4,6,5]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[2,7,3,1,5,4,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[2,7,3,1,5,6,4]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[2,7,3,1,6,4,5]=>[1,7,3,2,6,4,5]=>010011=>110010=>2
[2,7,3,1,6,5,4]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[2,7,3,4,1,5,6]=>[1,7,2,4,3,5,6]=>001001=>100100=>1
[2,7,3,4,1,6,5]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[2,7,3,4,5,1,6]=>[1,7,2,3,5,4,6]=>000101=>101000=>1
[2,7,3,4,5,6,1]=>[1,7,2,3,4,6,5]=>000011=>110000=>2
[2,7,3,4,6,1,5]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[2,7,3,4,6,5,1]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[2,7,3,5,1,4,6]=>[1,7,3,5,2,4,6]=>000101=>101000=>1
[2,7,3,5,1,6,4]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[2,7,3,5,4,1,6]=>[1,7,2,5,4,3,6]=>001101=>101100=>1
[2,7,3,5,4,6,1]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[2,7,3,5,6,1,4]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[2,7,3,5,6,4,1]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[2,7,3,6,1,4,5]=>[1,7,3,6,2,4,5]=>000011=>110000=>2
[2,7,3,6,1,5,4]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[2,7,3,6,4,1,5]=>[1,7,2,6,4,3,5]=>001011=>110100=>2
[2,7,3,6,4,5,1]=>[1,7,2,6,3,5,4]=>000111=>111000=>3
[2,7,3,6,5,1,4]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[2,7,3,6,5,4,1]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[2,7,4,1,3,5,6]=>[2,7,4,1,3,5,6]=>001001=>100100=>1
[2,7,4,1,3,6,5]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[2,7,4,1,5,3,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[2,7,4,1,5,6,3]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[2,7,4,1,6,3,5]=>[2,7,4,1,6,3,5]=>001011=>110100=>2
[2,7,4,1,6,5,3]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[2,7,4,3,1,5,6]=>[1,7,4,3,2,5,6]=>011001=>100110=>1
[2,7,4,3,1,6,5]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[2,7,4,3,5,1,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[2,7,4,3,5,6,1]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[2,7,4,3,6,1,5]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[2,7,4,3,6,5,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[2,7,4,5,1,3,6]=>[1,7,3,5,2,4,6]=>000101=>101000=>1
[2,7,4,5,1,6,3]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[2,7,4,5,3,1,6]=>[1,7,2,5,4,3,6]=>001101=>101100=>1
[2,7,4,5,3,6,1]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[2,7,4,5,6,1,3]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[2,7,4,5,6,3,1]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[2,7,4,6,1,3,5]=>[2,7,4,6,1,3,5]=>000011=>110000=>2
[2,7,4,6,1,5,3]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[2,7,4,6,3,1,5]=>[1,7,4,6,3,2,5]=>010011=>110010=>2
[2,7,4,6,3,5,1]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[2,7,4,6,5,1,3]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[2,7,4,6,5,3,1]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[2,7,5,1,3,4,6]=>[2,7,5,1,3,4,6]=>000101=>101000=>1
[2,7,5,1,3,6,4]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[2,7,5,1,4,3,6]=>[2,7,5,1,4,3,6]=>001101=>101100=>1
[2,7,5,1,4,6,3]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[2,7,5,1,6,3,4]=>[2,7,4,1,6,3,5]=>001011=>110100=>2
[2,7,5,1,6,4,3]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[2,7,5,3,1,4,6]=>[1,7,5,3,2,4,6]=>010101=>101010=>1
[2,7,5,3,1,6,4]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[2,7,5,3,4,1,6]=>[1,7,5,2,4,3,6]=>001101=>101100=>1
[2,7,5,3,4,6,1]=>[1,7,4,2,3,6,5]=>001011=>110100=>2
[2,7,5,3,6,1,4]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[2,7,5,3,6,4,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[2,7,5,4,1,3,6]=>[2,7,5,4,1,3,6]=>001101=>101100=>1
[2,7,5,4,1,6,3]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[2,7,5,4,3,1,6]=>[1,7,5,4,3,2,6]=>011101=>101110=>1
[2,7,5,4,3,6,1]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[2,7,5,4,6,1,3]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[2,7,5,4,6,3,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[2,7,5,6,1,3,4]=>[2,7,4,6,1,3,5]=>000011=>110000=>2
[2,7,5,6,1,4,3]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[2,7,5,6,3,1,4]=>[1,7,4,6,3,2,5]=>010011=>110010=>2
[2,7,5,6,3,4,1]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[2,7,5,6,4,1,3]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[2,7,5,6,4,3,1]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[2,7,6,1,3,4,5]=>[2,7,6,1,3,4,5]=>000011=>110000=>2
[2,7,6,1,3,5,4]=>[2,7,6,1,3,5,4]=>000111=>111000=>3
[2,7,6,1,4,3,5]=>[2,7,6,1,4,3,5]=>001011=>110100=>2
[2,7,6,1,4,5,3]=>[2,7,6,1,3,5,4]=>000111=>111000=>3
[2,7,6,1,5,3,4]=>[2,7,6,1,5,3,4]=>000111=>111000=>3
[2,7,6,1,5,4,3]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[2,7,6,3,1,4,5]=>[1,7,6,3,2,4,5]=>010011=>110010=>2
[2,7,6,3,1,5,4]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[2,7,6,3,4,1,5]=>[1,7,6,2,4,3,5]=>001011=>110100=>2
[2,7,6,3,4,5,1]=>[1,7,6,2,3,5,4]=>000111=>111000=>3
[2,7,6,3,5,1,4]=>[1,7,6,3,5,2,4]=>000111=>111000=>3
[2,7,6,3,5,4,1]=>[1,7,6,2,5,4,3]=>001111=>111100=>4
[2,7,6,4,1,3,5]=>[2,7,6,4,1,3,5]=>001011=>110100=>2
[2,7,6,4,1,5,3]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[2,7,6,4,3,1,5]=>[1,7,6,4,3,2,5]=>011011=>110110=>2
[2,7,6,4,3,5,1]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[2,7,6,4,5,1,3]=>[1,7,6,3,5,2,4]=>000111=>111000=>3
[2,7,6,4,5,3,1]=>[1,7,6,2,5,4,3]=>001111=>111100=>4
[2,7,6,5,1,3,4]=>[2,7,6,5,1,3,4]=>000111=>111000=>3
[2,7,6,5,1,4,3]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[2,7,6,5,3,1,4]=>[1,7,6,5,3,2,4]=>010111=>111010=>3
[2,7,6,5,3,4,1]=>[1,7,6,5,2,4,3]=>001111=>111100=>4
[2,7,6,5,4,1,3]=>[2,7,6,5,4,1,3]=>001111=>111100=>4
[2,7,6,5,4,3,1]=>[1,7,6,5,4,3,2]=>011111=>111110=>5
[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>010000=>000010=>0
[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>010001=>100010=>1
[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>010010=>010010=>0
[3,1,2,4,6,7,5]=>[3,1,2,4,5,7,6]=>010001=>100010=>1
[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>010001=>100010=>1
[3,1,2,4,7,6,5]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>010100=>001010=>0
[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[3,1,2,5,6,4,7]=>[3,1,2,4,6,5,7]=>010010=>010010=>0
[3,1,2,5,6,7,4]=>[3,1,2,4,5,7,6]=>010001=>100010=>1
[3,1,2,5,7,4,6]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[3,1,2,5,7,6,4]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>010010=>010010=>0
[3,1,2,6,4,7,5]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[3,1,2,6,5,4,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[3,1,2,6,5,7,4]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[3,1,2,6,7,4,5]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[3,1,2,6,7,5,4]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>010001=>100010=>1
[3,1,2,7,4,6,5]=>[3,1,2,7,4,6,5]=>010011=>110010=>2
[3,1,2,7,5,4,6]=>[3,1,2,7,5,4,6]=>010101=>101010=>1
[3,1,2,7,5,6,4]=>[3,1,2,7,4,6,5]=>010011=>110010=>2
[3,1,2,7,6,4,5]=>[3,1,2,7,6,4,5]=>010011=>110010=>2
[3,1,2,7,6,5,4]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[3,1,4,2,5,6,7]=>[2,1,4,3,5,6,7]=>101000=>000101=>0
[3,1,4,2,5,7,6]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,1,4,2,6,5,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[3,1,4,2,6,7,5]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,1,4,2,7,5,6]=>[2,1,4,3,7,5,6]=>101001=>100101=>1
[3,1,4,2,7,6,5]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,1,4,5,2,6,7]=>[2,1,3,5,4,6,7]=>100100=>001001=>0
[3,1,4,5,2,7,6]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,1,4,5,6,2,7]=>[2,1,3,4,6,5,7]=>100010=>010001=>0
[3,1,4,5,6,7,2]=>[2,1,3,4,5,7,6]=>100001=>100001=>1
[3,1,4,5,7,2,6]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[3,1,4,5,7,6,2]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[3,1,4,6,2,5,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[3,1,4,6,2,7,5]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,1,4,6,5,2,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[3,1,4,6,5,7,2]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,1,4,6,7,2,5]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[3,1,4,6,7,5,2]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[3,1,4,7,2,5,6]=>[2,1,4,7,3,5,6]=>100001=>100001=>1
[3,1,4,7,2,6,5]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,1,4,7,5,2,6]=>[2,1,3,7,5,4,6]=>100101=>101001=>1
[3,1,4,7,5,6,2]=>[2,1,3,7,4,6,5]=>100011=>110001=>2
[3,1,4,7,6,2,5]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[3,1,4,7,6,5,2]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[3,1,5,2,4,6,7]=>[3,1,5,2,4,6,7]=>010100=>001010=>0
[3,1,5,2,4,7,6]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[3,1,5,2,6,4,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[3,1,5,2,6,7,4]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,1,5,2,7,4,6]=>[3,1,5,2,7,4,6]=>010101=>101010=>1
[3,1,5,2,7,6,4]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,1,5,4,2,6,7]=>[2,1,5,4,3,6,7]=>101100=>001101=>0
[3,1,5,4,2,7,6]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,1,5,4,6,2,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[3,1,5,4,6,7,2]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,1,5,4,7,2,6]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[3,1,5,4,7,6,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,1,5,6,2,4,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[3,1,5,6,2,7,4]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,1,5,6,4,2,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[3,1,5,6,4,7,2]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,1,5,6,7,2,4]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[3,1,5,6,7,4,2]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[3,1,5,7,2,4,6]=>[3,1,5,7,2,4,6]=>010001=>100010=>1
[3,1,5,7,2,6,4]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,1,5,7,4,2,6]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[3,1,5,7,4,6,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,1,5,7,6,2,4]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[3,1,5,7,6,4,2]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[3,1,6,2,4,5,7]=>[3,1,6,2,4,5,7]=>010010=>010010=>0
[3,1,6,2,4,7,5]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[3,1,6,2,5,4,7]=>[3,1,6,2,5,4,7]=>010110=>011010=>0
[3,1,6,2,5,7,4]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[3,1,6,2,7,4,5]=>[3,1,5,2,7,4,6]=>010101=>101010=>1
[3,1,6,2,7,5,4]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,1,6,4,2,5,7]=>[2,1,6,4,3,5,7]=>101010=>010101=>0
[3,1,6,4,2,7,5]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,1,6,4,5,2,7]=>[2,1,6,3,5,4,7]=>100110=>011001=>0
[3,1,6,4,5,7,2]=>[2,1,5,3,4,7,6]=>100101=>101001=>1
[3,1,6,4,7,2,5]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[3,1,6,4,7,5,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,1,6,5,2,4,7]=>[3,1,6,5,2,4,7]=>010110=>011010=>0
[3,1,6,5,2,7,4]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,1,6,5,4,2,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[3,1,6,5,4,7,2]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,1,6,5,7,2,4]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[3,1,6,5,7,4,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,1,6,7,2,4,5]=>[3,1,5,7,2,4,6]=>010001=>100010=>1
[3,1,6,7,2,5,4]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,1,6,7,4,2,5]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[3,1,6,7,4,5,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,1,6,7,5,2,4]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[3,1,6,7,5,4,2]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[3,1,7,2,4,5,6]=>[3,1,7,2,4,5,6]=>010001=>100010=>1
[3,1,7,2,4,6,5]=>[3,1,7,2,4,6,5]=>010011=>110010=>2
[3,1,7,2,5,4,6]=>[3,1,7,2,5,4,6]=>010101=>101010=>1
[3,1,7,2,5,6,4]=>[3,1,7,2,4,6,5]=>010011=>110010=>2
[3,1,7,2,6,4,5]=>[3,1,7,2,6,4,5]=>010011=>110010=>2
[3,1,7,2,6,5,4]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[3,1,7,4,2,5,6]=>[2,1,7,4,3,5,6]=>101001=>100101=>1
[3,1,7,4,2,6,5]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[3,1,7,4,5,2,6]=>[2,1,7,3,5,4,6]=>100101=>101001=>1
[3,1,7,4,5,6,2]=>[2,1,7,3,4,6,5]=>100011=>110001=>2
[3,1,7,4,6,2,5]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[3,1,7,4,6,5,2]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[3,1,7,5,2,4,6]=>[3,1,7,5,2,4,6]=>010101=>101010=>1
[3,1,7,5,2,6,4]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[3,1,7,5,4,2,6]=>[2,1,7,5,4,3,6]=>101101=>101101=>1
[3,1,7,5,4,6,2]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[3,1,7,5,6,2,4]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[3,1,7,5,6,4,2]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[3,1,7,6,2,4,5]=>[3,1,7,6,2,4,5]=>010011=>110010=>2
[3,1,7,6,2,5,4]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[3,1,7,6,4,2,5]=>[2,1,7,6,4,3,5]=>101011=>110101=>2
[3,1,7,6,4,5,2]=>[2,1,7,6,3,5,4]=>100111=>111001=>3
[3,1,7,6,5,2,4]=>[3,1,7,6,5,2,4]=>010111=>111010=>3
[3,1,7,6,5,4,2]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000=>000011=>0
[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>110001=>100011=>1
[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>110010=>010011=>0
[3,2,1,4,6,7,5]=>[3,2,1,4,5,7,6]=>110001=>100011=>1
[3,2,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>110001=>100011=>1
[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>110100=>001011=>0
[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[3,2,1,5,6,4,7]=>[3,2,1,4,6,5,7]=>110010=>010011=>0
[3,2,1,5,6,7,4]=>[3,2,1,4,5,7,6]=>110001=>100011=>1
[3,2,1,5,7,4,6]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[3,2,1,5,7,6,4]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[3,2,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>110010=>010011=>0
[3,2,1,6,4,7,5]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[3,2,1,6,5,7,4]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[3,2,1,6,7,4,5]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[3,2,1,6,7,5,4]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[3,2,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>110001=>100011=>1
[3,2,1,7,4,6,5]=>[3,2,1,7,4,6,5]=>110011=>110011=>2
[3,2,1,7,5,4,6]=>[3,2,1,7,5,4,6]=>110101=>101011=>1
[3,2,1,7,5,6,4]=>[3,2,1,7,4,6,5]=>110011=>110011=>2
[3,2,1,7,6,4,5]=>[3,2,1,7,6,4,5]=>110011=>110011=>2
[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[3,2,4,1,5,6,7]=>[2,1,4,3,5,6,7]=>101000=>000101=>0
[3,2,4,1,5,7,6]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,2,4,1,6,5,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[3,2,4,1,6,7,5]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,2,4,1,7,5,6]=>[2,1,4,3,7,5,6]=>101001=>100101=>1
[3,2,4,1,7,6,5]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,2,4,5,1,6,7]=>[2,1,3,5,4,6,7]=>100100=>001001=>0
[3,2,4,5,1,7,6]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,2,4,5,6,1,7]=>[2,1,3,4,6,5,7]=>100010=>010001=>0
[3,2,4,5,6,7,1]=>[2,1,3,4,5,7,6]=>100001=>100001=>1
[3,2,4,5,7,1,6]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[3,2,4,5,7,6,1]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[3,2,4,6,1,5,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[3,2,4,6,1,7,5]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,2,4,6,5,1,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[3,2,4,6,5,7,1]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,2,4,6,7,1,5]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[3,2,4,6,7,5,1]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[3,2,4,7,1,5,6]=>[2,1,4,7,3,5,6]=>100001=>100001=>1
[3,2,4,7,1,6,5]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,2,4,7,5,1,6]=>[2,1,3,7,5,4,6]=>100101=>101001=>1
[3,2,4,7,5,6,1]=>[2,1,3,7,4,6,5]=>100011=>110001=>2
[3,2,4,7,6,1,5]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[3,2,4,7,6,5,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[3,2,5,1,4,6,7]=>[3,2,5,1,4,6,7]=>010100=>001010=>0
[3,2,5,1,4,7,6]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[3,2,5,1,6,4,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[3,2,5,1,6,7,4]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,2,5,1,7,4,6]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[3,2,5,1,7,6,4]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,2,5,4,1,6,7]=>[2,1,5,4,3,6,7]=>101100=>001101=>0
[3,2,5,4,1,7,6]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,2,5,4,6,1,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[3,2,5,4,6,7,1]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[3,2,5,4,7,1,6]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[3,2,5,4,7,6,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,2,5,6,1,4,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[3,2,5,6,1,7,4]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,2,5,6,4,1,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[3,2,5,6,4,7,1]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[3,2,5,6,7,1,4]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[3,2,5,6,7,4,1]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[3,2,5,7,1,4,6]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[3,2,5,7,1,6,4]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,2,5,7,4,1,6]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[3,2,5,7,4,6,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,2,5,7,6,1,4]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[3,2,5,7,6,4,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[3,2,6,1,4,5,7]=>[3,2,6,1,4,5,7]=>010010=>010010=>0
[3,2,6,1,4,7,5]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[3,2,6,1,5,4,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[3,2,6,1,5,7,4]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[3,2,6,1,7,4,5]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[3,2,6,1,7,5,4]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,2,6,4,1,5,7]=>[2,1,6,4,3,5,7]=>101010=>010101=>0
[3,2,6,4,1,7,5]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,2,6,4,5,1,7]=>[2,1,6,3,5,4,7]=>100110=>011001=>0
[3,2,6,4,5,7,1]=>[2,1,5,3,4,7,6]=>100101=>101001=>1
[3,2,6,4,7,1,5]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[3,2,6,4,7,5,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,2,6,5,1,4,7]=>[3,2,6,5,1,4,7]=>010110=>011010=>0
[3,2,6,5,1,7,4]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,2,6,5,4,1,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[3,2,6,5,4,7,1]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[3,2,6,5,7,1,4]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[3,2,6,5,7,4,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[3,2,6,7,1,4,5]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[3,2,6,7,1,5,4]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,2,6,7,4,1,5]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[3,2,6,7,4,5,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[3,2,6,7,5,1,4]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[3,2,6,7,5,4,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[3,2,7,1,4,5,6]=>[3,2,7,1,4,5,6]=>010001=>100010=>1
[3,2,7,1,4,6,5]=>[3,2,7,1,4,6,5]=>010011=>110010=>2
[3,2,7,1,5,4,6]=>[3,2,7,1,5,4,6]=>010101=>101010=>1
[3,2,7,1,5,6,4]=>[3,2,7,1,4,6,5]=>010011=>110010=>2
[3,2,7,1,6,4,5]=>[3,2,7,1,6,4,5]=>010011=>110010=>2
[3,2,7,1,6,5,4]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[3,2,7,4,1,5,6]=>[2,1,7,4,3,5,6]=>101001=>100101=>1
[3,2,7,4,1,6,5]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[3,2,7,4,5,1,6]=>[2,1,7,3,5,4,6]=>100101=>101001=>1
[3,2,7,4,5,6,1]=>[2,1,7,3,4,6,5]=>100011=>110001=>2
[3,2,7,4,6,1,5]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[3,2,7,4,6,5,1]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[3,2,7,5,1,4,6]=>[3,2,7,5,1,4,6]=>010101=>101010=>1
[3,2,7,5,1,6,4]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[3,2,7,5,4,1,6]=>[2,1,7,5,4,3,6]=>101101=>101101=>1
[3,2,7,5,4,6,1]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[3,2,7,5,6,1,4]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[3,2,7,5,6,4,1]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[3,2,7,6,1,4,5]=>[3,2,7,6,1,4,5]=>010011=>110010=>2
[3,2,7,6,1,5,4]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[3,2,7,6,4,1,5]=>[2,1,7,6,4,3,5]=>101011=>110101=>2
[3,2,7,6,4,5,1]=>[2,1,7,6,3,5,4]=>100111=>111001=>3
[3,2,7,6,5,1,4]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[3,2,7,6,5,4,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[3,4,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>001000=>000100=>0
[3,4,1,2,5,7,6]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[3,4,1,2,6,5,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[3,4,1,2,6,7,5]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[3,4,1,2,7,5,6]=>[2,4,1,3,7,5,6]=>001001=>100100=>1
[3,4,1,2,7,6,5]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,4,1,5,2,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[3,4,1,5,2,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,4,1,5,6,2,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[3,4,1,5,6,7,2]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[3,4,1,5,7,2,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[3,4,1,5,7,6,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[3,4,1,6,2,5,7]=>[2,4,1,6,3,5,7]=>001010=>010100=>0
[3,4,1,6,2,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,4,1,6,5,2,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[3,4,1,6,5,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,4,1,6,7,2,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[3,4,1,6,7,5,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[3,4,1,7,2,5,6]=>[2,4,1,7,3,5,6]=>001001=>100100=>1
[3,4,1,7,2,6,5]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[3,4,1,7,5,2,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[3,4,1,7,5,6,2]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[3,4,1,7,6,2,5]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[3,4,1,7,6,5,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,4,2,1,5,6,7]=>[1,4,3,2,5,6,7]=>011000=>000110=>0
[3,4,2,1,5,7,6]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[3,4,2,1,6,5,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[3,4,2,1,6,7,5]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[3,4,2,1,7,5,6]=>[1,4,3,2,7,5,6]=>011001=>100110=>1
[3,4,2,1,7,6,5]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,4,2,5,1,6,7]=>[1,3,2,5,4,6,7]=>010100=>001010=>0
[3,4,2,5,1,7,6]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,4,2,5,6,1,7]=>[1,3,2,4,6,5,7]=>010010=>010010=>0
[3,4,2,5,6,7,1]=>[1,3,2,4,5,7,6]=>010001=>100010=>1
[3,4,2,5,7,1,6]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[3,4,2,5,7,6,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[3,4,2,6,1,5,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[3,4,2,6,1,7,5]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,4,2,6,5,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[3,4,2,6,5,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,4,2,6,7,1,5]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[3,4,2,6,7,5,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[3,4,2,7,1,5,6]=>[1,4,3,7,2,5,6]=>001001=>100100=>1
[3,4,2,7,1,6,5]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,4,2,7,5,1,6]=>[1,3,2,7,5,4,6]=>010101=>101010=>1
[3,4,2,7,5,6,1]=>[1,3,2,7,4,6,5]=>010011=>110010=>2
[3,4,2,7,6,1,5]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[3,4,2,7,6,5,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,4,5,1,2,6,7]=>[1,3,5,2,4,6,7]=>000100=>001000=>0
[3,4,5,1,2,7,6]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[3,4,5,1,6,2,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[3,4,5,1,6,7,2]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[3,4,5,1,7,2,6]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[3,4,5,1,7,6,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,4,5,2,1,6,7]=>[1,2,5,4,3,6,7]=>001100=>001100=>0
[3,4,5,2,1,7,6]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[3,4,5,2,6,1,7]=>[1,2,4,3,6,5,7]=>001010=>010100=>0
[3,4,5,2,6,7,1]=>[1,2,4,3,5,7,6]=>001001=>100100=>1
[3,4,5,2,7,1,6]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[3,4,5,2,7,6,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,4,5,6,1,2,7]=>[1,2,4,6,3,5,7]=>000010=>010000=>0
[3,4,5,6,1,7,2]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[3,4,5,6,2,1,7]=>[1,2,3,6,5,4,7]=>000110=>011000=>0
[3,4,5,6,2,7,1]=>[1,2,3,5,4,7,6]=>000101=>101000=>1
[3,4,5,6,7,1,2]=>[1,2,3,5,7,4,6]=>000001=>100000=>1
[3,4,5,6,7,2,1]=>[1,2,3,4,7,6,5]=>000011=>110000=>2
[3,4,5,7,1,2,6]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[3,4,5,7,1,6,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[3,4,5,7,2,1,6]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[3,4,5,7,2,6,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[3,4,5,7,6,1,2]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[3,4,5,7,6,2,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[3,4,6,1,2,5,7]=>[2,4,6,1,3,5,7]=>000010=>010000=>0
[3,4,6,1,2,7,5]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[3,4,6,1,5,2,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[3,4,6,1,5,7,2]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[3,4,6,1,7,2,5]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[3,4,6,1,7,5,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,4,6,2,1,5,7]=>[1,4,6,3,2,5,7]=>010010=>010010=>0
[3,4,6,2,1,7,5]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[3,4,6,2,5,1,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[3,4,6,2,5,7,1]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[3,4,6,2,7,1,5]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[3,4,6,2,7,5,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,4,6,5,1,2,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[3,4,6,5,1,7,2]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[3,4,6,5,2,1,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[3,4,6,5,2,7,1]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[3,4,6,5,7,1,2]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[3,4,6,5,7,2,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,4,6,7,1,2,5]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[3,4,6,7,1,5,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[3,4,6,7,2,1,5]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[3,4,6,7,2,5,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[3,4,6,7,5,1,2]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[3,4,6,7,5,2,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[3,4,7,1,2,5,6]=>[2,4,7,1,3,5,6]=>000001=>100000=>1
[3,4,7,1,2,6,5]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[3,4,7,1,5,2,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[3,4,7,1,5,6,2]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[3,4,7,1,6,2,5]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[3,4,7,1,6,5,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,4,7,2,1,5,6]=>[1,4,7,3,2,5,6]=>010001=>100010=>1
[3,4,7,2,1,6,5]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[3,4,7,2,5,1,6]=>[1,3,7,2,5,4,6]=>000101=>101000=>1
[3,4,7,2,5,6,1]=>[1,3,7,2,4,6,5]=>000011=>110000=>2
[3,4,7,2,6,1,5]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[3,4,7,2,6,5,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,4,7,5,1,2,6]=>[1,3,7,5,2,4,6]=>000101=>101000=>1
[3,4,7,5,1,6,2]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[3,4,7,5,2,1,6]=>[1,2,7,5,4,3,6]=>001101=>101100=>1
[3,4,7,5,2,6,1]=>[1,2,7,4,3,6,5]=>001011=>110100=>2
[3,4,7,5,6,1,2]=>[1,2,7,4,6,3,5]=>000011=>110000=>2
[3,4,7,5,6,2,1]=>[1,2,7,3,6,5,4]=>000111=>111000=>3
[3,4,7,6,1,2,5]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[3,4,7,6,1,5,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[3,4,7,6,2,1,5]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[3,4,7,6,2,5,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[3,4,7,6,5,1,2]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[3,4,7,6,5,2,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[3,5,1,2,4,6,7]=>[3,5,1,2,4,6,7]=>000100=>001000=>0
[3,5,1,2,4,7,6]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[3,5,1,2,6,4,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[3,5,1,2,6,7,4]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[3,5,1,2,7,4,6]=>[3,5,1,2,7,4,6]=>000101=>101000=>1
[3,5,1,2,7,6,4]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,5,1,4,2,6,7]=>[2,5,1,4,3,6,7]=>001100=>001100=>0
[3,5,1,4,2,7,6]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,5,1,4,6,2,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[3,5,1,4,6,7,2]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[3,5,1,4,7,2,6]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[3,5,1,4,7,6,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,5,1,6,2,4,7]=>[2,4,1,6,3,5,7]=>001010=>010100=>0
[3,5,1,6,2,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,5,1,6,4,2,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[3,5,1,6,4,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,5,1,6,7,2,4]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[3,5,1,6,7,4,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[3,5,1,7,2,4,6]=>[3,5,1,7,2,4,6]=>000101=>101000=>1
[3,5,1,7,2,6,4]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[3,5,1,7,4,2,6]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[3,5,1,7,4,6,2]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[3,5,1,7,6,2,4]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[3,5,1,7,6,4,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,5,2,1,4,6,7]=>[3,5,2,1,4,6,7]=>100100=>001001=>0
[3,5,2,1,4,7,6]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[3,5,2,1,6,4,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[3,5,2,1,6,7,4]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[3,5,2,1,7,4,6]=>[3,5,2,1,7,4,6]=>100101=>101001=>1
[3,5,2,1,7,6,4]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,5,2,4,1,6,7]=>[2,5,1,4,3,6,7]=>001100=>001100=>0
[3,5,2,4,1,7,6]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,5,2,4,6,1,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[3,5,2,4,6,7,1]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[3,5,2,4,7,1,6]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[3,5,2,4,7,6,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,5,2,6,1,4,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[3,5,2,6,1,7,4]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,5,2,6,4,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[3,5,2,6,4,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,5,2,6,7,1,4]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[3,5,2,6,7,4,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[3,5,2,7,1,4,6]=>[3,5,2,7,1,4,6]=>000101=>101000=>1
[3,5,2,7,1,6,4]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,5,2,7,4,1,6]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[3,5,2,7,4,6,1]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[3,5,2,7,6,1,4]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[3,5,2,7,6,4,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,5,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>001100=>001100=>0
[3,5,4,1,2,7,6]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[3,5,4,1,6,2,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[3,5,4,1,6,7,2]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[3,5,4,1,7,2,6]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[3,5,4,1,7,6,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,5,4,2,1,6,7]=>[1,5,4,3,2,6,7]=>011100=>001110=>0
[3,5,4,2,1,7,6]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[3,5,4,2,6,1,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[3,5,4,2,6,7,1]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[3,5,4,2,7,1,6]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[3,5,4,2,7,6,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,5,4,6,1,2,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[3,5,4,6,1,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,5,4,6,2,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[3,5,4,6,2,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[3,5,4,6,7,1,2]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[3,5,4,6,7,2,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[3,5,4,7,1,2,6]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[3,5,4,7,1,6,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,5,4,7,2,1,6]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[3,5,4,7,2,6,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,5,4,7,6,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[3,5,4,7,6,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,5,6,1,2,4,7]=>[2,4,6,1,3,5,7]=>000010=>010000=>0
[3,5,6,1,2,7,4]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[3,5,6,1,4,2,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[3,5,6,1,4,7,2]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[3,5,6,1,7,2,4]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[3,5,6,1,7,4,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,5,6,2,1,4,7]=>[1,4,6,3,2,5,7]=>010010=>010010=>0
[3,5,6,2,1,7,4]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[3,5,6,2,4,1,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[3,5,6,2,4,7,1]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[3,5,6,2,7,1,4]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[3,5,6,2,7,4,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,5,6,4,1,2,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[3,5,6,4,1,7,2]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[3,5,6,4,2,1,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[3,5,6,4,2,7,1]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[3,5,6,4,7,1,2]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[3,5,6,4,7,2,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[3,5,6,7,1,2,4]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[3,5,6,7,1,4,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[3,5,6,7,2,1,4]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[3,5,6,7,2,4,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[3,5,6,7,4,1,2]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[3,5,6,7,4,2,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[3,5,7,1,2,4,6]=>[3,5,7,1,2,4,6]=>000001=>100000=>1
[3,5,7,1,2,6,4]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[3,5,7,1,4,2,6]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[3,5,7,1,4,6,2]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[3,5,7,1,6,2,4]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[3,5,7,1,6,4,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,5,7,2,1,4,6]=>[3,5,7,2,1,4,6]=>100001=>100001=>1
[3,5,7,2,1,6,4]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[3,5,7,2,4,1,6]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[3,5,7,2,4,6,1]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[3,5,7,2,6,1,4]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[3,5,7,2,6,4,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,5,7,4,1,2,6]=>[2,5,7,4,1,3,6]=>001001=>100100=>1
[3,5,7,4,1,6,2]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[3,5,7,4,2,1,6]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[3,5,7,4,2,6,1]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[3,5,7,4,6,1,2]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[3,5,7,4,6,2,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,5,7,6,1,2,4]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[3,5,7,6,1,4,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[3,5,7,6,2,1,4]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[3,5,7,6,2,4,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[3,5,7,6,4,1,2]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[3,5,7,6,4,2,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[3,6,1,2,4,5,7]=>[3,6,1,2,4,5,7]=>000010=>010000=>0
[3,6,1,2,4,7,5]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[3,6,1,2,5,4,7]=>[3,6,1,2,5,4,7]=>000110=>011000=>0
[3,6,1,2,5,7,4]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[3,6,1,2,7,4,5]=>[3,5,1,2,7,4,6]=>000101=>101000=>1
[3,6,1,2,7,5,4]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,6,1,4,2,5,7]=>[2,6,1,4,3,5,7]=>001010=>010100=>0
[3,6,1,4,2,7,5]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,6,1,4,5,2,7]=>[2,6,1,3,5,4,7]=>000110=>011000=>0
[3,6,1,4,5,7,2]=>[2,5,1,3,4,7,6]=>000101=>101000=>1
[3,6,1,4,7,2,5]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[3,6,1,4,7,5,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,6,1,5,2,4,7]=>[3,6,1,5,2,4,7]=>000110=>011000=>0
[3,6,1,5,2,7,4]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,6,1,5,4,2,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[3,6,1,5,4,7,2]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,6,1,5,7,2,4]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[3,6,1,5,7,4,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,6,1,7,2,4,5]=>[3,5,1,7,2,4,6]=>000101=>101000=>1
[3,6,1,7,2,5,4]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[3,6,1,7,4,2,5]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[3,6,1,7,4,5,2]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[3,6,1,7,5,2,4]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[3,6,1,7,5,4,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,6,2,1,4,5,7]=>[3,6,2,1,4,5,7]=>100010=>010001=>0
[3,6,2,1,4,7,5]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[3,6,2,1,5,4,7]=>[3,6,2,1,5,4,7]=>100110=>011001=>0
[3,6,2,1,5,7,4]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[3,6,2,1,7,4,5]=>[3,5,2,1,7,4,6]=>100101=>101001=>1
[3,6,2,1,7,5,4]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,6,2,4,1,5,7]=>[2,6,1,4,3,5,7]=>001010=>010100=>0
[3,6,2,4,1,7,5]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,6,2,4,5,1,7]=>[2,6,1,3,5,4,7]=>000110=>011000=>0
[3,6,2,4,5,7,1]=>[2,5,1,3,4,7,6]=>000101=>101000=>1
[3,6,2,4,7,1,5]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[3,6,2,4,7,5,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,6,2,5,1,4,7]=>[3,6,2,5,1,4,7]=>000110=>011000=>0
[3,6,2,5,1,7,4]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,6,2,5,4,1,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[3,6,2,5,4,7,1]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[3,6,2,5,7,1,4]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[3,6,2,5,7,4,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[3,6,2,7,1,4,5]=>[3,5,2,7,1,4,6]=>000101=>101000=>1
[3,6,2,7,1,5,4]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,6,2,7,4,1,5]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[3,6,2,7,4,5,1]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[3,6,2,7,5,1,4]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[3,6,2,7,5,4,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,6,4,1,2,5,7]=>[2,6,4,1,3,5,7]=>001010=>010100=>0
[3,6,4,1,2,7,5]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[3,6,4,1,5,2,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[3,6,4,1,5,7,2]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[3,6,4,1,7,2,5]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[3,6,4,1,7,5,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,6,4,2,1,5,7]=>[1,6,4,3,2,5,7]=>011010=>010110=>0
[3,6,4,2,1,7,5]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[3,6,4,2,5,1,7]=>[1,6,3,2,5,4,7]=>010110=>011010=>0
[3,6,4,2,5,7,1]=>[1,5,3,2,4,7,6]=>010101=>101010=>1
[3,6,4,2,7,1,5]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[3,6,4,2,7,5,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,6,4,5,1,2,7]=>[1,6,3,5,2,4,7]=>000110=>011000=>0
[3,6,4,5,1,7,2]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[3,6,4,5,2,1,7]=>[1,6,2,5,4,3,7]=>001110=>011100=>0
[3,6,4,5,2,7,1]=>[1,5,2,4,3,7,6]=>001101=>101100=>1
[3,6,4,5,7,1,2]=>[1,5,2,4,7,3,6]=>000101=>101000=>1
[3,6,4,5,7,2,1]=>[1,4,2,3,7,6,5]=>001011=>110100=>2
[3,6,4,7,1,2,5]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[3,6,4,7,1,5,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,6,4,7,2,1,5]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[3,6,4,7,2,5,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,6,4,7,5,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[3,6,4,7,5,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,6,5,1,2,4,7]=>[3,6,5,1,2,4,7]=>000110=>011000=>0
[3,6,5,1,2,7,4]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[3,6,5,1,4,2,7]=>[2,6,5,1,4,3,7]=>001110=>011100=>0
[3,6,5,1,4,7,2]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[3,6,5,1,7,2,4]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[3,6,5,1,7,4,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,6,5,2,1,4,7]=>[3,6,5,2,1,4,7]=>100110=>011001=>0
[3,6,5,2,1,7,4]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[3,6,5,2,4,1,7]=>[2,6,5,1,4,3,7]=>001110=>011100=>0
[3,6,5,2,4,7,1]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[3,6,5,2,7,1,4]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[3,6,5,2,7,4,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,6,5,4,1,2,7]=>[2,6,5,4,1,3,7]=>001110=>011100=>0
[3,6,5,4,1,7,2]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[3,6,5,4,2,1,7]=>[1,6,5,4,3,2,7]=>011110=>011110=>0
[3,6,5,4,2,7,1]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[3,6,5,4,7,1,2]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[3,6,5,4,7,2,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[3,6,5,7,1,2,4]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[3,6,5,7,1,4,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,6,5,7,2,1,4]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[3,6,5,7,2,4,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[3,6,5,7,4,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[3,6,5,7,4,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[3,6,7,1,2,4,5]=>[3,5,7,1,2,4,6]=>000001=>100000=>1
[3,6,7,1,2,5,4]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[3,6,7,1,4,2,5]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[3,6,7,1,4,5,2]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[3,6,7,1,5,2,4]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[3,6,7,1,5,4,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,6,7,2,1,4,5]=>[3,5,7,2,1,4,6]=>100001=>100001=>1
[3,6,7,2,1,5,4]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[3,6,7,2,4,1,5]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[3,6,7,2,4,5,1]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[3,6,7,2,5,1,4]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[3,6,7,2,5,4,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,6,7,4,1,2,5]=>[2,5,7,4,1,3,6]=>001001=>100100=>1
[3,6,7,4,1,5,2]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[3,6,7,4,2,1,5]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[3,6,7,4,2,5,1]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[3,6,7,4,5,1,2]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[3,6,7,4,5,2,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[3,6,7,5,1,2,4]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[3,6,7,5,1,4,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[3,6,7,5,2,1,4]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[3,6,7,5,2,4,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[3,6,7,5,4,1,2]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[3,6,7,5,4,2,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[3,7,1,2,4,5,6]=>[3,7,1,2,4,5,6]=>000001=>100000=>1
[3,7,1,2,4,6,5]=>[3,7,1,2,4,6,5]=>000011=>110000=>2
[3,7,1,2,5,4,6]=>[3,7,1,2,5,4,6]=>000101=>101000=>1
[3,7,1,2,5,6,4]=>[3,7,1,2,4,6,5]=>000011=>110000=>2
[3,7,1,2,6,4,5]=>[3,7,1,2,6,4,5]=>000011=>110000=>2
[3,7,1,2,6,5,4]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[3,7,1,4,2,5,6]=>[2,7,1,4,3,5,6]=>001001=>100100=>1
[3,7,1,4,2,6,5]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[3,7,1,4,5,2,6]=>[2,7,1,3,5,4,6]=>000101=>101000=>1
[3,7,1,4,5,6,2]=>[2,7,1,3,4,6,5]=>000011=>110000=>2
[3,7,1,4,6,2,5]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[3,7,1,4,6,5,2]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[3,7,1,5,2,4,6]=>[3,7,1,5,2,4,6]=>000101=>101000=>1
[3,7,1,5,2,6,4]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[3,7,1,5,4,2,6]=>[2,7,1,5,4,3,6]=>001101=>101100=>1
[3,7,1,5,4,6,2]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[3,7,1,5,6,2,4]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[3,7,1,5,6,4,2]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[3,7,1,6,2,4,5]=>[3,7,1,6,2,4,5]=>000011=>110000=>2
[3,7,1,6,2,5,4]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[3,7,1,6,4,2,5]=>[2,7,1,6,4,3,5]=>001011=>110100=>2
[3,7,1,6,4,5,2]=>[2,7,1,6,3,5,4]=>000111=>111000=>3
[3,7,1,6,5,2,4]=>[3,7,1,6,5,2,4]=>000111=>111000=>3
[3,7,1,6,5,4,2]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[3,7,2,1,4,5,6]=>[3,7,2,1,4,5,6]=>100001=>100001=>1
[3,7,2,1,4,6,5]=>[3,7,2,1,4,6,5]=>100011=>110001=>2
[3,7,2,1,5,4,6]=>[3,7,2,1,5,4,6]=>100101=>101001=>1
[3,7,2,1,5,6,4]=>[3,7,2,1,4,6,5]=>100011=>110001=>2
[3,7,2,1,6,4,5]=>[3,7,2,1,6,4,5]=>100011=>110001=>2
[3,7,2,1,6,5,4]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[3,7,2,4,1,5,6]=>[2,7,1,4,3,5,6]=>001001=>100100=>1
[3,7,2,4,1,6,5]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[3,7,2,4,5,1,6]=>[2,7,1,3,5,4,6]=>000101=>101000=>1
[3,7,2,4,5,6,1]=>[2,7,1,3,4,6,5]=>000011=>110000=>2
[3,7,2,4,6,1,5]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[3,7,2,4,6,5,1]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[3,7,2,5,1,4,6]=>[3,7,2,5,1,4,6]=>000101=>101000=>1
[3,7,2,5,1,6,4]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[3,7,2,5,4,1,6]=>[2,7,1,5,4,3,6]=>001101=>101100=>1
[3,7,2,5,4,6,1]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[3,7,2,5,6,1,4]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[3,7,2,5,6,4,1]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[3,7,2,6,1,4,5]=>[3,7,2,6,1,4,5]=>000011=>110000=>2
[3,7,2,6,1,5,4]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[3,7,2,6,4,1,5]=>[2,7,1,6,4,3,5]=>001011=>110100=>2
[3,7,2,6,4,5,1]=>[2,7,1,6,3,5,4]=>000111=>111000=>3
[3,7,2,6,5,1,4]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[3,7,2,6,5,4,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[3,7,4,1,2,5,6]=>[2,7,4,1,3,5,6]=>001001=>100100=>1
[3,7,4,1,2,6,5]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[3,7,4,1,5,2,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[3,7,4,1,5,6,2]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[3,7,4,1,6,2,5]=>[2,7,4,1,6,3,5]=>001011=>110100=>2
[3,7,4,1,6,5,2]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[3,7,4,2,1,5,6]=>[1,7,4,3,2,5,6]=>011001=>100110=>1
[3,7,4,2,1,6,5]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[3,7,4,2,5,1,6]=>[1,7,3,2,5,4,6]=>010101=>101010=>1
[3,7,4,2,5,6,1]=>[1,7,3,2,4,6,5]=>010011=>110010=>2
[3,7,4,2,6,1,5]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[3,7,4,2,6,5,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[3,7,4,5,1,2,6]=>[1,7,3,5,2,4,6]=>000101=>101000=>1
[3,7,4,5,1,6,2]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[3,7,4,5,2,1,6]=>[1,7,2,5,4,3,6]=>001101=>101100=>1
[3,7,4,5,2,6,1]=>[1,7,2,4,3,6,5]=>001011=>110100=>2
[3,7,4,5,6,1,2]=>[1,7,2,4,6,3,5]=>000011=>110000=>2
[3,7,4,5,6,2,1]=>[1,7,2,3,6,5,4]=>000111=>111000=>3
[3,7,4,6,1,2,5]=>[2,7,4,6,1,3,5]=>000011=>110000=>2
[3,7,4,6,1,5,2]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[3,7,4,6,2,1,5]=>[1,7,4,6,3,2,5]=>010011=>110010=>2
[3,7,4,6,2,5,1]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[3,7,4,6,5,1,2]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[3,7,4,6,5,2,1]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[3,7,5,1,2,4,6]=>[3,7,5,1,2,4,6]=>000101=>101000=>1
[3,7,5,1,2,6,4]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[3,7,5,1,4,2,6]=>[2,7,5,1,4,3,6]=>001101=>101100=>1
[3,7,5,1,4,6,2]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[3,7,5,1,6,2,4]=>[2,7,4,1,6,3,5]=>001011=>110100=>2
[3,7,5,1,6,4,2]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[3,7,5,2,1,4,6]=>[3,7,5,2,1,4,6]=>100101=>101001=>1
[3,7,5,2,1,6,4]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[3,7,5,2,4,1,6]=>[2,7,5,1,4,3,6]=>001101=>101100=>1
[3,7,5,2,4,6,1]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[3,7,5,2,6,1,4]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[3,7,5,2,6,4,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[3,7,5,4,1,2,6]=>[2,7,5,4,1,3,6]=>001101=>101100=>1
[3,7,5,4,1,6,2]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[3,7,5,4,2,1,6]=>[1,7,5,4,3,2,6]=>011101=>101110=>1
[3,7,5,4,2,6,1]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[3,7,5,4,6,1,2]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[3,7,5,4,6,2,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[3,7,5,6,1,2,4]=>[2,7,4,6,1,3,5]=>000011=>110000=>2
[3,7,5,6,1,4,2]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[3,7,5,6,2,1,4]=>[1,7,4,6,3,2,5]=>010011=>110010=>2
[3,7,5,6,2,4,1]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[3,7,5,6,4,1,2]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[3,7,5,6,4,2,1]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[3,7,6,1,2,4,5]=>[3,7,6,1,2,4,5]=>000011=>110000=>2
[3,7,6,1,2,5,4]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[3,7,6,1,4,2,5]=>[2,7,6,1,4,3,5]=>001011=>110100=>2
[3,7,6,1,4,5,2]=>[2,7,6,1,3,5,4]=>000111=>111000=>3
[3,7,6,1,5,2,4]=>[3,7,6,1,5,2,4]=>000111=>111000=>3
[3,7,6,1,5,4,2]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[3,7,6,2,1,4,5]=>[3,7,6,2,1,4,5]=>100011=>110001=>2
[3,7,6,2,1,5,4]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[3,7,6,2,4,1,5]=>[2,7,6,1,4,3,5]=>001011=>110100=>2
[3,7,6,2,4,5,1]=>[2,7,6,1,3,5,4]=>000111=>111000=>3
[3,7,6,2,5,1,4]=>[3,7,6,2,5,1,4]=>000111=>111000=>3
[3,7,6,2,5,4,1]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[3,7,6,4,1,2,5]=>[2,7,6,4,1,3,5]=>001011=>110100=>2
[3,7,6,4,1,5,2]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[3,7,6,4,2,1,5]=>[1,7,6,4,3,2,5]=>011011=>110110=>2
[3,7,6,4,2,5,1]=>[1,7,6,3,2,5,4]=>010111=>111010=>3
[3,7,6,4,5,1,2]=>[1,7,6,3,5,2,4]=>000111=>111000=>3
[3,7,6,4,5,2,1]=>[1,7,6,2,5,4,3]=>001111=>111100=>4
[3,7,6,5,1,2,4]=>[3,7,6,5,1,2,4]=>000111=>111000=>3
[3,7,6,5,1,4,2]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[3,7,6,5,2,1,4]=>[3,7,6,5,2,1,4]=>100111=>111001=>3
[3,7,6,5,2,4,1]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[3,7,6,5,4,1,2]=>[2,7,6,5,4,1,3]=>001111=>111100=>4
[3,7,6,5,4,2,1]=>[1,7,6,5,4,3,2]=>011111=>111110=>5
[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>001000=>000100=>0
[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>001001=>100100=>1
[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>001010=>010100=>0
[4,1,2,3,6,7,5]=>[4,1,2,3,5,7,6]=>001001=>100100=>1
[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>001001=>100100=>1
[4,1,2,3,7,6,5]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[4,1,2,5,3,6,7]=>[3,1,2,5,4,6,7]=>010100=>001010=>0
[4,1,2,5,3,7,6]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,1,2,5,6,3,7]=>[3,1,2,4,6,5,7]=>010010=>010010=>0
[4,1,2,5,6,7,3]=>[3,1,2,4,5,7,6]=>010001=>100010=>1
[4,1,2,5,7,3,6]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[4,1,2,5,7,6,3]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[4,1,2,6,3,5,7]=>[4,1,2,6,3,5,7]=>001010=>010100=>0
[4,1,2,6,3,7,5]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,1,2,6,5,3,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[4,1,2,6,5,7,3]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,1,2,6,7,3,5]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[4,1,2,6,7,5,3]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[4,1,2,7,3,5,6]=>[4,1,2,7,3,5,6]=>001001=>100100=>1
[4,1,2,7,3,6,5]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[4,1,2,7,5,3,6]=>[3,1,2,7,5,4,6]=>010101=>101010=>1
[4,1,2,7,5,6,3]=>[3,1,2,7,4,6,5]=>010011=>110010=>2
[4,1,2,7,6,3,5]=>[4,1,2,7,6,3,5]=>001011=>110100=>2
[4,1,2,7,6,5,3]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[4,1,3,2,5,6,7]=>[4,1,3,2,5,6,7]=>011000=>000110=>0
[4,1,3,2,5,7,6]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[4,1,3,2,6,5,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[4,1,3,2,6,7,5]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[4,1,3,2,7,5,6]=>[4,1,3,2,7,5,6]=>011001=>100110=>1
[4,1,3,2,7,6,5]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[4,1,3,5,2,6,7]=>[3,1,2,5,4,6,7]=>010100=>001010=>0
[4,1,3,5,2,7,6]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,1,3,5,6,2,7]=>[3,1,2,4,6,5,7]=>010010=>010010=>0
[4,1,3,5,6,7,2]=>[3,1,2,4,5,7,6]=>010001=>100010=>1
[4,1,3,5,7,2,6]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[4,1,3,5,7,6,2]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[4,1,3,6,2,5,7]=>[4,1,3,6,2,5,7]=>001010=>010100=>0
[4,1,3,6,2,7,5]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,1,3,6,5,2,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[4,1,3,6,5,7,2]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,1,3,6,7,2,5]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[4,1,3,6,7,5,2]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[4,1,3,7,2,5,6]=>[4,1,3,7,2,5,6]=>001001=>100100=>1
[4,1,3,7,2,6,5]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[4,1,3,7,5,2,6]=>[3,1,2,7,5,4,6]=>010101=>101010=>1
[4,1,3,7,5,6,2]=>[3,1,2,7,4,6,5]=>010011=>110010=>2
[4,1,3,7,6,2,5]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[4,1,3,7,6,5,2]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[4,1,5,2,3,6,7]=>[3,1,5,2,4,6,7]=>010100=>001010=>0
[4,1,5,2,3,7,6]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[4,1,5,2,6,3,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[4,1,5,2,6,7,3]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[4,1,5,2,7,3,6]=>[3,1,5,2,7,4,6]=>010101=>101010=>1
[4,1,5,2,7,6,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,1,5,3,2,6,7]=>[2,1,5,4,3,6,7]=>101100=>001101=>0
[4,1,5,3,2,7,6]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,1,5,3,6,2,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[4,1,5,3,6,7,2]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[4,1,5,3,7,2,6]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,1,5,3,7,6,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,1,5,6,2,3,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[4,1,5,6,2,7,3]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[4,1,5,6,3,2,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[4,1,5,6,3,7,2]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[4,1,5,6,7,2,3]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[4,1,5,6,7,3,2]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[4,1,5,7,2,3,6]=>[3,1,5,7,2,4,6]=>010001=>100010=>1
[4,1,5,7,2,6,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,1,5,7,3,2,6]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[4,1,5,7,3,6,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,1,5,7,6,2,3]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[4,1,5,7,6,3,2]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[4,1,6,2,3,5,7]=>[4,1,6,2,3,5,7]=>001010=>010100=>0
[4,1,6,2,3,7,5]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[4,1,6,2,5,3,7]=>[3,1,6,2,5,4,7]=>010110=>011010=>0
[4,1,6,2,5,7,3]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[4,1,6,2,7,3,5]=>[3,1,5,2,7,4,6]=>010101=>101010=>1
[4,1,6,2,7,5,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,1,6,3,2,5,7]=>[4,1,6,3,2,5,7]=>011010=>010110=>0
[4,1,6,3,2,7,5]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,1,6,3,5,2,7]=>[3,1,6,2,5,4,7]=>010110=>011010=>0
[4,1,6,3,5,7,2]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[4,1,6,3,7,2,5]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,1,6,3,7,5,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,1,6,5,2,3,7]=>[3,1,6,5,2,4,7]=>010110=>011010=>0
[4,1,6,5,2,7,3]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,1,6,5,3,2,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[4,1,6,5,3,7,2]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,1,6,5,7,2,3]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,1,6,5,7,3,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,1,6,7,2,3,5]=>[3,1,5,7,2,4,6]=>010001=>100010=>1
[4,1,6,7,2,5,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,1,6,7,3,2,5]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[4,1,6,7,3,5,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,1,6,7,5,2,3]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[4,1,6,7,5,3,2]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[4,1,7,2,3,5,6]=>[4,1,7,2,3,5,6]=>001001=>100100=>1
[4,1,7,2,3,6,5]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[4,1,7,2,5,3,6]=>[3,1,7,2,5,4,6]=>010101=>101010=>1
[4,1,7,2,5,6,3]=>[3,1,7,2,4,6,5]=>010011=>110010=>2
[4,1,7,2,6,3,5]=>[4,1,7,2,6,3,5]=>001011=>110100=>2
[4,1,7,2,6,5,3]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[4,1,7,3,2,5,6]=>[4,1,7,3,2,5,6]=>011001=>100110=>1
[4,1,7,3,2,6,5]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[4,1,7,3,5,2,6]=>[3,1,7,2,5,4,6]=>010101=>101010=>1
[4,1,7,3,5,6,2]=>[3,1,7,2,4,6,5]=>010011=>110010=>2
[4,1,7,3,6,2,5]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[4,1,7,3,6,5,2]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[4,1,7,5,2,3,6]=>[3,1,7,5,2,4,6]=>010101=>101010=>1
[4,1,7,5,2,6,3]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[4,1,7,5,3,2,6]=>[2,1,7,5,4,3,6]=>101101=>101101=>1
[4,1,7,5,3,6,2]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[4,1,7,5,6,2,3]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[4,1,7,5,6,3,2]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[4,1,7,6,2,3,5]=>[4,1,7,6,2,3,5]=>001011=>110100=>2
[4,1,7,6,2,5,3]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[4,1,7,6,3,2,5]=>[4,1,7,6,3,2,5]=>011011=>110110=>2
[4,1,7,6,3,5,2]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[4,1,7,6,5,2,3]=>[3,1,7,6,5,2,4]=>010111=>111010=>3
[4,1,7,6,5,3,2]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[4,2,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>101000=>000101=>0
[4,2,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>101001=>100101=>1
[4,2,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>101010=>010101=>0
[4,2,1,3,6,7,5]=>[4,2,1,3,5,7,6]=>101001=>100101=>1
[4,2,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>101001=>100101=>1
[4,2,1,3,7,6,5]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[4,2,1,5,3,6,7]=>[3,2,1,5,4,6,7]=>110100=>001011=>0
[4,2,1,5,3,7,6]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,2,1,5,6,3,7]=>[3,2,1,4,6,5,7]=>110010=>010011=>0
[4,2,1,5,6,7,3]=>[3,2,1,4,5,7,6]=>110001=>100011=>1
[4,2,1,5,7,3,6]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[4,2,1,5,7,6,3]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[4,2,1,6,3,5,7]=>[4,2,1,6,3,5,7]=>101010=>010101=>0
[4,2,1,6,3,7,5]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,2,1,6,5,3,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[4,2,1,6,5,7,3]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,2,1,6,7,3,5]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[4,2,1,6,7,5,3]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[4,2,1,7,3,5,6]=>[4,2,1,7,3,5,6]=>101001=>100101=>1
[4,2,1,7,3,6,5]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[4,2,1,7,5,3,6]=>[3,2,1,7,5,4,6]=>110101=>101011=>1
[4,2,1,7,5,6,3]=>[3,2,1,7,4,6,5]=>110011=>110011=>2
[4,2,1,7,6,3,5]=>[4,2,1,7,6,3,5]=>101011=>110101=>2
[4,2,1,7,6,5,3]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>011000=>000110=>0
[4,2,3,1,5,7,6]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[4,2,3,1,6,5,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[4,2,3,1,6,7,5]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[4,2,3,1,7,5,6]=>[4,1,3,2,7,5,6]=>011001=>100110=>1
[4,2,3,1,7,6,5]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[4,2,3,5,1,6,7]=>[3,1,2,5,4,6,7]=>010100=>001010=>0
[4,2,3,5,1,7,6]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,2,3,5,6,1,7]=>[3,1,2,4,6,5,7]=>010010=>010010=>0
[4,2,3,5,6,7,1]=>[3,1,2,4,5,7,6]=>010001=>100010=>1
[4,2,3,5,7,1,6]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[4,2,3,5,7,6,1]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[4,2,3,6,1,5,7]=>[4,1,3,6,2,5,7]=>001010=>010100=>0
[4,2,3,6,1,7,5]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,2,3,6,5,1,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[4,2,3,6,5,7,1]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[4,2,3,6,7,1,5]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[4,2,3,6,7,5,1]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[4,2,3,7,1,5,6]=>[4,1,3,7,2,5,6]=>001001=>100100=>1
[4,2,3,7,1,6,5]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[4,2,3,7,5,1,6]=>[3,1,2,7,5,4,6]=>010101=>101010=>1
[4,2,3,7,5,6,1]=>[3,1,2,7,4,6,5]=>010011=>110010=>2
[4,2,3,7,6,1,5]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[4,2,3,7,6,5,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[4,2,5,1,3,6,7]=>[3,2,5,1,4,6,7]=>010100=>001010=>0
[4,2,5,1,3,7,6]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[4,2,5,1,6,3,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[4,2,5,1,6,7,3]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[4,2,5,1,7,3,6]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[4,2,5,1,7,6,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,2,5,3,1,6,7]=>[2,1,5,4,3,6,7]=>101100=>001101=>0
[4,2,5,3,1,7,6]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,2,5,3,6,1,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[4,2,5,3,6,7,1]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[4,2,5,3,7,1,6]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,2,5,3,7,6,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,2,5,6,1,3,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[4,2,5,6,1,7,3]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[4,2,5,6,3,1,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[4,2,5,6,3,7,1]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[4,2,5,6,7,1,3]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[4,2,5,6,7,3,1]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[4,2,5,7,1,3,6]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[4,2,5,7,1,6,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,2,5,7,3,1,6]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[4,2,5,7,3,6,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,2,5,7,6,1,3]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[4,2,5,7,6,3,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[4,2,6,1,3,5,7]=>[4,2,6,1,3,5,7]=>001010=>010100=>0
[4,2,6,1,3,7,5]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[4,2,6,1,5,3,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[4,2,6,1,5,7,3]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[4,2,6,1,7,3,5]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[4,2,6,1,7,5,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,2,6,3,1,5,7]=>[4,1,6,3,2,5,7]=>011010=>010110=>0
[4,2,6,3,1,7,5]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,2,6,3,5,1,7]=>[3,1,6,2,5,4,7]=>010110=>011010=>0
[4,2,6,3,5,7,1]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[4,2,6,3,7,1,5]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,2,6,3,7,5,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,2,6,5,1,3,7]=>[3,2,6,5,1,4,7]=>010110=>011010=>0
[4,2,6,5,1,7,3]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,2,6,5,3,1,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[4,2,6,5,3,7,1]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,2,6,5,7,1,3]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,2,6,5,7,3,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,2,6,7,1,3,5]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[4,2,6,7,1,5,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,2,6,7,3,1,5]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[4,2,6,7,3,5,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,2,6,7,5,1,3]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[4,2,6,7,5,3,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[4,2,7,1,3,5,6]=>[4,2,7,1,3,5,6]=>001001=>100100=>1
[4,2,7,1,3,6,5]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[4,2,7,1,5,3,6]=>[3,2,7,1,5,4,6]=>010101=>101010=>1
[4,2,7,1,5,6,3]=>[3,2,7,1,4,6,5]=>010011=>110010=>2
[4,2,7,1,6,3,5]=>[4,2,7,1,6,3,5]=>001011=>110100=>2
[4,2,7,1,6,5,3]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[4,2,7,3,1,5,6]=>[4,1,7,3,2,5,6]=>011001=>100110=>1
[4,2,7,3,1,6,5]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[4,2,7,3,5,1,6]=>[3,1,7,2,5,4,6]=>010101=>101010=>1
[4,2,7,3,5,6,1]=>[3,1,7,2,4,6,5]=>010011=>110010=>2
[4,2,7,3,6,1,5]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[4,2,7,3,6,5,1]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[4,2,7,5,1,3,6]=>[3,2,7,5,1,4,6]=>010101=>101010=>1
[4,2,7,5,1,6,3]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[4,2,7,5,3,1,6]=>[2,1,7,5,4,3,6]=>101101=>101101=>1
[4,2,7,5,3,6,1]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[4,2,7,5,6,1,3]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[4,2,7,5,6,3,1]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[4,2,7,6,1,3,5]=>[4,2,7,6,1,3,5]=>001011=>110100=>2
[4,2,7,6,1,5,3]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[4,2,7,6,3,1,5]=>[4,1,7,6,3,2,5]=>011011=>110110=>2
[4,2,7,6,3,5,1]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[4,2,7,6,5,1,3]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[4,2,7,6,5,3,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[4,3,1,2,5,6,7]=>[4,3,1,2,5,6,7]=>011000=>000110=>0
[4,3,1,2,5,7,6]=>[4,3,1,2,5,7,6]=>011001=>100110=>1
[4,3,1,2,6,5,7]=>[4,3,1,2,6,5,7]=>011010=>010110=>0
[4,3,1,2,6,7,5]=>[4,3,1,2,5,7,6]=>011001=>100110=>1
[4,3,1,2,7,5,6]=>[4,3,1,2,7,5,6]=>011001=>100110=>1
[4,3,1,2,7,6,5]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[4,3,1,5,2,6,7]=>[3,2,1,5,4,6,7]=>110100=>001011=>0
[4,3,1,5,2,7,6]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,3,1,5,6,2,7]=>[3,2,1,4,6,5,7]=>110010=>010011=>0
[4,3,1,5,6,7,2]=>[3,2,1,4,5,7,6]=>110001=>100011=>1
[4,3,1,5,7,2,6]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[4,3,1,5,7,6,2]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[4,3,1,6,2,5,7]=>[4,3,1,6,2,5,7]=>011010=>010110=>0
[4,3,1,6,2,7,5]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,3,1,6,5,2,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[4,3,1,6,5,7,2]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,3,1,6,7,2,5]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[4,3,1,6,7,5,2]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[4,3,1,7,2,5,6]=>[4,3,1,7,2,5,6]=>011001=>100110=>1
[4,3,1,7,2,6,5]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[4,3,1,7,5,2,6]=>[3,2,1,7,5,4,6]=>110101=>101011=>1
[4,3,1,7,5,6,2]=>[3,2,1,7,4,6,5]=>110011=>110011=>2
[4,3,1,7,6,2,5]=>[4,3,1,7,6,2,5]=>011011=>110110=>2
[4,3,1,7,6,5,2]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000=>000111=>0
[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>111001=>100111=>1
[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>111010=>010111=>0
[4,3,2,1,6,7,5]=>[4,3,2,1,5,7,6]=>111001=>100111=>1
[4,3,2,1,7,5,6]=>[4,3,2,1,7,5,6]=>111001=>100111=>1
[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[4,3,2,5,1,6,7]=>[3,2,1,5,4,6,7]=>110100=>001011=>0
[4,3,2,5,1,7,6]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,3,2,5,6,1,7]=>[3,2,1,4,6,5,7]=>110010=>010011=>0
[4,3,2,5,6,7,1]=>[3,2,1,4,5,7,6]=>110001=>100011=>1
[4,3,2,5,7,1,6]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[4,3,2,5,7,6,1]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[4,3,2,6,1,5,7]=>[4,3,2,6,1,5,7]=>011010=>010110=>0
[4,3,2,6,1,7,5]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,3,2,6,5,1,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[4,3,2,6,5,7,1]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[4,3,2,6,7,1,5]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[4,3,2,6,7,5,1]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[4,3,2,7,1,5,6]=>[4,3,2,7,1,5,6]=>011001=>100110=>1
[4,3,2,7,1,6,5]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[4,3,2,7,5,1,6]=>[3,2,1,7,5,4,6]=>110101=>101011=>1
[4,3,2,7,5,6,1]=>[3,2,1,7,4,6,5]=>110011=>110011=>2
[4,3,2,7,6,1,5]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[4,3,2,7,6,5,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[4,3,5,1,2,6,7]=>[3,2,5,1,4,6,7]=>010100=>001010=>0
[4,3,5,1,2,7,6]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[4,3,5,1,6,2,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[4,3,5,1,6,7,2]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[4,3,5,1,7,2,6]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[4,3,5,1,7,6,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,3,5,2,1,6,7]=>[2,1,5,4,3,6,7]=>101100=>001101=>0
[4,3,5,2,1,7,6]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,3,5,2,6,1,7]=>[2,1,4,3,6,5,7]=>101010=>010101=>0
[4,3,5,2,6,7,1]=>[2,1,4,3,5,7,6]=>101001=>100101=>1
[4,3,5,2,7,1,6]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,3,5,2,7,6,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,3,5,6,1,2,7]=>[2,1,4,6,3,5,7]=>100010=>010001=>0
[4,3,5,6,1,7,2]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[4,3,5,6,2,1,7]=>[2,1,3,6,5,4,7]=>100110=>011001=>0
[4,3,5,6,2,7,1]=>[2,1,3,5,4,7,6]=>100101=>101001=>1
[4,3,5,6,7,1,2]=>[2,1,3,5,7,4,6]=>100001=>100001=>1
[4,3,5,6,7,2,1]=>[2,1,3,4,7,6,5]=>100011=>110001=>2
[4,3,5,7,1,2,6]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[4,3,5,7,1,6,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,3,5,7,2,1,6]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[4,3,5,7,2,6,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,3,5,7,6,1,2]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[4,3,5,7,6,2,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[4,3,6,1,2,5,7]=>[4,3,6,1,2,5,7]=>001010=>010100=>0
[4,3,6,1,2,7,5]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[4,3,6,1,5,2,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[4,3,6,1,5,7,2]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[4,3,6,1,7,2,5]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[4,3,6,1,7,5,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,3,6,2,1,5,7]=>[4,3,6,2,1,5,7]=>101010=>010101=>0
[4,3,6,2,1,7,5]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,3,6,2,5,1,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[4,3,6,2,5,7,1]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[4,3,6,2,7,1,5]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,3,6,2,7,5,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,3,6,5,1,2,7]=>[3,2,6,5,1,4,7]=>010110=>011010=>0
[4,3,6,5,1,7,2]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,3,6,5,2,1,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[4,3,6,5,2,7,1]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[4,3,6,5,7,1,2]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[4,3,6,5,7,2,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[4,3,6,7,1,2,5]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[4,3,6,7,1,5,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,3,6,7,2,1,5]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[4,3,6,7,2,5,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[4,3,6,7,5,1,2]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[4,3,6,7,5,2,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[4,3,7,1,2,5,6]=>[4,3,7,1,2,5,6]=>001001=>100100=>1
[4,3,7,1,2,6,5]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[4,3,7,1,5,2,6]=>[3,2,7,1,5,4,6]=>010101=>101010=>1
[4,3,7,1,5,6,2]=>[3,2,7,1,4,6,5]=>010011=>110010=>2
[4,3,7,1,6,2,5]=>[4,3,7,1,6,2,5]=>001011=>110100=>2
[4,3,7,1,6,5,2]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[4,3,7,2,1,5,6]=>[4,3,7,2,1,5,6]=>101001=>100101=>1
[4,3,7,2,1,6,5]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[4,3,7,2,5,1,6]=>[3,2,7,1,5,4,6]=>010101=>101010=>1
[4,3,7,2,5,6,1]=>[3,2,7,1,4,6,5]=>010011=>110010=>2
[4,3,7,2,6,1,5]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[4,3,7,2,6,5,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[4,3,7,5,1,2,6]=>[3,2,7,5,1,4,6]=>010101=>101010=>1
[4,3,7,5,1,6,2]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[4,3,7,5,2,1,6]=>[2,1,7,5,4,3,6]=>101101=>101101=>1
[4,3,7,5,2,6,1]=>[2,1,7,4,3,6,5]=>101011=>110101=>2
[4,3,7,5,6,1,2]=>[2,1,7,4,6,3,5]=>100011=>110001=>2
[4,3,7,5,6,2,1]=>[2,1,7,3,6,5,4]=>100111=>111001=>3
[4,3,7,6,1,2,5]=>[4,3,7,6,1,2,5]=>001011=>110100=>2
[4,3,7,6,1,5,2]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[4,3,7,6,2,1,5]=>[4,3,7,6,2,1,5]=>101011=>110101=>2
[4,3,7,6,2,5,1]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[4,3,7,6,5,1,2]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[4,3,7,6,5,2,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[4,5,1,2,3,6,7]=>[3,5,1,2,4,6,7]=>000100=>001000=>0
[4,5,1,2,3,7,6]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[4,5,1,2,6,3,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[4,5,1,2,6,7,3]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[4,5,1,2,7,3,6]=>[3,5,1,2,7,4,6]=>000101=>101000=>1
[4,5,1,2,7,6,3]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,5,1,3,2,6,7]=>[2,5,1,4,3,6,7]=>001100=>001100=>0
[4,5,1,3,2,7,6]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,5,1,3,6,2,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[4,5,1,3,6,7,2]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[4,5,1,3,7,2,6]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[4,5,1,3,7,6,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,5,1,6,2,3,7]=>[2,4,1,6,3,5,7]=>001010=>010100=>0
[4,5,1,6,2,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[4,5,1,6,3,2,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[4,5,1,6,3,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[4,5,1,6,7,2,3]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[4,5,1,6,7,3,2]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[4,5,1,7,2,3,6]=>[3,5,1,7,2,4,6]=>000101=>101000=>1
[4,5,1,7,2,6,3]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[4,5,1,7,3,2,6]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[4,5,1,7,3,6,2]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[4,5,1,7,6,2,3]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[4,5,1,7,6,3,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[4,5,2,1,3,6,7]=>[3,5,2,1,4,6,7]=>100100=>001001=>0
[4,5,2,1,3,7,6]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[4,5,2,1,6,3,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[4,5,2,1,6,7,3]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[4,5,2,1,7,3,6]=>[3,5,2,1,7,4,6]=>100101=>101001=>1
[4,5,2,1,7,6,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,5,2,3,1,6,7]=>[2,5,1,4,3,6,7]=>001100=>001100=>0
[4,5,2,3,1,7,6]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,5,2,3,6,1,7]=>[2,4,1,3,6,5,7]=>001010=>010100=>0
[4,5,2,3,6,7,1]=>[2,4,1,3,5,7,6]=>001001=>100100=>1
[4,5,2,3,7,1,6]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[4,5,2,3,7,6,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,5,2,6,1,3,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[4,5,2,6,1,7,3]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[4,5,2,6,3,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[4,5,2,6,3,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[4,5,2,6,7,1,3]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[4,5,2,6,7,3,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[4,5,2,7,1,3,6]=>[3,5,2,7,1,4,6]=>000101=>101000=>1
[4,5,2,7,1,6,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,5,2,7,3,1,6]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[4,5,2,7,3,6,1]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[4,5,2,7,6,1,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[4,5,2,7,6,3,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[4,5,3,1,2,6,7]=>[2,5,4,1,3,6,7]=>001100=>001100=>0
[4,5,3,1,2,7,6]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[4,5,3,1,6,2,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[4,5,3,1,6,7,2]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[4,5,3,1,7,2,6]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[4,5,3,1,7,6,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,5,3,2,1,6,7]=>[1,5,4,3,2,6,7]=>011100=>001110=>0
[4,5,3,2,1,7,6]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[4,5,3,2,6,1,7]=>[1,4,3,2,6,5,7]=>011010=>010110=>0
[4,5,3,2,6,7,1]=>[1,4,3,2,5,7,6]=>011001=>100110=>1
[4,5,3,2,7,1,6]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[4,5,3,2,7,6,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,5,3,6,1,2,7]=>[1,4,3,6,2,5,7]=>001010=>010100=>0
[4,5,3,6,1,7,2]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[4,5,3,6,2,1,7]=>[1,3,2,6,5,4,7]=>010110=>011010=>0
[4,5,3,6,2,7,1]=>[1,3,2,5,4,7,6]=>010101=>101010=>1
[4,5,3,6,7,1,2]=>[1,3,2,5,7,4,6]=>010001=>100010=>1
[4,5,3,6,7,2,1]=>[1,3,2,4,7,6,5]=>010011=>110010=>2
[4,5,3,7,1,2,6]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[4,5,3,7,1,6,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,5,3,7,2,1,6]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[4,5,3,7,2,6,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,5,3,7,6,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[4,5,3,7,6,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[4,5,6,1,2,3,7]=>[2,4,6,1,3,5,7]=>000010=>010000=>0
[4,5,6,1,2,7,3]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[4,5,6,1,3,2,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[4,5,6,1,3,7,2]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[4,5,6,1,7,2,3]=>[1,3,5,2,7,4,6]=>000101=>101000=>1
[4,5,6,1,7,3,2]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[4,5,6,2,1,3,7]=>[1,4,6,3,2,5,7]=>010010=>010010=>0
[4,5,6,2,1,7,3]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[4,5,6,2,3,1,7]=>[1,3,6,2,5,4,7]=>000110=>011000=>0
[4,5,6,2,3,7,1]=>[1,3,5,2,4,7,6]=>000101=>101000=>1
[4,5,6,2,7,1,3]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[4,5,6,2,7,3,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[4,5,6,3,1,2,7]=>[1,3,6,5,2,4,7]=>000110=>011000=>0
[4,5,6,3,1,7,2]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[4,5,6,3,2,1,7]=>[1,2,6,5,4,3,7]=>001110=>011100=>0
[4,5,6,3,2,7,1]=>[1,2,5,4,3,7,6]=>001101=>101100=>1
[4,5,6,3,7,1,2]=>[1,2,5,4,7,3,6]=>000101=>101000=>1
[4,5,6,3,7,2,1]=>[1,2,4,3,7,6,5]=>001011=>110100=>2
[4,5,6,7,1,2,3]=>[1,3,5,7,2,4,6]=>000001=>100000=>1
[4,5,6,7,1,3,2]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[4,5,6,7,2,1,3]=>[1,2,5,7,4,3,6]=>001001=>100100=>1
[4,5,6,7,2,3,1]=>[1,2,4,7,3,6,5]=>000011=>110000=>2
[4,5,6,7,3,1,2]=>[1,2,4,7,6,3,5]=>000011=>110000=>2
[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>000111=>111000=>3
[4,5,7,1,2,3,6]=>[3,5,7,1,2,4,6]=>000001=>100000=>1
[4,5,7,1,2,6,3]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[4,5,7,1,3,2,6]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[4,5,7,1,3,6,2]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[4,5,7,1,6,2,3]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[4,5,7,1,6,3,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[4,5,7,2,1,3,6]=>[3,5,7,2,1,4,6]=>100001=>100001=>1
[4,5,7,2,1,6,3]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[4,5,7,2,3,1,6]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[4,5,7,2,3,6,1]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[4,5,7,2,6,1,3]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[4,5,7,2,6,3,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[4,5,7,3,1,2,6]=>[2,5,7,4,1,3,6]=>001001=>100100=>1
[4,5,7,3,1,6,2]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[4,5,7,3,2,1,6]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[4,5,7,3,2,6,1]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[4,5,7,3,6,1,2]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[4,5,7,3,6,2,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[4,5,7,6,1,2,3]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[4,5,7,6,1,3,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[4,5,7,6,2,1,3]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[4,5,7,6,2,3,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[4,5,7,6,3,1,2]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[4,5,7,6,3,2,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[4,6,1,2,3,5,7]=>[4,6,1,2,3,5,7]=>000010=>010000=>0
[4,6,1,2,3,7,5]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[4,6,1,2,5,3,7]=>[3,6,1,2,5,4,7]=>000110=>011000=>0
[4,6,1,2,5,7,3]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[4,6,1,2,7,3,5]=>[3,5,1,2,7,4,6]=>000101=>101000=>1
[4,6,1,2,7,5,3]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,6,1,3,2,5,7]=>[4,6,1,3,2,5,7]=>010010=>010010=>0
[4,6,1,3,2,7,5]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,1,3,5,2,7]=>[3,6,1,2,5,4,7]=>000110=>011000=>0
[4,6,1,3,5,7,2]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[4,6,1,3,7,2,5]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[4,6,1,3,7,5,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,6,1,5,2,3,7]=>[3,6,1,5,2,4,7]=>000110=>011000=>0
[4,6,1,5,2,7,3]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,1,5,3,2,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[4,6,1,5,3,7,2]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,1,5,7,2,3]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[4,6,1,5,7,3,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,6,1,7,2,3,5]=>[3,5,1,7,2,4,6]=>000101=>101000=>1
[4,6,1,7,2,5,3]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[4,6,1,7,3,2,5]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[4,6,1,7,3,5,2]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[4,6,1,7,5,2,3]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[4,6,1,7,5,3,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[4,6,2,1,3,5,7]=>[4,6,2,1,3,5,7]=>100010=>010001=>0
[4,6,2,1,3,7,5]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[4,6,2,1,5,3,7]=>[3,6,2,1,5,4,7]=>100110=>011001=>0
[4,6,2,1,5,7,3]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[4,6,2,1,7,3,5]=>[3,5,2,1,7,4,6]=>100101=>101001=>1
[4,6,2,1,7,5,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,6,2,3,1,5,7]=>[4,6,1,3,2,5,7]=>010010=>010010=>0
[4,6,2,3,1,7,5]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,2,3,5,1,7]=>[3,6,1,2,5,4,7]=>000110=>011000=>0
[4,6,2,3,5,7,1]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[4,6,2,3,7,1,5]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[4,6,2,3,7,5,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,6,2,5,1,3,7]=>[3,6,2,5,1,4,7]=>000110=>011000=>0
[4,6,2,5,1,7,3]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,2,5,3,1,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[4,6,2,5,3,7,1]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,2,5,7,1,3]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[4,6,2,5,7,3,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,6,2,7,1,3,5]=>[3,5,2,7,1,4,6]=>000101=>101000=>1
[4,6,2,7,1,5,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,6,2,7,3,1,5]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[4,6,2,7,3,5,1]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[4,6,2,7,5,1,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[4,6,2,7,5,3,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[4,6,3,1,2,5,7]=>[4,6,3,1,2,5,7]=>010010=>010010=>0
[4,6,3,1,2,7,5]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[4,6,3,1,5,2,7]=>[3,6,2,1,5,4,7]=>100110=>011001=>0
[4,6,3,1,5,7,2]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[4,6,3,1,7,2,5]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[4,6,3,1,7,5,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,6,3,2,1,5,7]=>[4,6,3,2,1,5,7]=>110010=>010011=>0
[4,6,3,2,1,7,5]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[4,6,3,2,5,1,7]=>[3,6,2,1,5,4,7]=>100110=>011001=>0
[4,6,3,2,5,7,1]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[4,6,3,2,7,1,5]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[4,6,3,2,7,5,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,6,3,5,1,2,7]=>[3,6,2,5,1,4,7]=>000110=>011000=>0
[4,6,3,5,1,7,2]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,3,5,2,1,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[4,6,3,5,2,7,1]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[4,6,3,5,7,1,2]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[4,6,3,5,7,2,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[4,6,3,7,1,2,5]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[4,6,3,7,1,5,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,6,3,7,2,1,5]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[4,6,3,7,2,5,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,6,3,7,5,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[4,6,3,7,5,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[4,6,5,1,2,3,7]=>[3,6,5,1,2,4,7]=>000110=>011000=>0
[4,6,5,1,2,7,3]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[4,6,5,1,3,2,7]=>[2,6,5,1,4,3,7]=>001110=>011100=>0
[4,6,5,1,3,7,2]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[4,6,5,1,7,2,3]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[4,6,5,1,7,3,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,6,5,2,1,3,7]=>[3,6,5,2,1,4,7]=>100110=>011001=>0
[4,6,5,2,1,7,3]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[4,6,5,2,3,1,7]=>[2,6,5,1,4,3,7]=>001110=>011100=>0
[4,6,5,2,3,7,1]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[4,6,5,2,7,1,3]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[4,6,5,2,7,3,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,6,5,3,1,2,7]=>[2,6,5,4,1,3,7]=>001110=>011100=>0
[4,6,5,3,1,7,2]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[4,6,5,3,2,1,7]=>[1,6,5,4,3,2,7]=>011110=>011110=>0
[4,6,5,3,2,7,1]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[4,6,5,3,7,1,2]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[4,6,5,3,7,2,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[4,6,5,7,1,2,3]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[4,6,5,7,1,3,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,6,5,7,2,1,3]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[4,6,5,7,2,3,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[4,6,5,7,3,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[4,6,5,7,3,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[4,6,7,1,2,3,5]=>[3,5,7,1,2,4,6]=>000001=>100000=>1
[4,6,7,1,2,5,3]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[4,6,7,1,3,2,5]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[4,6,7,1,3,5,2]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[4,6,7,1,5,2,3]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[4,6,7,1,5,3,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[4,6,7,2,1,3,5]=>[3,5,7,2,1,4,6]=>100001=>100001=>1
[4,6,7,2,1,5,3]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[4,6,7,2,3,1,5]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[4,6,7,2,3,5,1]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[4,6,7,2,5,1,3]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[4,6,7,2,5,3,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[4,6,7,3,1,2,5]=>[2,5,7,4,1,3,6]=>001001=>100100=>1
[4,6,7,3,1,5,2]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[4,6,7,3,2,1,5]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[4,6,7,3,2,5,1]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[4,6,7,3,5,1,2]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[4,6,7,3,5,2,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[4,6,7,5,1,2,3]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[4,6,7,5,1,3,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[4,6,7,5,2,1,3]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[4,6,7,5,2,3,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[4,6,7,5,3,1,2]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[4,6,7,5,3,2,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[4,7,1,2,3,5,6]=>[4,7,1,2,3,5,6]=>000001=>100000=>1
[4,7,1,2,3,6,5]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[4,7,1,2,5,3,6]=>[3,7,1,2,5,4,6]=>000101=>101000=>1
[4,7,1,2,5,6,3]=>[3,7,1,2,4,6,5]=>000011=>110000=>2
[4,7,1,2,6,3,5]=>[4,7,1,2,6,3,5]=>000011=>110000=>2
[4,7,1,2,6,5,3]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[4,7,1,3,2,5,6]=>[4,7,1,3,2,5,6]=>010001=>100010=>1
[4,7,1,3,2,6,5]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[4,7,1,3,5,2,6]=>[3,7,1,2,5,4,6]=>000101=>101000=>1
[4,7,1,3,5,6,2]=>[3,7,1,2,4,6,5]=>000011=>110000=>2
[4,7,1,3,6,2,5]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[4,7,1,3,6,5,2]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[4,7,1,5,2,3,6]=>[3,7,1,5,2,4,6]=>000101=>101000=>1
[4,7,1,5,2,6,3]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[4,7,1,5,3,2,6]=>[2,7,1,5,4,3,6]=>001101=>101100=>1
[4,7,1,5,3,6,2]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[4,7,1,5,6,2,3]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[4,7,1,5,6,3,2]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[4,7,1,6,2,3,5]=>[4,7,1,6,2,3,5]=>000011=>110000=>2
[4,7,1,6,2,5,3]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[4,7,1,6,3,2,5]=>[4,7,1,6,3,2,5]=>010011=>110010=>2
[4,7,1,6,3,5,2]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[4,7,1,6,5,2,3]=>[3,7,1,6,5,2,4]=>000111=>111000=>3
[4,7,1,6,5,3,2]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[4,7,2,1,3,5,6]=>[4,7,2,1,3,5,6]=>100001=>100001=>1
[4,7,2,1,3,6,5]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[4,7,2,1,5,3,6]=>[3,7,2,1,5,4,6]=>100101=>101001=>1
[4,7,2,1,5,6,3]=>[3,7,2,1,4,6,5]=>100011=>110001=>2
[4,7,2,1,6,3,5]=>[4,7,2,1,6,3,5]=>100011=>110001=>2
[4,7,2,1,6,5,3]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[4,7,2,3,1,5,6]=>[4,7,1,3,2,5,6]=>010001=>100010=>1
[4,7,2,3,1,6,5]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[4,7,2,3,5,1,6]=>[3,7,1,2,5,4,6]=>000101=>101000=>1
[4,7,2,3,5,6,1]=>[3,7,1,2,4,6,5]=>000011=>110000=>2
[4,7,2,3,6,1,5]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[4,7,2,3,6,5,1]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[4,7,2,5,1,3,6]=>[3,7,2,5,1,4,6]=>000101=>101000=>1
[4,7,2,5,1,6,3]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[4,7,2,5,3,1,6]=>[2,7,1,5,4,3,6]=>001101=>101100=>1
[4,7,2,5,3,6,1]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[4,7,2,5,6,1,3]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[4,7,2,5,6,3,1]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[4,7,2,6,1,3,5]=>[4,7,2,6,1,3,5]=>000011=>110000=>2
[4,7,2,6,1,5,3]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[4,7,2,6,3,1,5]=>[4,7,1,6,3,2,5]=>010011=>110010=>2
[4,7,2,6,3,5,1]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[4,7,2,6,5,1,3]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[4,7,2,6,5,3,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[4,7,3,1,2,5,6]=>[4,7,3,1,2,5,6]=>010001=>100010=>1
[4,7,3,1,2,6,5]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[4,7,3,1,5,2,6]=>[3,7,2,1,5,4,6]=>100101=>101001=>1
[4,7,3,1,5,6,2]=>[3,7,2,1,4,6,5]=>100011=>110001=>2
[4,7,3,1,6,2,5]=>[4,7,3,1,6,2,5]=>010011=>110010=>2
[4,7,3,1,6,5,2]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[4,7,3,2,1,5,6]=>[4,7,3,2,1,5,6]=>110001=>100011=>1
[4,7,3,2,1,6,5]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[4,7,3,2,5,1,6]=>[3,7,2,1,5,4,6]=>100101=>101001=>1
[4,7,3,2,5,6,1]=>[3,7,2,1,4,6,5]=>100011=>110001=>2
[4,7,3,2,6,1,5]=>[4,7,3,2,6,1,5]=>010011=>110010=>2
[4,7,3,2,6,5,1]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[4,7,3,5,1,2,6]=>[3,7,2,5,1,4,6]=>000101=>101000=>1
[4,7,3,5,1,6,2]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[4,7,3,5,2,1,6]=>[2,7,1,5,4,3,6]=>001101=>101100=>1
[4,7,3,5,2,6,1]=>[2,7,1,4,3,6,5]=>001011=>110100=>2
[4,7,3,5,6,1,2]=>[2,7,1,4,6,3,5]=>000011=>110000=>2
[4,7,3,5,6,2,1]=>[2,7,1,3,6,5,4]=>000111=>111000=>3
[4,7,3,6,1,2,5]=>[4,7,3,6,1,2,5]=>000011=>110000=>2
[4,7,3,6,1,5,2]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[4,7,3,6,2,1,5]=>[4,7,3,6,2,1,5]=>100011=>110001=>2
[4,7,3,6,2,5,1]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[4,7,3,6,5,1,2]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[4,7,3,6,5,2,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[4,7,5,1,2,3,6]=>[3,7,5,1,2,4,6]=>000101=>101000=>1
[4,7,5,1,2,6,3]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[4,7,5,1,3,2,6]=>[2,7,5,1,4,3,6]=>001101=>101100=>1
[4,7,5,1,3,6,2]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[4,7,5,1,6,2,3]=>[2,7,4,1,6,3,5]=>001011=>110100=>2
[4,7,5,1,6,3,2]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[4,7,5,2,1,3,6]=>[3,7,5,2,1,4,6]=>100101=>101001=>1
[4,7,5,2,1,6,3]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[4,7,5,2,3,1,6]=>[2,7,5,1,4,3,6]=>001101=>101100=>1
[4,7,5,2,3,6,1]=>[2,7,4,1,3,6,5]=>001011=>110100=>2
[4,7,5,2,6,1,3]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[4,7,5,2,6,3,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[4,7,5,3,1,2,6]=>[2,7,5,4,1,3,6]=>001101=>101100=>1
[4,7,5,3,1,6,2]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[4,7,5,3,2,1,6]=>[1,7,5,4,3,2,6]=>011101=>101110=>1
[4,7,5,3,2,6,1]=>[1,7,4,3,2,6,5]=>011011=>110110=>2
[4,7,5,3,6,1,2]=>[1,7,4,3,6,2,5]=>001011=>110100=>2
[4,7,5,3,6,2,1]=>[1,7,3,2,6,5,4]=>010111=>111010=>3
[4,7,5,6,1,2,3]=>[2,7,4,6,1,3,5]=>000011=>110000=>2
[4,7,5,6,1,3,2]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[4,7,5,6,2,1,3]=>[1,7,4,6,3,2,5]=>010011=>110010=>2
[4,7,5,6,2,3,1]=>[1,7,3,6,2,5,4]=>000111=>111000=>3
[4,7,5,6,3,1,2]=>[1,7,3,6,5,2,4]=>000111=>111000=>3
[4,7,5,6,3,2,1]=>[1,7,2,6,5,4,3]=>001111=>111100=>4
[4,7,6,1,2,3,5]=>[4,7,6,1,2,3,5]=>000011=>110000=>2
[4,7,6,1,2,5,3]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[4,7,6,1,3,2,5]=>[4,7,6,1,3,2,5]=>010011=>110010=>2
[4,7,6,1,3,5,2]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[4,7,6,1,5,2,3]=>[3,7,6,1,5,2,4]=>000111=>111000=>3
[4,7,6,1,5,3,2]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[4,7,6,2,1,3,5]=>[4,7,6,2,1,3,5]=>100011=>110001=>2
[4,7,6,2,1,5,3]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[4,7,6,2,3,1,5]=>[4,7,6,1,3,2,5]=>010011=>110010=>2
[4,7,6,2,3,5,1]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[4,7,6,2,5,1,3]=>[3,7,6,2,5,1,4]=>000111=>111000=>3
[4,7,6,2,5,3,1]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[4,7,6,3,1,2,5]=>[4,7,6,3,1,2,5]=>010011=>110010=>2
[4,7,6,3,1,5,2]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[4,7,6,3,2,1,5]=>[4,7,6,3,2,1,5]=>110011=>110011=>2
[4,7,6,3,2,5,1]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[4,7,6,3,5,1,2]=>[3,7,6,2,5,1,4]=>000111=>111000=>3
[4,7,6,3,5,2,1]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[4,7,6,5,1,2,3]=>[3,7,6,5,1,2,4]=>000111=>111000=>3
[4,7,6,5,1,3,2]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[4,7,6,5,2,1,3]=>[3,7,6,5,2,1,4]=>100111=>111001=>3
[4,7,6,5,2,3,1]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[4,7,6,5,3,1,2]=>[2,7,6,5,4,1,3]=>001111=>111100=>4
[4,7,6,5,3,2,1]=>[1,7,6,5,4,3,2]=>011111=>111110=>5
[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>000100=>001000=>0
[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>000101=>101000=>1
[5,1,2,3,6,4,7]=>[4,1,2,3,6,5,7]=>001010=>010100=>0
[5,1,2,3,6,7,4]=>[4,1,2,3,5,7,6]=>001001=>100100=>1
[5,1,2,3,7,4,6]=>[5,1,2,3,7,4,6]=>000101=>101000=>1
[5,1,2,3,7,6,4]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[5,1,2,4,3,6,7]=>[5,1,2,4,3,6,7]=>001100=>001100=>0
[5,1,2,4,3,7,6]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[5,1,2,4,6,3,7]=>[4,1,2,3,6,5,7]=>001010=>010100=>0
[5,1,2,4,6,7,3]=>[4,1,2,3,5,7,6]=>001001=>100100=>1
[5,1,2,4,7,3,6]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[5,1,2,4,7,6,3]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[5,1,2,6,3,4,7]=>[4,1,2,6,3,5,7]=>001010=>010100=>0
[5,1,2,6,3,7,4]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,1,2,6,4,3,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[5,1,2,6,4,7,3]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,1,2,6,7,3,4]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[5,1,2,6,7,4,3]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[5,1,2,7,3,4,6]=>[5,1,2,7,3,4,6]=>000101=>101000=>1
[5,1,2,7,3,6,4]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[5,1,2,7,4,3,6]=>[5,1,2,7,4,3,6]=>001101=>101100=>1
[5,1,2,7,4,6,3]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[5,1,2,7,6,3,4]=>[4,1,2,7,6,3,5]=>001011=>110100=>2
[5,1,2,7,6,4,3]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[5,1,3,2,4,6,7]=>[5,1,3,2,4,6,7]=>010100=>001010=>0
[5,1,3,2,4,7,6]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[5,1,3,2,6,4,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,1,3,2,6,7,4]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,1,3,2,7,4,6]=>[5,1,3,2,7,4,6]=>010101=>101010=>1
[5,1,3,2,7,6,4]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,1,3,4,2,6,7]=>[5,1,2,4,3,6,7]=>001100=>001100=>0
[5,1,3,4,2,7,6]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[5,1,3,4,6,2,7]=>[4,1,2,3,6,5,7]=>001010=>010100=>0
[5,1,3,4,6,7,2]=>[4,1,2,3,5,7,6]=>001001=>100100=>1
[5,1,3,4,7,2,6]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[5,1,3,4,7,6,2]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[5,1,3,6,2,4,7]=>[4,1,3,6,2,5,7]=>001010=>010100=>0
[5,1,3,6,2,7,4]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,1,3,6,4,2,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[5,1,3,6,4,7,2]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,1,3,6,7,2,4]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[5,1,3,6,7,4,2]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[5,1,3,7,2,4,6]=>[5,1,3,7,2,4,6]=>000101=>101000=>1
[5,1,3,7,2,6,4]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,1,3,7,4,2,6]=>[5,1,2,7,4,3,6]=>001101=>101100=>1
[5,1,3,7,4,6,2]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[5,1,3,7,6,2,4]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[5,1,3,7,6,4,2]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[5,1,4,2,3,6,7]=>[5,1,4,2,3,6,7]=>001100=>001100=>0
[5,1,4,2,3,7,6]=>[5,1,4,2,3,7,6]=>001101=>101100=>1
[5,1,4,2,6,3,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,1,4,2,6,7,3]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,1,4,2,7,3,6]=>[5,1,4,2,7,3,6]=>001101=>101100=>1
[5,1,4,2,7,6,3]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,1,4,3,2,6,7]=>[5,1,4,3,2,6,7]=>011100=>001110=>0
[5,1,4,3,2,7,6]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[5,1,4,3,6,2,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,1,4,3,6,7,2]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,1,4,3,7,2,6]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[5,1,4,3,7,6,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,1,4,6,2,3,7]=>[4,1,3,6,2,5,7]=>001010=>010100=>0
[5,1,4,6,2,7,3]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,1,4,6,3,2,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[5,1,4,6,3,7,2]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,1,4,6,7,2,3]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[5,1,4,6,7,3,2]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[5,1,4,7,2,3,6]=>[5,1,4,7,2,3,6]=>000101=>101000=>1
[5,1,4,7,2,6,3]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,1,4,7,3,2,6]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[5,1,4,7,3,6,2]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,1,4,7,6,2,3]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[5,1,4,7,6,3,2]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[5,1,6,2,3,4,7]=>[4,1,6,2,3,5,7]=>001010=>010100=>0
[5,1,6,2,3,7,4]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[5,1,6,2,4,3,7]=>[3,1,6,2,5,4,7]=>010110=>011010=>0
[5,1,6,2,4,7,3]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[5,1,6,2,7,3,4]=>[3,1,5,2,7,4,6]=>010101=>101010=>1
[5,1,6,2,7,4,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,1,6,3,2,4,7]=>[4,1,6,3,2,5,7]=>011010=>010110=>0
[5,1,6,3,2,7,4]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,1,6,3,4,2,7]=>[3,1,6,2,5,4,7]=>010110=>011010=>0
[5,1,6,3,4,7,2]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[5,1,6,3,7,2,4]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,1,6,3,7,4,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,1,6,4,2,3,7]=>[3,1,6,5,2,4,7]=>010110=>011010=>0
[5,1,6,4,2,7,3]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,1,6,4,3,2,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[5,1,6,4,3,7,2]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,1,6,4,7,2,3]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,1,6,4,7,3,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,1,6,7,2,3,4]=>[3,1,5,7,2,4,6]=>010001=>100010=>1
[5,1,6,7,2,4,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,1,6,7,3,2,4]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[5,1,6,7,3,4,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,1,6,7,4,2,3]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[5,1,6,7,4,3,2]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[5,1,7,2,3,4,6]=>[5,1,7,2,3,4,6]=>000101=>101000=>1
[5,1,7,2,3,6,4]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[5,1,7,2,4,3,6]=>[5,1,7,2,4,3,6]=>001101=>101100=>1
[5,1,7,2,4,6,3]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[5,1,7,2,6,3,4]=>[4,1,7,2,6,3,5]=>001011=>110100=>2
[5,1,7,2,6,4,3]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[5,1,7,3,2,4,6]=>[5,1,7,3,2,4,6]=>010101=>101010=>1
[5,1,7,3,2,6,4]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,1,7,3,4,2,6]=>[5,1,7,2,4,3,6]=>001101=>101100=>1
[5,1,7,3,4,6,2]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[5,1,7,3,6,2,4]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[5,1,7,3,6,4,2]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[5,1,7,4,2,3,6]=>[5,1,7,4,2,3,6]=>001101=>101100=>1
[5,1,7,4,2,6,3]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,1,7,4,3,2,6]=>[5,1,7,4,3,2,6]=>011101=>101110=>1
[5,1,7,4,3,6,2]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,1,7,4,6,2,3]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[5,1,7,4,6,3,2]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[5,1,7,6,2,3,4]=>[4,1,7,6,2,3,5]=>001011=>110100=>2
[5,1,7,6,2,4,3]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[5,1,7,6,3,2,4]=>[4,1,7,6,3,2,5]=>011011=>110110=>2
[5,1,7,6,3,4,2]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[5,1,7,6,4,2,3]=>[3,1,7,6,5,2,4]=>010111=>111010=>3
[5,1,7,6,4,3,2]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[5,2,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>100100=>001001=>0
[5,2,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>100101=>101001=>1
[5,2,1,3,6,4,7]=>[4,2,1,3,6,5,7]=>101010=>010101=>0
[5,2,1,3,6,7,4]=>[4,2,1,3,5,7,6]=>101001=>100101=>1
[5,2,1,3,7,4,6]=>[5,2,1,3,7,4,6]=>100101=>101001=>1
[5,2,1,3,7,6,4]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[5,2,1,4,3,6,7]=>[5,2,1,4,3,6,7]=>101100=>001101=>0
[5,2,1,4,3,7,6]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[5,2,1,4,6,3,7]=>[4,2,1,3,6,5,7]=>101010=>010101=>0
[5,2,1,4,6,7,3]=>[4,2,1,3,5,7,6]=>101001=>100101=>1
[5,2,1,4,7,3,6]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[5,2,1,4,7,6,3]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[5,2,1,6,3,4,7]=>[4,2,1,6,3,5,7]=>101010=>010101=>0
[5,2,1,6,3,7,4]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,2,1,6,4,3,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[5,2,1,6,4,7,3]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,2,1,6,7,3,4]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[5,2,1,6,7,4,3]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[5,2,1,7,3,4,6]=>[5,2,1,7,3,4,6]=>100101=>101001=>1
[5,2,1,7,3,6,4]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[5,2,1,7,4,3,6]=>[5,2,1,7,4,3,6]=>101101=>101101=>1
[5,2,1,7,4,6,3]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[5,2,1,7,6,3,4]=>[4,2,1,7,6,3,5]=>101011=>110101=>2
[5,2,1,7,6,4,3]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[5,2,3,1,4,6,7]=>[5,1,3,2,4,6,7]=>010100=>001010=>0
[5,2,3,1,4,7,6]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[5,2,3,1,6,4,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,2,3,1,6,7,4]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,2,3,1,7,4,6]=>[5,1,3,2,7,4,6]=>010101=>101010=>1
[5,2,3,1,7,6,4]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>001100=>001100=>0
[5,2,3,4,1,7,6]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[5,2,3,4,6,1,7]=>[4,1,2,3,6,5,7]=>001010=>010100=>0
[5,2,3,4,6,7,1]=>[4,1,2,3,5,7,6]=>001001=>100100=>1
[5,2,3,4,7,1,6]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[5,2,3,4,7,6,1]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[5,2,3,6,1,4,7]=>[4,1,3,6,2,5,7]=>001010=>010100=>0
[5,2,3,6,1,7,4]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,2,3,6,4,1,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[5,2,3,6,4,7,1]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,2,3,6,7,1,4]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[5,2,3,6,7,4,1]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[5,2,3,7,1,4,6]=>[5,1,3,7,2,4,6]=>000101=>101000=>1
[5,2,3,7,1,6,4]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,2,3,7,4,1,6]=>[5,1,2,7,4,3,6]=>001101=>101100=>1
[5,2,3,7,4,6,1]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[5,2,3,7,6,1,4]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[5,2,3,7,6,4,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[5,2,4,1,3,6,7]=>[5,2,4,1,3,6,7]=>001100=>001100=>0
[5,2,4,1,3,7,6]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[5,2,4,1,6,3,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,2,4,1,6,7,3]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,2,4,1,7,3,6]=>[5,2,4,1,7,3,6]=>001101=>101100=>1
[5,2,4,1,7,6,3]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,2,4,3,1,6,7]=>[5,1,4,3,2,6,7]=>011100=>001110=>0
[5,2,4,3,1,7,6]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[5,2,4,3,6,1,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,2,4,3,6,7,1]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,2,4,3,7,1,6]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[5,2,4,3,7,6,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,2,4,6,1,3,7]=>[4,1,3,6,2,5,7]=>001010=>010100=>0
[5,2,4,6,1,7,3]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,2,4,6,3,1,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[5,2,4,6,3,7,1]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,2,4,6,7,1,3]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[5,2,4,6,7,3,1]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[5,2,4,7,1,3,6]=>[5,2,4,7,1,3,6]=>000101=>101000=>1
[5,2,4,7,1,6,3]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,2,4,7,3,1,6]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[5,2,4,7,3,6,1]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,2,4,7,6,1,3]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[5,2,4,7,6,3,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[5,2,6,1,3,4,7]=>[4,2,6,1,3,5,7]=>001010=>010100=>0
[5,2,6,1,3,7,4]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,2,6,1,4,3,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[5,2,6,1,4,7,3]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,2,6,1,7,3,4]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[5,2,6,1,7,4,3]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,2,6,3,1,4,7]=>[4,1,6,3,2,5,7]=>011010=>010110=>0
[5,2,6,3,1,7,4]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,2,6,3,4,1,7]=>[3,1,6,2,5,4,7]=>010110=>011010=>0
[5,2,6,3,4,7,1]=>[3,1,5,2,4,7,6]=>010101=>101010=>1
[5,2,6,3,7,1,4]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,2,6,3,7,4,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,2,6,4,1,3,7]=>[3,2,6,5,1,4,7]=>010110=>011010=>0
[5,2,6,4,1,7,3]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,2,6,4,3,1,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[5,2,6,4,3,7,1]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,2,6,4,7,1,3]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,2,6,4,7,3,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,2,6,7,1,3,4]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[5,2,6,7,1,4,3]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,2,6,7,3,1,4]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[5,2,6,7,3,4,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,2,6,7,4,1,3]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[5,2,6,7,4,3,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[5,2,7,1,3,4,6]=>[5,2,7,1,3,4,6]=>000101=>101000=>1
[5,2,7,1,3,6,4]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[5,2,7,1,4,3,6]=>[5,2,7,1,4,3,6]=>001101=>101100=>1
[5,2,7,1,4,6,3]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[5,2,7,1,6,3,4]=>[4,2,7,1,6,3,5]=>001011=>110100=>2
[5,2,7,1,6,4,3]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[5,2,7,3,1,4,6]=>[5,1,7,3,2,4,6]=>010101=>101010=>1
[5,2,7,3,1,6,4]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,2,7,3,4,1,6]=>[5,1,7,2,4,3,6]=>001101=>101100=>1
[5,2,7,3,4,6,1]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[5,2,7,3,6,1,4]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[5,2,7,3,6,4,1]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[5,2,7,4,1,3,6]=>[5,2,7,4,1,3,6]=>001101=>101100=>1
[5,2,7,4,1,6,3]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,2,7,4,3,1,6]=>[5,1,7,4,3,2,6]=>011101=>101110=>1
[5,2,7,4,3,6,1]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,2,7,4,6,1,3]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[5,2,7,4,6,3,1]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[5,2,7,6,1,3,4]=>[4,2,7,6,1,3,5]=>001011=>110100=>2
[5,2,7,6,1,4,3]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[5,2,7,6,3,1,4]=>[4,1,7,6,3,2,5]=>011011=>110110=>2
[5,2,7,6,3,4,1]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[5,2,7,6,4,1,3]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[5,2,7,6,4,3,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[5,3,1,2,4,6,7]=>[5,3,1,2,4,6,7]=>010100=>001010=>0
[5,3,1,2,4,7,6]=>[5,3,1,2,4,7,6]=>010101=>101010=>1
[5,3,1,2,6,4,7]=>[4,3,1,2,6,5,7]=>011010=>010110=>0
[5,3,1,2,6,7,4]=>[4,3,1,2,5,7,6]=>011001=>100110=>1
[5,3,1,2,7,4,6]=>[5,3,1,2,7,4,6]=>010101=>101010=>1
[5,3,1,2,7,6,4]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[5,3,1,4,2,6,7]=>[5,2,1,4,3,6,7]=>101100=>001101=>0
[5,3,1,4,2,7,6]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[5,3,1,4,6,2,7]=>[4,2,1,3,6,5,7]=>101010=>010101=>0
[5,3,1,4,6,7,2]=>[4,2,1,3,5,7,6]=>101001=>100101=>1
[5,3,1,4,7,2,6]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[5,3,1,4,7,6,2]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[5,3,1,6,2,4,7]=>[4,3,1,6,2,5,7]=>011010=>010110=>0
[5,3,1,6,2,7,4]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,3,1,6,4,2,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[5,3,1,6,4,7,2]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,3,1,6,7,2,4]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[5,3,1,6,7,4,2]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[5,3,1,7,2,4,6]=>[5,3,1,7,2,4,6]=>010101=>101010=>1
[5,3,1,7,2,6,4]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[5,3,1,7,4,2,6]=>[5,2,1,7,4,3,6]=>101101=>101101=>1
[5,3,1,7,4,6,2]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[5,3,1,7,6,2,4]=>[4,3,1,7,6,2,5]=>011011=>110110=>2
[5,3,1,7,6,4,2]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[5,3,2,1,4,6,7]=>[5,3,2,1,4,6,7]=>110100=>001011=>0
[5,3,2,1,4,7,6]=>[5,3,2,1,4,7,6]=>110101=>101011=>1
[5,3,2,1,6,4,7]=>[4,3,2,1,6,5,7]=>111010=>010111=>0
[5,3,2,1,6,7,4]=>[4,3,2,1,5,7,6]=>111001=>100111=>1
[5,3,2,1,7,4,6]=>[5,3,2,1,7,4,6]=>110101=>101011=>1
[5,3,2,1,7,6,4]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[5,3,2,4,1,6,7]=>[5,2,1,4,3,6,7]=>101100=>001101=>0
[5,3,2,4,1,7,6]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[5,3,2,4,6,1,7]=>[4,2,1,3,6,5,7]=>101010=>010101=>0
[5,3,2,4,6,7,1]=>[4,2,1,3,5,7,6]=>101001=>100101=>1
[5,3,2,4,7,1,6]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[5,3,2,4,7,6,1]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[5,3,2,6,1,4,7]=>[4,3,2,6,1,5,7]=>011010=>010110=>0
[5,3,2,6,1,7,4]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,3,2,6,4,1,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[5,3,2,6,4,7,1]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,3,2,6,7,1,4]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[5,3,2,6,7,4,1]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[5,3,2,7,1,4,6]=>[5,3,2,7,1,4,6]=>010101=>101010=>1
[5,3,2,7,1,6,4]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[5,3,2,7,4,1,6]=>[5,2,1,7,4,3,6]=>101101=>101101=>1
[5,3,2,7,4,6,1]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[5,3,2,7,6,1,4]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[5,3,2,7,6,4,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[5,3,4,1,2,6,7]=>[5,2,4,1,3,6,7]=>001100=>001100=>0
[5,3,4,1,2,7,6]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[5,3,4,1,6,2,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,3,4,1,6,7,2]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,3,4,1,7,2,6]=>[5,2,4,1,7,3,6]=>001101=>101100=>1
[5,3,4,1,7,6,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,3,4,2,1,6,7]=>[5,1,4,3,2,6,7]=>011100=>001110=>0
[5,3,4,2,1,7,6]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[5,3,4,2,6,1,7]=>[4,1,3,2,6,5,7]=>011010=>010110=>0
[5,3,4,2,6,7,1]=>[4,1,3,2,5,7,6]=>011001=>100110=>1
[5,3,4,2,7,1,6]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[5,3,4,2,7,6,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[5,3,4,6,1,2,7]=>[4,1,3,6,2,5,7]=>001010=>010100=>0
[5,3,4,6,1,7,2]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,3,4,6,2,1,7]=>[3,1,2,6,5,4,7]=>010110=>011010=>0
[5,3,4,6,2,7,1]=>[3,1,2,5,4,7,6]=>010101=>101010=>1
[5,3,4,6,7,1,2]=>[3,1,2,5,7,4,6]=>010001=>100010=>1
[5,3,4,6,7,2,1]=>[3,1,2,4,7,6,5]=>010011=>110010=>2
[5,3,4,7,1,2,6]=>[5,2,4,7,1,3,6]=>000101=>101000=>1
[5,3,4,7,1,6,2]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,3,4,7,2,1,6]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[5,3,4,7,2,6,1]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[5,3,4,7,6,1,2]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[5,3,4,7,6,2,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[5,3,6,1,2,4,7]=>[4,3,6,1,2,5,7]=>001010=>010100=>0
[5,3,6,1,2,7,4]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,3,6,1,4,2,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[5,3,6,1,4,7,2]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,3,6,1,7,2,4]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[5,3,6,1,7,4,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,3,6,2,1,4,7]=>[4,3,6,2,1,5,7]=>101010=>010101=>0
[5,3,6,2,1,7,4]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,3,6,2,4,1,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[5,3,6,2,4,7,1]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,3,6,2,7,1,4]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,3,6,2,7,4,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,3,6,4,1,2,7]=>[3,2,6,5,1,4,7]=>010110=>011010=>0
[5,3,6,4,1,7,2]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,3,6,4,2,1,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[5,3,6,4,2,7,1]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,3,6,4,7,1,2]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,3,6,4,7,2,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,3,6,7,1,2,4]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[5,3,6,7,1,4,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,3,6,7,2,1,4]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[5,3,6,7,2,4,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,3,6,7,4,1,2]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[5,3,6,7,4,2,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[5,3,7,1,2,4,6]=>[5,3,7,1,2,4,6]=>000101=>101000=>1
[5,3,7,1,2,6,4]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[5,3,7,1,4,2,6]=>[5,2,7,1,4,3,6]=>001101=>101100=>1
[5,3,7,1,4,6,2]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[5,3,7,1,6,2,4]=>[4,3,7,1,6,2,5]=>001011=>110100=>2
[5,3,7,1,6,4,2]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[5,3,7,2,1,4,6]=>[5,3,7,2,1,4,6]=>100101=>101001=>1
[5,3,7,2,1,6,4]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[5,3,7,2,4,1,6]=>[5,2,7,1,4,3,6]=>001101=>101100=>1
[5,3,7,2,4,6,1]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[5,3,7,2,6,1,4]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[5,3,7,2,6,4,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[5,3,7,4,1,2,6]=>[5,2,7,4,1,3,6]=>001101=>101100=>1
[5,3,7,4,1,6,2]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,3,7,4,2,1,6]=>[5,1,7,4,3,2,6]=>011101=>101110=>1
[5,3,7,4,2,6,1]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[5,3,7,4,6,1,2]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[5,3,7,4,6,2,1]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[5,3,7,6,1,2,4]=>[4,3,7,6,1,2,5]=>001011=>110100=>2
[5,3,7,6,1,4,2]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[5,3,7,6,2,1,4]=>[4,3,7,6,2,1,5]=>101011=>110101=>2
[5,3,7,6,2,4,1]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[5,3,7,6,4,1,2]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[5,3,7,6,4,2,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[5,4,1,2,3,6,7]=>[5,4,1,2,3,6,7]=>001100=>001100=>0
[5,4,1,2,3,7,6]=>[5,4,1,2,3,7,6]=>001101=>101100=>1
[5,4,1,2,6,3,7]=>[4,3,1,2,6,5,7]=>011010=>010110=>0
[5,4,1,2,6,7,3]=>[4,3,1,2,5,7,6]=>011001=>100110=>1
[5,4,1,2,7,3,6]=>[5,4,1,2,7,3,6]=>001101=>101100=>1
[5,4,1,2,7,6,3]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[5,4,1,3,2,6,7]=>[5,4,1,3,2,6,7]=>011100=>001110=>0
[5,4,1,3,2,7,6]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[5,4,1,3,6,2,7]=>[4,3,1,2,6,5,7]=>011010=>010110=>0
[5,4,1,3,6,7,2]=>[4,3,1,2,5,7,6]=>011001=>100110=>1
[5,4,1,3,7,2,6]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[5,4,1,3,7,6,2]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[5,4,1,6,2,3,7]=>[4,3,1,6,2,5,7]=>011010=>010110=>0
[5,4,1,6,2,7,3]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,4,1,6,3,2,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[5,4,1,6,3,7,2]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,4,1,6,7,2,3]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[5,4,1,6,7,3,2]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[5,4,1,7,2,3,6]=>[5,4,1,7,2,3,6]=>001101=>101100=>1
[5,4,1,7,2,6,3]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[5,4,1,7,3,2,6]=>[5,4,1,7,3,2,6]=>011101=>101110=>1
[5,4,1,7,3,6,2]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[5,4,1,7,6,2,3]=>[4,3,1,7,6,2,5]=>011011=>110110=>2
[5,4,1,7,6,3,2]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[5,4,2,1,3,6,7]=>[5,4,2,1,3,6,7]=>101100=>001101=>0
[5,4,2,1,3,7,6]=>[5,4,2,1,3,7,6]=>101101=>101101=>1
[5,4,2,1,6,3,7]=>[4,3,2,1,6,5,7]=>111010=>010111=>0
[5,4,2,1,6,7,3]=>[4,3,2,1,5,7,6]=>111001=>100111=>1
[5,4,2,1,7,3,6]=>[5,4,2,1,7,3,6]=>101101=>101101=>1
[5,4,2,1,7,6,3]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[5,4,2,3,1,6,7]=>[5,4,1,3,2,6,7]=>011100=>001110=>0
[5,4,2,3,1,7,6]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[5,4,2,3,6,1,7]=>[4,3,1,2,6,5,7]=>011010=>010110=>0
[5,4,2,3,6,7,1]=>[4,3,1,2,5,7,6]=>011001=>100110=>1
[5,4,2,3,7,1,6]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[5,4,2,3,7,6,1]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[5,4,2,6,1,3,7]=>[4,3,2,6,1,5,7]=>011010=>010110=>0
[5,4,2,6,1,7,3]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,4,2,6,3,1,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[5,4,2,6,3,7,1]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,4,2,6,7,1,3]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[5,4,2,6,7,3,1]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[5,4,2,7,1,3,6]=>[5,4,2,7,1,3,6]=>001101=>101100=>1
[5,4,2,7,1,6,3]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[5,4,2,7,3,1,6]=>[5,4,1,7,3,2,6]=>011101=>101110=>1
[5,4,2,7,3,6,1]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[5,4,2,7,6,1,3]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[5,4,2,7,6,3,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[5,4,3,1,2,6,7]=>[5,4,3,1,2,6,7]=>011100=>001110=>0
[5,4,3,1,2,7,6]=>[5,4,3,1,2,7,6]=>011101=>101110=>1
[5,4,3,1,6,2,7]=>[4,3,2,1,6,5,7]=>111010=>010111=>0
[5,4,3,1,6,7,2]=>[4,3,2,1,5,7,6]=>111001=>100111=>1
[5,4,3,1,7,2,6]=>[5,4,3,1,7,2,6]=>011101=>101110=>1
[5,4,3,1,7,6,2]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100=>001111=>0
[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>111101=>101111=>1
[5,4,3,2,6,1,7]=>[4,3,2,1,6,5,7]=>111010=>010111=>0
[5,4,3,2,6,7,1]=>[4,3,2,1,5,7,6]=>111001=>100111=>1
[5,4,3,2,7,1,6]=>[5,4,3,2,7,1,6]=>011101=>101110=>1
[5,4,3,2,7,6,1]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[5,4,3,6,1,2,7]=>[4,3,2,6,1,5,7]=>011010=>010110=>0
[5,4,3,6,1,7,2]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,4,3,6,2,1,7]=>[3,2,1,6,5,4,7]=>110110=>011011=>0
[5,4,3,6,2,7,1]=>[3,2,1,5,4,7,6]=>110101=>101011=>1
[5,4,3,6,7,1,2]=>[3,2,1,5,7,4,6]=>110001=>100011=>1
[5,4,3,6,7,2,1]=>[3,2,1,4,7,6,5]=>110011=>110011=>2
[5,4,3,7,1,2,6]=>[5,4,3,7,1,2,6]=>001101=>101100=>1
[5,4,3,7,1,6,2]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[5,4,3,7,2,1,6]=>[5,4,3,7,2,1,6]=>101101=>101101=>1
[5,4,3,7,2,6,1]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[5,4,3,7,6,1,2]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[5,4,3,7,6,2,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[5,4,6,1,2,3,7]=>[4,3,6,1,2,5,7]=>001010=>010100=>0
[5,4,6,1,2,7,3]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,4,6,1,3,2,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[5,4,6,1,3,7,2]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,4,6,1,7,2,3]=>[3,2,5,1,7,4,6]=>010101=>101010=>1
[5,4,6,1,7,3,2]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,4,6,2,1,3,7]=>[4,3,6,2,1,5,7]=>101010=>010101=>0
[5,4,6,2,1,7,3]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,4,6,2,3,1,7]=>[3,2,6,1,5,4,7]=>010110=>011010=>0
[5,4,6,2,3,7,1]=>[3,2,5,1,4,7,6]=>010101=>101010=>1
[5,4,6,2,7,1,3]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,4,6,2,7,3,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,4,6,3,1,2,7]=>[3,2,6,5,1,4,7]=>010110=>011010=>0
[5,4,6,3,1,7,2]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,4,6,3,2,1,7]=>[2,1,6,5,4,3,7]=>101110=>011101=>0
[5,4,6,3,2,7,1]=>[2,1,5,4,3,7,6]=>101101=>101101=>1
[5,4,6,3,7,1,2]=>[2,1,5,4,7,3,6]=>100101=>101001=>1
[5,4,6,3,7,2,1]=>[2,1,4,3,7,6,5]=>101011=>110101=>2
[5,4,6,7,1,2,3]=>[3,2,5,7,1,4,6]=>010001=>100010=>1
[5,4,6,7,1,3,2]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,4,6,7,2,1,3]=>[2,1,5,7,4,3,6]=>101001=>100101=>1
[5,4,6,7,2,3,1]=>[2,1,4,7,3,6,5]=>100011=>110001=>2
[5,4,6,7,3,1,2]=>[2,1,4,7,6,3,5]=>100011=>110001=>2
[5,4,6,7,3,2,1]=>[2,1,3,7,6,5,4]=>100111=>111001=>3
[5,4,7,1,2,3,6]=>[5,4,7,1,2,3,6]=>000101=>101000=>1
[5,4,7,1,2,6,3]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[5,4,7,1,3,2,6]=>[5,4,7,1,3,2,6]=>010101=>101010=>1
[5,4,7,1,3,6,2]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[5,4,7,1,6,2,3]=>[4,3,7,1,6,2,5]=>001011=>110100=>2
[5,4,7,1,6,3,2]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[5,4,7,2,1,3,6]=>[5,4,7,2,1,3,6]=>100101=>101001=>1
[5,4,7,2,1,6,3]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[5,4,7,2,3,1,6]=>[5,4,7,1,3,2,6]=>010101=>101010=>1
[5,4,7,2,3,6,1]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[5,4,7,2,6,1,3]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[5,4,7,2,6,3,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[5,4,7,3,1,2,6]=>[5,4,7,3,1,2,6]=>010101=>101010=>1
[5,4,7,3,1,6,2]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[5,4,7,3,2,1,6]=>[5,4,7,3,2,1,6]=>110101=>101011=>1
[5,4,7,3,2,6,1]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[5,4,7,3,6,1,2]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[5,4,7,3,6,2,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[5,4,7,6,1,2,3]=>[4,3,7,6,1,2,5]=>001011=>110100=>2
[5,4,7,6,1,3,2]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[5,4,7,6,2,1,3]=>[4,3,7,6,2,1,5]=>101011=>110101=>2
[5,4,7,6,2,3,1]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[5,4,7,6,3,1,2]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[5,4,7,6,3,2,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[5,6,1,2,3,4,7]=>[4,6,1,2,3,5,7]=>000010=>010000=>0
[5,6,1,2,3,7,4]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[5,6,1,2,4,3,7]=>[3,6,1,2,5,4,7]=>000110=>011000=>0
[5,6,1,2,4,7,3]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[5,6,1,2,7,3,4]=>[3,5,1,2,7,4,6]=>000101=>101000=>1
[5,6,1,2,7,4,3]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[5,6,1,3,2,4,7]=>[4,6,1,3,2,5,7]=>010010=>010010=>0
[5,6,1,3,2,7,4]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,1,3,4,2,7]=>[3,6,1,2,5,4,7]=>000110=>011000=>0
[5,6,1,3,4,7,2]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[5,6,1,3,7,2,4]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[5,6,1,3,7,4,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[5,6,1,4,2,3,7]=>[3,6,1,5,2,4,7]=>000110=>011000=>0
[5,6,1,4,2,7,3]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,1,4,3,2,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[5,6,1,4,3,7,2]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,1,4,7,2,3]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[5,6,1,4,7,3,2]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[5,6,1,7,2,3,4]=>[3,5,1,7,2,4,6]=>000101=>101000=>1
[5,6,1,7,2,4,3]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[5,6,1,7,3,2,4]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[5,6,1,7,3,4,2]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[5,6,1,7,4,2,3]=>[2,4,1,7,6,3,5]=>001011=>110100=>2
[5,6,1,7,4,3,2]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[5,6,2,1,3,4,7]=>[4,6,2,1,3,5,7]=>100010=>010001=>0
[5,6,2,1,3,7,4]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[5,6,2,1,4,3,7]=>[3,6,2,1,5,4,7]=>100110=>011001=>0
[5,6,2,1,4,7,3]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[5,6,2,1,7,3,4]=>[3,5,2,1,7,4,6]=>100101=>101001=>1
[5,6,2,1,7,4,3]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[5,6,2,3,1,4,7]=>[4,6,1,3,2,5,7]=>010010=>010010=>0
[5,6,2,3,1,7,4]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,2,3,4,1,7]=>[3,6,1,2,5,4,7]=>000110=>011000=>0
[5,6,2,3,4,7,1]=>[3,5,1,2,4,7,6]=>000101=>101000=>1
[5,6,2,3,7,1,4]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[5,6,2,3,7,4,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[5,6,2,4,1,3,7]=>[3,6,2,5,1,4,7]=>000110=>011000=>0
[5,6,2,4,1,7,3]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,2,4,3,1,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[5,6,2,4,3,7,1]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,2,4,7,1,3]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[5,6,2,4,7,3,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[5,6,2,7,1,3,4]=>[3,5,2,7,1,4,6]=>000101=>101000=>1
[5,6,2,7,1,4,3]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[5,6,2,7,3,1,4]=>[2,5,1,7,4,3,6]=>001101=>101100=>1
[5,6,2,7,3,4,1]=>[2,4,1,7,3,6,5]=>001011=>110100=>2
[5,6,2,7,4,1,3]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[5,6,2,7,4,3,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[5,6,3,1,2,4,7]=>[4,6,3,1,2,5,7]=>010010=>010010=>0
[5,6,3,1,2,7,4]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[5,6,3,1,4,2,7]=>[3,6,2,1,5,4,7]=>100110=>011001=>0
[5,6,3,1,4,7,2]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[5,6,3,1,7,2,4]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[5,6,3,1,7,4,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[5,6,3,2,1,4,7]=>[4,6,3,2,1,5,7]=>110010=>010011=>0
[5,6,3,2,1,7,4]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[5,6,3,2,4,1,7]=>[3,6,2,1,5,4,7]=>100110=>011001=>0
[5,6,3,2,4,7,1]=>[3,5,2,1,4,7,6]=>100101=>101001=>1
[5,6,3,2,7,1,4]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[5,6,3,2,7,4,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[5,6,3,4,1,2,7]=>[3,6,2,5,1,4,7]=>000110=>011000=>0
[5,6,3,4,1,7,2]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,3,4,2,1,7]=>[2,6,1,5,4,3,7]=>001110=>011100=>0
[5,6,3,4,2,7,1]=>[2,5,1,4,3,7,6]=>001101=>101100=>1
[5,6,3,4,7,1,2]=>[2,5,1,4,7,3,6]=>000101=>101000=>1
[5,6,3,4,7,2,1]=>[2,4,1,3,7,6,5]=>001011=>110100=>2
[5,6,3,7,1,2,4]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[5,6,3,7,1,4,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[5,6,3,7,2,1,4]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[5,6,3,7,2,4,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[5,6,3,7,4,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[5,6,3,7,4,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[5,6,4,1,2,3,7]=>[3,6,5,1,2,4,7]=>000110=>011000=>0
[5,6,4,1,2,7,3]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[5,6,4,1,3,2,7]=>[2,6,5,1,4,3,7]=>001110=>011100=>0
[5,6,4,1,3,7,2]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[5,6,4,1,7,2,3]=>[2,5,4,1,7,3,6]=>001101=>101100=>1
[5,6,4,1,7,3,2]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[5,6,4,2,1,3,7]=>[3,6,5,2,1,4,7]=>100110=>011001=>0
[5,6,4,2,1,7,3]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[5,6,4,2,3,1,7]=>[2,6,5,1,4,3,7]=>001110=>011100=>0
[5,6,4,2,3,7,1]=>[2,5,4,1,3,7,6]=>001101=>101100=>1
[5,6,4,2,7,1,3]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[5,6,4,2,7,3,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[5,6,4,3,1,2,7]=>[2,6,5,4,1,3,7]=>001110=>011100=>0
[5,6,4,3,1,7,2]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[5,6,4,3,2,1,7]=>[1,6,5,4,3,2,7]=>011110=>011110=>0
[5,6,4,3,2,7,1]=>[1,5,4,3,2,7,6]=>011101=>101110=>1
[5,6,4,3,7,1,2]=>[1,5,4,3,7,2,6]=>001101=>101100=>1
[5,6,4,3,7,2,1]=>[1,4,3,2,7,6,5]=>011011=>110110=>2
[5,6,4,7,1,2,3]=>[2,5,4,7,1,3,6]=>000101=>101000=>1
[5,6,4,7,1,3,2]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[5,6,4,7,2,1,3]=>[1,5,4,7,3,2,6]=>010101=>101010=>1
[5,6,4,7,2,3,1]=>[1,4,3,7,2,6,5]=>001011=>110100=>2
[5,6,4,7,3,1,2]=>[1,4,3,7,6,2,5]=>001011=>110100=>2
[5,6,4,7,3,2,1]=>[1,3,2,7,6,5,4]=>010111=>111010=>3
[5,6,7,1,2,3,4]=>[3,5,7,1,2,4,6]=>000001=>100000=>1
[5,6,7,1,2,4,3]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[5,6,7,1,3,2,4]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[5,6,7,1,3,4,2]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[5,6,7,1,4,2,3]=>[2,4,7,1,6,3,5]=>000011=>110000=>2
[5,6,7,1,4,3,2]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[5,6,7,2,1,3,4]=>[3,5,7,2,1,4,6]=>100001=>100001=>1
[5,6,7,2,1,4,3]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[5,6,7,2,3,1,4]=>[2,5,7,1,4,3,6]=>001001=>100100=>1
[5,6,7,2,3,4,1]=>[2,4,7,1,3,6,5]=>000011=>110000=>2
[5,6,7,2,4,1,3]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[5,6,7,2,4,3,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[5,6,7,3,1,2,4]=>[2,5,7,4,1,3,6]=>001001=>100100=>1
[5,6,7,3,1,4,2]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[5,6,7,3,2,1,4]=>[1,5,7,4,3,2,6]=>011001=>100110=>1
[5,6,7,3,2,4,1]=>[1,4,7,3,2,6,5]=>010011=>110010=>2
[5,6,7,3,4,1,2]=>[1,4,7,3,6,2,5]=>000011=>110000=>2
[5,6,7,3,4,2,1]=>[1,3,7,2,6,5,4]=>000111=>111000=>3
[5,6,7,4,1,2,3]=>[2,4,7,6,1,3,5]=>000011=>110000=>2
[5,6,7,4,1,3,2]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[5,6,7,4,2,1,3]=>[1,4,7,6,3,2,5]=>010011=>110010=>2
[5,6,7,4,2,3,1]=>[1,3,7,6,2,5,4]=>000111=>111000=>3
[5,6,7,4,3,1,2]=>[1,3,7,6,5,2,4]=>000111=>111000=>3
[5,6,7,4,3,2,1]=>[1,2,7,6,5,4,3]=>001111=>111100=>4
[5,7,1,2,3,4,6]=>[5,7,1,2,3,4,6]=>000001=>100000=>1
[5,7,1,2,3,6,4]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[5,7,1,2,4,3,6]=>[5,7,1,2,4,3,6]=>001001=>100100=>1
[5,7,1,2,4,6,3]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[5,7,1,2,6,3,4]=>[4,7,1,2,6,3,5]=>000011=>110000=>2
[5,7,1,2,6,4,3]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[5,7,1,3,2,4,6]=>[5,7,1,3,2,4,6]=>010001=>100010=>1
[5,7,1,3,2,6,4]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,1,3,4,2,6]=>[5,7,1,2,4,3,6]=>001001=>100100=>1
[5,7,1,3,4,6,2]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[5,7,1,3,6,2,4]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[5,7,1,3,6,4,2]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[5,7,1,4,2,3,6]=>[5,7,1,4,2,3,6]=>001001=>100100=>1
[5,7,1,4,2,6,3]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,1,4,3,2,6]=>[5,7,1,4,3,2,6]=>011001=>100110=>1
[5,7,1,4,3,6,2]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,1,4,6,2,3]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[5,7,1,4,6,3,2]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[5,7,1,6,2,3,4]=>[4,7,1,6,2,3,5]=>000011=>110000=>2
[5,7,1,6,2,4,3]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[5,7,1,6,3,2,4]=>[4,7,1,6,3,2,5]=>010011=>110010=>2
[5,7,1,6,3,4,2]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[5,7,1,6,4,2,3]=>[3,7,1,6,5,2,4]=>000111=>111000=>3
[5,7,1,6,4,3,2]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[5,7,2,1,3,4,6]=>[5,7,2,1,3,4,6]=>100001=>100001=>1
[5,7,2,1,3,6,4]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[5,7,2,1,4,3,6]=>[5,7,2,1,4,3,6]=>101001=>100101=>1
[5,7,2,1,4,6,3]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[5,7,2,1,6,3,4]=>[4,7,2,1,6,3,5]=>100011=>110001=>2
[5,7,2,1,6,4,3]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[5,7,2,3,1,4,6]=>[5,7,1,3,2,4,6]=>010001=>100010=>1
[5,7,2,3,1,6,4]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,2,3,4,1,6]=>[5,7,1,2,4,3,6]=>001001=>100100=>1
[5,7,2,3,4,6,1]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[5,7,2,3,6,1,4]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[5,7,2,3,6,4,1]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[5,7,2,4,1,3,6]=>[5,7,2,4,1,3,6]=>001001=>100100=>1
[5,7,2,4,1,6,3]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,2,4,3,1,6]=>[5,7,1,4,3,2,6]=>011001=>100110=>1
[5,7,2,4,3,6,1]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,2,4,6,1,3]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[5,7,2,4,6,3,1]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[5,7,2,6,1,3,4]=>[4,7,2,6,1,3,5]=>000011=>110000=>2
[5,7,2,6,1,4,3]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[5,7,2,6,3,1,4]=>[4,7,1,6,3,2,5]=>010011=>110010=>2
[5,7,2,6,3,4,1]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[5,7,2,6,4,1,3]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[5,7,2,6,4,3,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[5,7,3,1,2,4,6]=>[5,7,3,1,2,4,6]=>010001=>100010=>1
[5,7,3,1,2,6,4]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[5,7,3,1,4,2,6]=>[5,7,2,1,4,3,6]=>101001=>100101=>1
[5,7,3,1,4,6,2]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[5,7,3,1,6,2,4]=>[4,7,3,1,6,2,5]=>010011=>110010=>2
[5,7,3,1,6,4,2]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[5,7,3,2,1,4,6]=>[5,7,3,2,1,4,6]=>110001=>100011=>1
[5,7,3,2,1,6,4]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[5,7,3,2,4,1,6]=>[5,7,2,1,4,3,6]=>101001=>100101=>1
[5,7,3,2,4,6,1]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[5,7,3,2,6,1,4]=>[4,7,3,2,6,1,5]=>010011=>110010=>2
[5,7,3,2,6,4,1]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[5,7,3,4,1,2,6]=>[5,7,2,4,1,3,6]=>001001=>100100=>1
[5,7,3,4,1,6,2]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,3,4,2,1,6]=>[5,7,1,4,3,2,6]=>011001=>100110=>1
[5,7,3,4,2,6,1]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[5,7,3,4,6,1,2]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[5,7,3,4,6,2,1]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[5,7,3,6,1,2,4]=>[4,7,3,6,1,2,5]=>000011=>110000=>2
[5,7,3,6,1,4,2]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[5,7,3,6,2,1,4]=>[4,7,3,6,2,1,5]=>100011=>110001=>2
[5,7,3,6,2,4,1]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[5,7,3,6,4,1,2]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[5,7,3,6,4,2,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[5,7,4,1,2,3,6]=>[5,7,4,1,2,3,6]=>001001=>100100=>1
[5,7,4,1,2,6,3]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[5,7,4,1,3,2,6]=>[5,7,4,1,3,2,6]=>011001=>100110=>1
[5,7,4,1,3,6,2]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[5,7,4,1,6,2,3]=>[4,7,3,1,6,2,5]=>010011=>110010=>2
[5,7,4,1,6,3,2]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[5,7,4,2,1,3,6]=>[5,7,4,2,1,3,6]=>101001=>100101=>1
[5,7,4,2,1,6,3]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[5,7,4,2,3,1,6]=>[5,7,4,1,3,2,6]=>011001=>100110=>1
[5,7,4,2,3,6,1]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[5,7,4,2,6,1,3]=>[4,7,3,2,6,1,5]=>010011=>110010=>2
[5,7,4,2,6,3,1]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[5,7,4,3,1,2,6]=>[5,7,4,3,1,2,6]=>011001=>100110=>1
[5,7,4,3,1,6,2]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[5,7,4,3,2,1,6]=>[5,7,4,3,2,1,6]=>111001=>100111=>1
[5,7,4,3,2,6,1]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[5,7,4,3,6,1,2]=>[4,7,3,2,6,1,5]=>010011=>110010=>2
[5,7,4,3,6,2,1]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[5,7,4,6,1,2,3]=>[4,7,3,6,1,2,5]=>000011=>110000=>2
[5,7,4,6,1,3,2]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[5,7,4,6,2,1,3]=>[4,7,3,6,2,1,5]=>100011=>110001=>2
[5,7,4,6,2,3,1]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[5,7,4,6,3,1,2]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[5,7,4,6,3,2,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[5,7,6,1,2,3,4]=>[4,7,6,1,2,3,5]=>000011=>110000=>2
[5,7,6,1,2,4,3]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[5,7,6,1,3,2,4]=>[4,7,6,1,3,2,5]=>010011=>110010=>2
[5,7,6,1,3,4,2]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[5,7,6,1,4,2,3]=>[3,7,6,1,5,2,4]=>000111=>111000=>3
[5,7,6,1,4,3,2]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[5,7,6,2,1,3,4]=>[4,7,6,2,1,3,5]=>100011=>110001=>2
[5,7,6,2,1,4,3]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[5,7,6,2,3,1,4]=>[4,7,6,1,3,2,5]=>010011=>110010=>2
[5,7,6,2,3,4,1]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[5,7,6,2,4,1,3]=>[3,7,6,2,5,1,4]=>000111=>111000=>3
[5,7,6,2,4,3,1]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[5,7,6,3,1,2,4]=>[4,7,6,3,1,2,5]=>010011=>110010=>2
[5,7,6,3,1,4,2]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[5,7,6,3,2,1,4]=>[4,7,6,3,2,1,5]=>110011=>110011=>2
[5,7,6,3,2,4,1]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[5,7,6,3,4,1,2]=>[3,7,6,2,5,1,4]=>000111=>111000=>3
[5,7,6,3,4,2,1]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[5,7,6,4,1,2,3]=>[3,7,6,5,1,2,4]=>000111=>111000=>3
[5,7,6,4,1,3,2]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[5,7,6,4,2,1,3]=>[3,7,6,5,2,1,4]=>100111=>111001=>3
[5,7,6,4,2,3,1]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[5,7,6,4,3,1,2]=>[2,7,6,5,4,1,3]=>001111=>111100=>4
[5,7,6,4,3,2,1]=>[1,7,6,5,4,3,2]=>011111=>111110=>5
[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>000010=>010000=>0
[6,1,2,3,4,7,5]=>[5,1,2,3,4,7,6]=>000101=>101000=>1
[6,1,2,3,5,4,7]=>[6,1,2,3,5,4,7]=>000110=>011000=>0
[6,1,2,3,5,7,4]=>[5,1,2,3,4,7,6]=>000101=>101000=>1
[6,1,2,3,7,4,5]=>[5,1,2,3,7,4,6]=>000101=>101000=>1
[6,1,2,3,7,5,4]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,1,2,4,3,5,7]=>[6,1,2,4,3,5,7]=>001010=>010100=>0
[6,1,2,4,3,7,5]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,2,4,5,3,7]=>[6,1,2,3,5,4,7]=>000110=>011000=>0
[6,1,2,4,5,7,3]=>[5,1,2,3,4,7,6]=>000101=>101000=>1
[6,1,2,4,7,3,5]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,1,2,4,7,5,3]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,1,2,5,3,4,7]=>[6,1,2,5,3,4,7]=>000110=>011000=>0
[6,1,2,5,3,7,4]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,2,5,4,3,7]=>[6,1,2,5,4,3,7]=>001110=>011100=>0
[6,1,2,5,4,7,3]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,2,5,7,3,4]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,1,2,5,7,4,3]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,1,2,7,3,4,5]=>[5,1,2,7,3,4,6]=>000101=>101000=>1
[6,1,2,7,3,5,4]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[6,1,2,7,4,3,5]=>[5,1,2,7,4,3,6]=>001101=>101100=>1
[6,1,2,7,4,5,3]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[6,1,2,7,5,3,4]=>[4,1,2,7,6,3,5]=>001011=>110100=>2
[6,1,2,7,5,4,3]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,1,3,2,4,5,7]=>[6,1,3,2,4,5,7]=>010010=>010010=>0
[6,1,3,2,4,7,5]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,1,3,2,5,4,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,1,3,2,5,7,4]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,1,3,2,7,4,5]=>[5,1,3,2,7,4,6]=>010101=>101010=>1
[6,1,3,2,7,5,4]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,1,3,4,2,5,7]=>[6,1,2,4,3,5,7]=>001010=>010100=>0
[6,1,3,4,2,7,5]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,3,4,5,2,7]=>[6,1,2,3,5,4,7]=>000110=>011000=>0
[6,1,3,4,5,7,2]=>[5,1,2,3,4,7,6]=>000101=>101000=>1
[6,1,3,4,7,2,5]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,1,3,4,7,5,2]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,1,3,5,2,4,7]=>[6,1,3,5,2,4,7]=>000110=>011000=>0
[6,1,3,5,2,7,4]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,3,5,4,2,7]=>[6,1,2,5,4,3,7]=>001110=>011100=>0
[6,1,3,5,4,7,2]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,3,5,7,2,4]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,1,3,5,7,4,2]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,1,3,7,2,4,5]=>[5,1,3,7,2,4,6]=>000101=>101000=>1
[6,1,3,7,2,5,4]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,1,3,7,4,2,5]=>[5,1,2,7,4,3,6]=>001101=>101100=>1
[6,1,3,7,4,5,2]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[6,1,3,7,5,2,4]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,1,3,7,5,4,2]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,1,4,2,3,5,7]=>[6,1,4,2,3,5,7]=>001010=>010100=>0
[6,1,4,2,3,7,5]=>[5,1,4,2,3,7,6]=>001101=>101100=>1
[6,1,4,2,5,3,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,1,4,2,5,7,3]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,1,4,2,7,3,5]=>[5,1,4,2,7,3,6]=>001101=>101100=>1
[6,1,4,2,7,5,3]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,1,4,3,2,5,7]=>[6,1,4,3,2,5,7]=>011010=>010110=>0
[6,1,4,3,2,7,5]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,1,4,3,5,2,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,1,4,3,5,7,2]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,1,4,3,7,2,5]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,1,4,3,7,5,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,1,4,5,2,3,7]=>[6,1,3,5,2,4,7]=>000110=>011000=>0
[6,1,4,5,2,7,3]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,4,5,3,2,7]=>[6,1,2,5,4,3,7]=>001110=>011100=>0
[6,1,4,5,3,7,2]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,1,4,5,7,2,3]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,1,4,5,7,3,2]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,1,4,7,2,3,5]=>[5,1,4,7,2,3,6]=>000101=>101000=>1
[6,1,4,7,2,5,3]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,1,4,7,3,2,5]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[6,1,4,7,3,5,2]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,1,4,7,5,2,3]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,1,4,7,5,3,2]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,1,5,2,3,4,7]=>[6,1,5,2,3,4,7]=>000110=>011000=>0
[6,1,5,2,3,7,4]=>[5,1,4,2,3,7,6]=>001101=>101100=>1
[6,1,5,2,4,3,7]=>[6,1,5,2,4,3,7]=>001110=>011100=>0
[6,1,5,2,4,7,3]=>[5,1,4,2,3,7,6]=>001101=>101100=>1
[6,1,5,2,7,3,4]=>[5,1,4,2,7,3,6]=>001101=>101100=>1
[6,1,5,2,7,4,3]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,1,5,3,2,4,7]=>[6,1,5,3,2,4,7]=>010110=>011010=>0
[6,1,5,3,2,7,4]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,1,5,3,4,2,7]=>[6,1,5,2,4,3,7]=>001110=>011100=>0
[6,1,5,3,4,7,2]=>[5,1,4,2,3,7,6]=>001101=>101100=>1
[6,1,5,3,7,2,4]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,1,5,3,7,4,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,1,5,4,2,3,7]=>[6,1,5,4,2,3,7]=>001110=>011100=>0
[6,1,5,4,2,7,3]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,1,5,4,3,2,7]=>[6,1,5,4,3,2,7]=>011110=>011110=>0
[6,1,5,4,3,7,2]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,1,5,4,7,2,3]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,1,5,4,7,3,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,1,5,7,2,3,4]=>[5,1,4,7,2,3,6]=>000101=>101000=>1
[6,1,5,7,2,4,3]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,1,5,7,3,2,4]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[6,1,5,7,3,4,2]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,1,5,7,4,2,3]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,1,5,7,4,3,2]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,1,7,2,3,4,5]=>[5,1,7,2,3,4,6]=>000101=>101000=>1
[6,1,7,2,3,5,4]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[6,1,7,2,4,3,5]=>[5,1,7,2,4,3,6]=>001101=>101100=>1
[6,1,7,2,4,5,3]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[6,1,7,2,5,3,4]=>[4,1,7,2,6,3,5]=>001011=>110100=>2
[6,1,7,2,5,4,3]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[6,1,7,3,2,4,5]=>[5,1,7,3,2,4,6]=>010101=>101010=>1
[6,1,7,3,2,5,4]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,1,7,3,4,2,5]=>[5,1,7,2,4,3,6]=>001101=>101100=>1
[6,1,7,3,4,5,2]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[6,1,7,3,5,2,4]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[6,1,7,3,5,4,2]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[6,1,7,4,2,3,5]=>[5,1,7,4,2,3,6]=>001101=>101100=>1
[6,1,7,4,2,5,3]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,1,7,4,3,2,5]=>[5,1,7,4,3,2,6]=>011101=>101110=>1
[6,1,7,4,3,5,2]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,1,7,4,5,2,3]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[6,1,7,4,5,3,2]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[6,1,7,5,2,3,4]=>[4,1,7,6,2,3,5]=>001011=>110100=>2
[6,1,7,5,2,4,3]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[6,1,7,5,3,2,4]=>[4,1,7,6,3,2,5]=>011011=>110110=>2
[6,1,7,5,3,4,2]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[6,1,7,5,4,2,3]=>[3,1,7,6,5,2,4]=>010111=>111010=>3
[6,1,7,5,4,3,2]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[6,2,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>100010=>010001=>0
[6,2,1,3,4,7,5]=>[5,2,1,3,4,7,6]=>100101=>101001=>1
[6,2,1,3,5,4,7]=>[6,2,1,3,5,4,7]=>100110=>011001=>0
[6,2,1,3,5,7,4]=>[5,2,1,3,4,7,6]=>100101=>101001=>1
[6,2,1,3,7,4,5]=>[5,2,1,3,7,4,6]=>100101=>101001=>1
[6,2,1,3,7,5,4]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,2,1,4,3,5,7]=>[6,2,1,4,3,5,7]=>101010=>010101=>0
[6,2,1,4,3,7,5]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,2,1,4,5,3,7]=>[6,2,1,3,5,4,7]=>100110=>011001=>0
[6,2,1,4,5,7,3]=>[5,2,1,3,4,7,6]=>100101=>101001=>1
[6,2,1,4,7,3,5]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,2,1,4,7,5,3]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,2,1,5,3,4,7]=>[6,2,1,5,3,4,7]=>100110=>011001=>0
[6,2,1,5,3,7,4]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,2,1,5,4,3,7]=>[6,2,1,5,4,3,7]=>101110=>011101=>0
[6,2,1,5,4,7,3]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,2,1,5,7,3,4]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,2,1,5,7,4,3]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,2,1,7,3,4,5]=>[5,2,1,7,3,4,6]=>100101=>101001=>1
[6,2,1,7,3,5,4]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[6,2,1,7,4,3,5]=>[5,2,1,7,4,3,6]=>101101=>101101=>1
[6,2,1,7,4,5,3]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[6,2,1,7,5,3,4]=>[4,2,1,7,6,3,5]=>101011=>110101=>2
[6,2,1,7,5,4,3]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,2,3,1,4,5,7]=>[6,1,3,2,4,5,7]=>010010=>010010=>0
[6,2,3,1,4,7,5]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,2,3,1,5,4,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,2,3,1,5,7,4]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,2,3,1,7,4,5]=>[5,1,3,2,7,4,6]=>010101=>101010=>1
[6,2,3,1,7,5,4]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,2,3,4,1,5,7]=>[6,1,2,4,3,5,7]=>001010=>010100=>0
[6,2,3,4,1,7,5]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>000110=>011000=>0
[6,2,3,4,5,7,1]=>[5,1,2,3,4,7,6]=>000101=>101000=>1
[6,2,3,4,7,1,5]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,2,3,4,7,5,1]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,2,3,5,1,4,7]=>[6,1,3,5,2,4,7]=>000110=>011000=>0
[6,2,3,5,1,7,4]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,2,3,5,4,1,7]=>[6,1,2,5,4,3,7]=>001110=>011100=>0
[6,2,3,5,4,7,1]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,2,3,5,7,1,4]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,2,3,5,7,4,1]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,2,3,7,1,4,5]=>[5,1,3,7,2,4,6]=>000101=>101000=>1
[6,2,3,7,1,5,4]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,2,3,7,4,1,5]=>[5,1,2,7,4,3,6]=>001101=>101100=>1
[6,2,3,7,4,5,1]=>[4,1,2,7,3,6,5]=>001011=>110100=>2
[6,2,3,7,5,1,4]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,2,3,7,5,4,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,2,4,1,3,5,7]=>[6,2,4,1,3,5,7]=>001010=>010100=>0
[6,2,4,1,3,7,5]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,2,4,1,5,3,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,2,4,1,5,7,3]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,2,4,1,7,3,5]=>[5,2,4,1,7,3,6]=>001101=>101100=>1
[6,2,4,1,7,5,3]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,2,4,3,1,5,7]=>[6,1,4,3,2,5,7]=>011010=>010110=>0
[6,2,4,3,1,7,5]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,2,4,3,5,1,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,2,4,3,5,7,1]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,2,4,3,7,1,5]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,2,4,3,7,5,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,2,4,5,1,3,7]=>[6,1,3,5,2,4,7]=>000110=>011000=>0
[6,2,4,5,1,7,3]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,2,4,5,3,1,7]=>[6,1,2,5,4,3,7]=>001110=>011100=>0
[6,2,4,5,3,7,1]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,2,4,5,7,1,3]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,2,4,5,7,3,1]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,2,4,7,1,3,5]=>[5,2,4,7,1,3,6]=>000101=>101000=>1
[6,2,4,7,1,5,3]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,2,4,7,3,1,5]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[6,2,4,7,3,5,1]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,2,4,7,5,1,3]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,2,4,7,5,3,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,2,5,1,3,4,7]=>[6,2,5,1,3,4,7]=>000110=>011000=>0
[6,2,5,1,3,7,4]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,2,5,1,4,3,7]=>[6,2,5,1,4,3,7]=>001110=>011100=>0
[6,2,5,1,4,7,3]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,2,5,1,7,3,4]=>[5,2,4,1,7,3,6]=>001101=>101100=>1
[6,2,5,1,7,4,3]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,2,5,3,1,4,7]=>[6,1,5,3,2,4,7]=>010110=>011010=>0
[6,2,5,3,1,7,4]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,2,5,3,4,1,7]=>[6,1,5,2,4,3,7]=>001110=>011100=>0
[6,2,5,3,4,7,1]=>[5,1,4,2,3,7,6]=>001101=>101100=>1
[6,2,5,3,7,1,4]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,2,5,3,7,4,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,2,5,4,1,3,7]=>[6,2,5,4,1,3,7]=>001110=>011100=>0
[6,2,5,4,1,7,3]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,2,5,4,3,1,7]=>[6,1,5,4,3,2,7]=>011110=>011110=>0
[6,2,5,4,3,7,1]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,2,5,4,7,1,3]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,2,5,4,7,3,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,2,5,7,1,3,4]=>[5,2,4,7,1,3,6]=>000101=>101000=>1
[6,2,5,7,1,4,3]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,2,5,7,3,1,4]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[6,2,5,7,3,4,1]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,2,5,7,4,1,3]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,2,5,7,4,3,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,2,7,1,3,4,5]=>[5,2,7,1,3,4,6]=>000101=>101000=>1
[6,2,7,1,3,5,4]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[6,2,7,1,4,3,5]=>[5,2,7,1,4,3,6]=>001101=>101100=>1
[6,2,7,1,4,5,3]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[6,2,7,1,5,3,4]=>[4,2,7,1,6,3,5]=>001011=>110100=>2
[6,2,7,1,5,4,3]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,2,7,3,1,4,5]=>[5,1,7,3,2,4,6]=>010101=>101010=>1
[6,2,7,3,1,5,4]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,2,7,3,4,1,5]=>[5,1,7,2,4,3,6]=>001101=>101100=>1
[6,2,7,3,4,5,1]=>[4,1,7,2,3,6,5]=>001011=>110100=>2
[6,2,7,3,5,1,4]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[6,2,7,3,5,4,1]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[6,2,7,4,1,3,5]=>[5,2,7,4,1,3,6]=>001101=>101100=>1
[6,2,7,4,1,5,3]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,2,7,4,3,1,5]=>[5,1,7,4,3,2,6]=>011101=>101110=>1
[6,2,7,4,3,5,1]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,2,7,4,5,1,3]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[6,2,7,4,5,3,1]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[6,2,7,5,1,3,4]=>[4,2,7,6,1,3,5]=>001011=>110100=>2
[6,2,7,5,1,4,3]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[6,2,7,5,3,1,4]=>[4,1,7,6,3,2,5]=>011011=>110110=>2
[6,2,7,5,3,4,1]=>[3,1,7,6,2,5,4]=>010111=>111010=>3
[6,2,7,5,4,1,3]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[6,2,7,5,4,3,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[6,3,1,2,4,5,7]=>[6,3,1,2,4,5,7]=>010010=>010010=>0
[6,3,1,2,4,7,5]=>[5,3,1,2,4,7,6]=>010101=>101010=>1
[6,3,1,2,5,4,7]=>[6,3,1,2,5,4,7]=>010110=>011010=>0
[6,3,1,2,5,7,4]=>[5,3,1,2,4,7,6]=>010101=>101010=>1
[6,3,1,2,7,4,5]=>[5,3,1,2,7,4,6]=>010101=>101010=>1
[6,3,1,2,7,5,4]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,3,1,4,2,5,7]=>[6,2,1,4,3,5,7]=>101010=>010101=>0
[6,3,1,4,2,7,5]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,3,1,4,5,2,7]=>[6,2,1,3,5,4,7]=>100110=>011001=>0
[6,3,1,4,5,7,2]=>[5,2,1,3,4,7,6]=>100101=>101001=>1
[6,3,1,4,7,2,5]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,3,1,4,7,5,2]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,3,1,5,2,4,7]=>[6,3,1,5,2,4,7]=>010110=>011010=>0
[6,3,1,5,2,7,4]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,3,1,5,4,2,7]=>[6,2,1,5,4,3,7]=>101110=>011101=>0
[6,3,1,5,4,7,2]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,3,1,5,7,2,4]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,3,1,5,7,4,2]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,3,1,7,2,4,5]=>[5,3,1,7,2,4,6]=>010101=>101010=>1
[6,3,1,7,2,5,4]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[6,3,1,7,4,2,5]=>[5,2,1,7,4,3,6]=>101101=>101101=>1
[6,3,1,7,4,5,2]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[6,3,1,7,5,2,4]=>[4,3,1,7,6,2,5]=>011011=>110110=>2
[6,3,1,7,5,4,2]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,3,2,1,4,5,7]=>[6,3,2,1,4,5,7]=>110010=>010011=>0
[6,3,2,1,4,7,5]=>[5,3,2,1,4,7,6]=>110101=>101011=>1
[6,3,2,1,5,4,7]=>[6,3,2,1,5,4,7]=>110110=>011011=>0
[6,3,2,1,5,7,4]=>[5,3,2,1,4,7,6]=>110101=>101011=>1
[6,3,2,1,7,4,5]=>[5,3,2,1,7,4,6]=>110101=>101011=>1
[6,3,2,1,7,5,4]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,3,2,4,1,5,7]=>[6,2,1,4,3,5,7]=>101010=>010101=>0
[6,3,2,4,1,7,5]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,3,2,4,5,1,7]=>[6,2,1,3,5,4,7]=>100110=>011001=>0
[6,3,2,4,5,7,1]=>[5,2,1,3,4,7,6]=>100101=>101001=>1
[6,3,2,4,7,1,5]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,3,2,4,7,5,1]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,3,2,5,1,4,7]=>[6,3,2,5,1,4,7]=>010110=>011010=>0
[6,3,2,5,1,7,4]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,3,2,5,4,1,7]=>[6,2,1,5,4,3,7]=>101110=>011101=>0
[6,3,2,5,4,7,1]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,3,2,5,7,1,4]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,3,2,5,7,4,1]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,3,2,7,1,4,5]=>[5,3,2,7,1,4,6]=>010101=>101010=>1
[6,3,2,7,1,5,4]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,3,2,7,4,1,5]=>[5,2,1,7,4,3,6]=>101101=>101101=>1
[6,3,2,7,4,5,1]=>[4,2,1,7,3,6,5]=>101011=>110101=>2
[6,3,2,7,5,1,4]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[6,3,2,7,5,4,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,3,4,1,2,5,7]=>[6,2,4,1,3,5,7]=>001010=>010100=>0
[6,3,4,1,2,7,5]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,3,4,1,5,2,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,3,4,1,5,7,2]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,3,4,1,7,2,5]=>[5,2,4,1,7,3,6]=>001101=>101100=>1
[6,3,4,1,7,5,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,3,4,2,1,5,7]=>[6,1,4,3,2,5,7]=>011010=>010110=>0
[6,3,4,2,1,7,5]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,3,4,2,5,1,7]=>[6,1,3,2,5,4,7]=>010110=>011010=>0
[6,3,4,2,5,7,1]=>[5,1,3,2,4,7,6]=>010101=>101010=>1
[6,3,4,2,7,1,5]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,3,4,2,7,5,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,3,4,5,1,2,7]=>[6,1,3,5,2,4,7]=>000110=>011000=>0
[6,3,4,5,1,7,2]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,3,4,5,2,1,7]=>[6,1,2,5,4,3,7]=>001110=>011100=>0
[6,3,4,5,2,7,1]=>[5,1,2,4,3,7,6]=>001101=>101100=>1
[6,3,4,5,7,1,2]=>[5,1,2,4,7,3,6]=>000101=>101000=>1
[6,3,4,5,7,2,1]=>[4,1,2,3,7,6,5]=>001011=>110100=>2
[6,3,4,7,1,2,5]=>[5,2,4,7,1,3,6]=>000101=>101000=>1
[6,3,4,7,1,5,2]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,3,4,7,2,1,5]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[6,3,4,7,2,5,1]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,3,4,7,5,1,2]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,3,4,7,5,2,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,3,5,1,2,4,7]=>[6,3,5,1,2,4,7]=>000110=>011000=>0
[6,3,5,1,2,7,4]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,3,5,1,4,2,7]=>[6,2,5,1,4,3,7]=>001110=>011100=>0
[6,3,5,1,4,7,2]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,3,5,1,7,2,4]=>[5,2,4,1,7,3,6]=>001101=>101100=>1
[6,3,5,1,7,4,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,3,5,2,1,4,7]=>[6,3,5,2,1,4,7]=>100110=>011001=>0
[6,3,5,2,1,7,4]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,3,5,2,4,1,7]=>[6,2,5,1,4,3,7]=>001110=>011100=>0
[6,3,5,2,4,7,1]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,3,5,2,7,1,4]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,3,5,2,7,4,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,3,5,4,1,2,7]=>[6,2,5,4,1,3,7]=>001110=>011100=>0
[6,3,5,4,1,7,2]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,3,5,4,2,1,7]=>[6,1,5,4,3,2,7]=>011110=>011110=>0
[6,3,5,4,2,7,1]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,3,5,4,7,1,2]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,3,5,4,7,2,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,3,5,7,1,2,4]=>[5,2,4,7,1,3,6]=>000101=>101000=>1
[6,3,5,7,1,4,2]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,3,5,7,2,1,4]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[6,3,5,7,2,4,1]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,3,5,7,4,1,2]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,3,5,7,4,2,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,3,7,1,2,4,5]=>[5,3,7,1,2,4,6]=>000101=>101000=>1
[6,3,7,1,2,5,4]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[6,3,7,1,4,2,5]=>[5,2,7,1,4,3,6]=>001101=>101100=>1
[6,3,7,1,4,5,2]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[6,3,7,1,5,2,4]=>[4,3,7,1,6,2,5]=>001011=>110100=>2
[6,3,7,1,5,4,2]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,3,7,2,1,4,5]=>[5,3,7,2,1,4,6]=>100101=>101001=>1
[6,3,7,2,1,5,4]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[6,3,7,2,4,1,5]=>[5,2,7,1,4,3,6]=>001101=>101100=>1
[6,3,7,2,4,5,1]=>[4,2,7,1,3,6,5]=>001011=>110100=>2
[6,3,7,2,5,1,4]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[6,3,7,2,5,4,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,3,7,4,1,2,5]=>[5,2,7,4,1,3,6]=>001101=>101100=>1
[6,3,7,4,1,5,2]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,3,7,4,2,1,5]=>[5,1,7,4,3,2,6]=>011101=>101110=>1
[6,3,7,4,2,5,1]=>[4,1,7,3,2,6,5]=>011011=>110110=>2
[6,3,7,4,5,1,2]=>[4,1,7,3,6,2,5]=>001011=>110100=>2
[6,3,7,4,5,2,1]=>[3,1,7,2,6,5,4]=>010111=>111010=>3
[6,3,7,5,1,2,4]=>[4,3,7,6,1,2,5]=>001011=>110100=>2
[6,3,7,5,1,4,2]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[6,3,7,5,2,1,4]=>[4,3,7,6,2,1,5]=>101011=>110101=>2
[6,3,7,5,2,4,1]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[6,3,7,5,4,1,2]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[6,3,7,5,4,2,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[6,4,1,2,3,5,7]=>[6,4,1,2,3,5,7]=>001010=>010100=>0
[6,4,1,2,3,7,5]=>[5,4,1,2,3,7,6]=>001101=>101100=>1
[6,4,1,2,5,3,7]=>[6,3,1,2,5,4,7]=>010110=>011010=>0
[6,4,1,2,5,7,3]=>[5,3,1,2,4,7,6]=>010101=>101010=>1
[6,4,1,2,7,3,5]=>[5,4,1,2,7,3,6]=>001101=>101100=>1
[6,4,1,2,7,5,3]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,4,1,3,2,5,7]=>[6,4,1,3,2,5,7]=>011010=>010110=>0
[6,4,1,3,2,7,5]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,4,1,3,5,2,7]=>[6,3,1,2,5,4,7]=>010110=>011010=>0
[6,4,1,3,5,7,2]=>[5,3,1,2,4,7,6]=>010101=>101010=>1
[6,4,1,3,7,2,5]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[6,4,1,3,7,5,2]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,4,1,5,2,3,7]=>[6,3,1,5,2,4,7]=>010110=>011010=>0
[6,4,1,5,2,7,3]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,4,1,5,3,2,7]=>[6,2,1,5,4,3,7]=>101110=>011101=>0
[6,4,1,5,3,7,2]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,4,1,5,7,2,3]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,4,1,5,7,3,2]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,4,1,7,2,3,5]=>[5,4,1,7,2,3,6]=>001101=>101100=>1
[6,4,1,7,2,5,3]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[6,4,1,7,3,2,5]=>[5,4,1,7,3,2,6]=>011101=>101110=>1
[6,4,1,7,3,5,2]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[6,4,1,7,5,2,3]=>[4,3,1,7,6,2,5]=>011011=>110110=>2
[6,4,1,7,5,3,2]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,4,2,1,3,5,7]=>[6,4,2,1,3,5,7]=>101010=>010101=>0
[6,4,2,1,3,7,5]=>[5,4,2,1,3,7,6]=>101101=>101101=>1
[6,4,2,1,5,3,7]=>[6,3,2,1,5,4,7]=>110110=>011011=>0
[6,4,2,1,5,7,3]=>[5,3,2,1,4,7,6]=>110101=>101011=>1
[6,4,2,1,7,3,5]=>[5,4,2,1,7,3,6]=>101101=>101101=>1
[6,4,2,1,7,5,3]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,4,2,3,1,5,7]=>[6,4,1,3,2,5,7]=>011010=>010110=>0
[6,4,2,3,1,7,5]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,4,2,3,5,1,7]=>[6,3,1,2,5,4,7]=>010110=>011010=>0
[6,4,2,3,5,7,1]=>[5,3,1,2,4,7,6]=>010101=>101010=>1
[6,4,2,3,7,1,5]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[6,4,2,3,7,5,1]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,4,2,5,1,3,7]=>[6,3,2,5,1,4,7]=>010110=>011010=>0
[6,4,2,5,1,7,3]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,4,2,5,3,1,7]=>[6,2,1,5,4,3,7]=>101110=>011101=>0
[6,4,2,5,3,7,1]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,4,2,5,7,1,3]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,4,2,5,7,3,1]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,4,2,7,1,3,5]=>[5,4,2,7,1,3,6]=>001101=>101100=>1
[6,4,2,7,1,5,3]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,4,2,7,3,1,5]=>[5,4,1,7,3,2,6]=>011101=>101110=>1
[6,4,2,7,3,5,1]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[6,4,2,7,5,1,3]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[6,4,2,7,5,3,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,4,3,1,2,5,7]=>[6,4,3,1,2,5,7]=>011010=>010110=>0
[6,4,3,1,2,7,5]=>[5,4,3,1,2,7,6]=>011101=>101110=>1
[6,4,3,1,5,2,7]=>[6,3,2,1,5,4,7]=>110110=>011011=>0
[6,4,3,1,5,7,2]=>[5,3,2,1,4,7,6]=>110101=>101011=>1
[6,4,3,1,7,2,5]=>[5,4,3,1,7,2,6]=>011101=>101110=>1
[6,4,3,1,7,5,2]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,4,3,2,1,5,7]=>[6,4,3,2,1,5,7]=>111010=>010111=>0
[6,4,3,2,1,7,5]=>[5,4,3,2,1,7,6]=>111101=>101111=>1
[6,4,3,2,5,1,7]=>[6,3,2,1,5,4,7]=>110110=>011011=>0
[6,4,3,2,5,7,1]=>[5,3,2,1,4,7,6]=>110101=>101011=>1
[6,4,3,2,7,1,5]=>[5,4,3,2,7,1,6]=>011101=>101110=>1
[6,4,3,2,7,5,1]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,4,3,5,1,2,7]=>[6,3,2,5,1,4,7]=>010110=>011010=>0
[6,4,3,5,1,7,2]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,4,3,5,2,1,7]=>[6,2,1,5,4,3,7]=>101110=>011101=>0
[6,4,3,5,2,7,1]=>[5,2,1,4,3,7,6]=>101101=>101101=>1
[6,4,3,5,7,1,2]=>[5,2,1,4,7,3,6]=>100101=>101001=>1
[6,4,3,5,7,2,1]=>[4,2,1,3,7,6,5]=>101011=>110101=>2
[6,4,3,7,1,2,5]=>[5,4,3,7,1,2,6]=>001101=>101100=>1
[6,4,3,7,1,5,2]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,4,3,7,2,1,5]=>[5,4,3,7,2,1,6]=>101101=>101101=>1
[6,4,3,7,2,5,1]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,4,3,7,5,1,2]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[6,4,3,7,5,2,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,4,5,1,2,3,7]=>[6,3,5,1,2,4,7]=>000110=>011000=>0
[6,4,5,1,2,7,3]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,4,5,1,3,2,7]=>[6,2,5,1,4,3,7]=>001110=>011100=>0
[6,4,5,1,3,7,2]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,4,5,1,7,2,3]=>[5,2,4,1,7,3,6]=>001101=>101100=>1
[6,4,5,1,7,3,2]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,4,5,2,1,3,7]=>[6,3,5,2,1,4,7]=>100110=>011001=>0
[6,4,5,2,1,7,3]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,4,5,2,3,1,7]=>[6,2,5,1,4,3,7]=>001110=>011100=>0
[6,4,5,2,3,7,1]=>[5,2,4,1,3,7,6]=>001101=>101100=>1
[6,4,5,2,7,1,3]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,4,5,2,7,3,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,4,5,3,1,2,7]=>[6,2,5,4,1,3,7]=>001110=>011100=>0
[6,4,5,3,1,7,2]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,4,5,3,2,1,7]=>[6,1,5,4,3,2,7]=>011110=>011110=>0
[6,4,5,3,2,7,1]=>[5,1,4,3,2,7,6]=>011101=>101110=>1
[6,4,5,3,7,1,2]=>[5,1,4,3,7,2,6]=>001101=>101100=>1
[6,4,5,3,7,2,1]=>[4,1,3,2,7,6,5]=>011011=>110110=>2
[6,4,5,7,1,2,3]=>[5,2,4,7,1,3,6]=>000101=>101000=>1
[6,4,5,7,1,3,2]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,4,5,7,2,1,3]=>[5,1,4,7,3,2,6]=>010101=>101010=>1
[6,4,5,7,2,3,1]=>[4,1,3,7,2,6,5]=>001011=>110100=>2
[6,4,5,7,3,1,2]=>[4,1,3,7,6,2,5]=>001011=>110100=>2
[6,4,5,7,3,2,1]=>[3,1,2,7,6,5,4]=>010111=>111010=>3
[6,4,7,1,2,3,5]=>[5,4,7,1,2,3,6]=>000101=>101000=>1
[6,4,7,1,2,5,3]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[6,4,7,1,3,2,5]=>[5,4,7,1,3,2,6]=>010101=>101010=>1
[6,4,7,1,3,5,2]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[6,4,7,1,5,2,3]=>[4,3,7,1,6,2,5]=>001011=>110100=>2
[6,4,7,1,5,3,2]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,4,7,2,1,3,5]=>[5,4,7,2,1,3,6]=>100101=>101001=>1
[6,4,7,2,1,5,3]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[6,4,7,2,3,1,5]=>[5,4,7,1,3,2,6]=>010101=>101010=>1
[6,4,7,2,3,5,1]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[6,4,7,2,5,1,3]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[6,4,7,2,5,3,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,4,7,3,1,2,5]=>[5,4,7,3,1,2,6]=>010101=>101010=>1
[6,4,7,3,1,5,2]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[6,4,7,3,2,1,5]=>[5,4,7,3,2,1,6]=>110101=>101011=>1
[6,4,7,3,2,5,1]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[6,4,7,3,5,1,2]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[6,4,7,3,5,2,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,4,7,5,1,2,3]=>[4,3,7,6,1,2,5]=>001011=>110100=>2
[6,4,7,5,1,3,2]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[6,4,7,5,2,1,3]=>[4,3,7,6,2,1,5]=>101011=>110101=>2
[6,4,7,5,2,3,1]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[6,4,7,5,3,1,2]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[6,4,7,5,3,2,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[6,5,1,2,3,4,7]=>[6,5,1,2,3,4,7]=>000110=>011000=>0
[6,5,1,2,3,7,4]=>[5,4,1,2,3,7,6]=>001101=>101100=>1
[6,5,1,2,4,3,7]=>[6,5,1,2,4,3,7]=>001110=>011100=>0
[6,5,1,2,4,7,3]=>[5,4,1,2,3,7,6]=>001101=>101100=>1
[6,5,1,2,7,3,4]=>[5,4,1,2,7,3,6]=>001101=>101100=>1
[6,5,1,2,7,4,3]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,5,1,3,2,4,7]=>[6,5,1,3,2,4,7]=>010110=>011010=>0
[6,5,1,3,2,7,4]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,1,3,4,2,7]=>[6,5,1,2,4,3,7]=>001110=>011100=>0
[6,5,1,3,4,7,2]=>[5,4,1,2,3,7,6]=>001101=>101100=>1
[6,5,1,3,7,2,4]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[6,5,1,3,7,4,2]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,5,1,4,2,3,7]=>[6,5,1,4,2,3,7]=>001110=>011100=>0
[6,5,1,4,2,7,3]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,1,4,3,2,7]=>[6,5,1,4,3,2,7]=>011110=>011110=>0
[6,5,1,4,3,7,2]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,1,4,7,2,3]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[6,5,1,4,7,3,2]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,5,1,7,2,3,4]=>[5,4,1,7,2,3,6]=>001101=>101100=>1
[6,5,1,7,2,4,3]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[6,5,1,7,3,2,4]=>[5,4,1,7,3,2,6]=>011101=>101110=>1
[6,5,1,7,3,4,2]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[6,5,1,7,4,2,3]=>[4,3,1,7,6,2,5]=>011011=>110110=>2
[6,5,1,7,4,3,2]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,5,2,1,3,4,7]=>[6,5,2,1,3,4,7]=>100110=>011001=>0
[6,5,2,1,3,7,4]=>[5,4,2,1,3,7,6]=>101101=>101101=>1
[6,5,2,1,4,3,7]=>[6,5,2,1,4,3,7]=>101110=>011101=>0
[6,5,2,1,4,7,3]=>[5,4,2,1,3,7,6]=>101101=>101101=>1
[6,5,2,1,7,3,4]=>[5,4,2,1,7,3,6]=>101101=>101101=>1
[6,5,2,1,7,4,3]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,5,2,3,1,4,7]=>[6,5,1,3,2,4,7]=>010110=>011010=>0
[6,5,2,3,1,7,4]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,2,3,4,1,7]=>[6,5,1,2,4,3,7]=>001110=>011100=>0
[6,5,2,3,4,7,1]=>[5,4,1,2,3,7,6]=>001101=>101100=>1
[6,5,2,3,7,1,4]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[6,5,2,3,7,4,1]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,5,2,4,1,3,7]=>[6,5,2,4,1,3,7]=>001110=>011100=>0
[6,5,2,4,1,7,3]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,2,4,3,1,7]=>[6,5,1,4,3,2,7]=>011110=>011110=>0
[6,5,2,4,3,7,1]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,2,4,7,1,3]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[6,5,2,4,7,3,1]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,5,2,7,1,3,4]=>[5,4,2,7,1,3,6]=>001101=>101100=>1
[6,5,2,7,1,4,3]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,5,2,7,3,1,4]=>[5,4,1,7,3,2,6]=>011101=>101110=>1
[6,5,2,7,3,4,1]=>[4,3,1,7,2,6,5]=>011011=>110110=>2
[6,5,2,7,4,1,3]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[6,5,2,7,4,3,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,5,3,1,2,4,7]=>[6,5,3,1,2,4,7]=>010110=>011010=>0
[6,5,3,1,2,7,4]=>[5,4,3,1,2,7,6]=>011101=>101110=>1
[6,5,3,1,4,2,7]=>[6,5,2,1,4,3,7]=>101110=>011101=>0
[6,5,3,1,4,7,2]=>[5,4,2,1,3,7,6]=>101101=>101101=>1
[6,5,3,1,7,2,4]=>[5,4,3,1,7,2,6]=>011101=>101110=>1
[6,5,3,1,7,4,2]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,5,3,2,1,4,7]=>[6,5,3,2,1,4,7]=>110110=>011011=>0
[6,5,3,2,1,7,4]=>[5,4,3,2,1,7,6]=>111101=>101111=>1
[6,5,3,2,4,1,7]=>[6,5,2,1,4,3,7]=>101110=>011101=>0
[6,5,3,2,4,7,1]=>[5,4,2,1,3,7,6]=>101101=>101101=>1
[6,5,3,2,7,1,4]=>[5,4,3,2,7,1,6]=>011101=>101110=>1
[6,5,3,2,7,4,1]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,5,3,4,1,2,7]=>[6,5,2,4,1,3,7]=>001110=>011100=>0
[6,5,3,4,1,7,2]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>011110=>011110=>0
[6,5,3,4,2,7,1]=>[5,4,1,3,2,7,6]=>011101=>101110=>1
[6,5,3,4,7,1,2]=>[5,4,1,3,7,2,6]=>001101=>101100=>1
[6,5,3,4,7,2,1]=>[4,3,1,2,7,6,5]=>011011=>110110=>2
[6,5,3,7,1,2,4]=>[5,4,3,7,1,2,6]=>001101=>101100=>1
[6,5,3,7,1,4,2]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,5,3,7,2,1,4]=>[5,4,3,7,2,1,6]=>101101=>101101=>1
[6,5,3,7,2,4,1]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,5,3,7,4,1,2]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[6,5,3,7,4,2,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,5,4,1,2,3,7]=>[6,5,4,1,2,3,7]=>001110=>011100=>0
[6,5,4,1,2,7,3]=>[5,4,3,1,2,7,6]=>011101=>101110=>1
[6,5,4,1,3,2,7]=>[6,5,4,1,3,2,7]=>011110=>011110=>0
[6,5,4,1,3,7,2]=>[5,4,3,1,2,7,6]=>011101=>101110=>1
[6,5,4,1,7,2,3]=>[5,4,3,1,7,2,6]=>011101=>101110=>1
[6,5,4,1,7,3,2]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,5,4,2,1,3,7]=>[6,5,4,2,1,3,7]=>101110=>011101=>0
[6,5,4,2,1,7,3]=>[5,4,3,2,1,7,6]=>111101=>101111=>1
[6,5,4,2,3,1,7]=>[6,5,4,1,3,2,7]=>011110=>011110=>0
[6,5,4,2,3,7,1]=>[5,4,3,1,2,7,6]=>011101=>101110=>1
[6,5,4,2,7,1,3]=>[5,4,3,2,7,1,6]=>011101=>101110=>1
[6,5,4,2,7,3,1]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,5,4,3,1,2,7]=>[6,5,4,3,1,2,7]=>011110=>011110=>0
[6,5,4,3,1,7,2]=>[5,4,3,2,1,7,6]=>111101=>101111=>1
[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110=>011111=>0
[6,5,4,3,2,7,1]=>[5,4,3,2,1,7,6]=>111101=>101111=>1
[6,5,4,3,7,1,2]=>[5,4,3,2,7,1,6]=>011101=>101110=>1
[6,5,4,3,7,2,1]=>[4,3,2,1,7,6,5]=>111011=>110111=>2
[6,5,4,7,1,2,3]=>[5,4,3,7,1,2,6]=>001101=>101100=>1
[6,5,4,7,1,3,2]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,5,4,7,2,1,3]=>[5,4,3,7,2,1,6]=>101101=>101101=>1
[6,5,4,7,2,3,1]=>[4,3,2,7,1,6,5]=>011011=>110110=>2
[6,5,4,7,3,1,2]=>[4,3,2,7,6,1,5]=>011011=>110110=>2
[6,5,4,7,3,2,1]=>[3,2,1,7,6,5,4]=>110111=>111011=>3
[6,5,7,1,2,3,4]=>[5,4,7,1,2,3,6]=>000101=>101000=>1
[6,5,7,1,2,4,3]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[6,5,7,1,3,2,4]=>[5,4,7,1,3,2,6]=>010101=>101010=>1
[6,5,7,1,3,4,2]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[6,5,7,1,4,2,3]=>[4,3,7,1,6,2,5]=>001011=>110100=>2
[6,5,7,1,4,3,2]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,5,7,2,1,3,4]=>[5,4,7,2,1,3,6]=>100101=>101001=>1
[6,5,7,2,1,4,3]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[6,5,7,2,3,1,4]=>[5,4,7,1,3,2,6]=>010101=>101010=>1
[6,5,7,2,3,4,1]=>[4,3,7,1,2,6,5]=>001011=>110100=>2
[6,5,7,2,4,1,3]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[6,5,7,2,4,3,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,5,7,3,1,2,4]=>[5,4,7,3,1,2,6]=>010101=>101010=>1
[6,5,7,3,1,4,2]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[6,5,7,3,2,1,4]=>[5,4,7,3,2,1,6]=>110101=>101011=>1
[6,5,7,3,2,4,1]=>[4,3,7,2,1,6,5]=>101011=>110101=>2
[6,5,7,3,4,1,2]=>[4,3,7,2,6,1,5]=>001011=>110100=>2
[6,5,7,3,4,2,1]=>[3,2,7,1,6,5,4]=>010111=>111010=>3
[6,5,7,4,1,2,3]=>[4,3,7,6,1,2,5]=>001011=>110100=>2
[6,5,7,4,1,3,2]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[6,5,7,4,2,1,3]=>[4,3,7,6,2,1,5]=>101011=>110101=>2
[6,5,7,4,2,3,1]=>[3,2,7,6,1,5,4]=>010111=>111010=>3
[6,5,7,4,3,1,2]=>[3,2,7,6,5,1,4]=>010111=>111010=>3
[6,5,7,4,3,2,1]=>[2,1,7,6,5,4,3]=>101111=>111101=>4
[6,7,1,2,3,4,5]=>[5,7,1,2,3,4,6]=>000001=>100000=>1
[6,7,1,2,3,5,4]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[6,7,1,2,4,3,5]=>[5,7,1,2,4,3,6]=>001001=>100100=>1
[6,7,1,2,4,5,3]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[6,7,1,2,5,3,4]=>[4,7,1,2,6,3,5]=>000011=>110000=>2
[6,7,1,2,5,4,3]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[6,7,1,3,2,4,5]=>[5,7,1,3,2,4,6]=>010001=>100010=>1
[6,7,1,3,2,5,4]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,1,3,4,2,5]=>[5,7,1,2,4,3,6]=>001001=>100100=>1
[6,7,1,3,4,5,2]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[6,7,1,3,5,2,4]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[6,7,1,3,5,4,2]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[6,7,1,4,2,3,5]=>[5,7,1,4,2,3,6]=>001001=>100100=>1
[6,7,1,4,2,5,3]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,1,4,3,2,5]=>[5,7,1,4,3,2,6]=>011001=>100110=>1
[6,7,1,4,3,5,2]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,1,4,5,2,3]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[6,7,1,4,5,3,2]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[6,7,1,5,2,3,4]=>[4,7,1,6,2,3,5]=>000011=>110000=>2
[6,7,1,5,2,4,3]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[6,7,1,5,3,2,4]=>[4,7,1,6,3,2,5]=>010011=>110010=>2
[6,7,1,5,3,4,2]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[6,7,1,5,4,2,3]=>[3,7,1,6,5,2,4]=>000111=>111000=>3
[6,7,1,5,4,3,2]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[6,7,2,1,3,4,5]=>[5,7,2,1,3,4,6]=>100001=>100001=>1
[6,7,2,1,3,5,4]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[6,7,2,1,4,3,5]=>[5,7,2,1,4,3,6]=>101001=>100101=>1
[6,7,2,1,4,5,3]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[6,7,2,1,5,3,4]=>[4,7,2,1,6,3,5]=>100011=>110001=>2
[6,7,2,1,5,4,3]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[6,7,2,3,1,4,5]=>[5,7,1,3,2,4,6]=>010001=>100010=>1
[6,7,2,3,1,5,4]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,2,3,4,1,5]=>[5,7,1,2,4,3,6]=>001001=>100100=>1
[6,7,2,3,4,5,1]=>[4,7,1,2,3,6,5]=>000011=>110000=>2
[6,7,2,3,5,1,4]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[6,7,2,3,5,4,1]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[6,7,2,4,1,3,5]=>[5,7,2,4,1,3,6]=>001001=>100100=>1
[6,7,2,4,1,5,3]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,2,4,3,1,5]=>[5,7,1,4,3,2,6]=>011001=>100110=>1
[6,7,2,4,3,5,1]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,2,4,5,1,3]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[6,7,2,4,5,3,1]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[6,7,2,5,1,3,4]=>[4,7,2,6,1,3,5]=>000011=>110000=>2
[6,7,2,5,1,4,3]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[6,7,2,5,3,1,4]=>[4,7,1,6,3,2,5]=>010011=>110010=>2
[6,7,2,5,3,4,1]=>[3,7,1,6,2,5,4]=>000111=>111000=>3
[6,7,2,5,4,1,3]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[6,7,2,5,4,3,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[6,7,3,1,2,4,5]=>[5,7,3,1,2,4,6]=>010001=>100010=>1
[6,7,3,1,2,5,4]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[6,7,3,1,4,2,5]=>[5,7,2,1,4,3,6]=>101001=>100101=>1
[6,7,3,1,4,5,2]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[6,7,3,1,5,2,4]=>[4,7,3,1,6,2,5]=>010011=>110010=>2
[6,7,3,1,5,4,2]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[6,7,3,2,1,4,5]=>[5,7,3,2,1,4,6]=>110001=>100011=>1
[6,7,3,2,1,5,4]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[6,7,3,2,4,1,5]=>[5,7,2,1,4,3,6]=>101001=>100101=>1
[6,7,3,2,4,5,1]=>[4,7,2,1,3,6,5]=>100011=>110001=>2
[6,7,3,2,5,1,4]=>[4,7,3,2,6,1,5]=>010011=>110010=>2
[6,7,3,2,5,4,1]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[6,7,3,4,1,2,5]=>[5,7,2,4,1,3,6]=>001001=>100100=>1
[6,7,3,4,1,5,2]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,3,4,2,1,5]=>[5,7,1,4,3,2,6]=>011001=>100110=>1
[6,7,3,4,2,5,1]=>[4,7,1,3,2,6,5]=>010011=>110010=>2
[6,7,3,4,5,1,2]=>[4,7,1,3,6,2,5]=>000011=>110000=>2
[6,7,3,4,5,2,1]=>[3,7,1,2,6,5,4]=>000111=>111000=>3
[6,7,3,5,1,2,4]=>[4,7,3,6,1,2,5]=>000011=>110000=>2
[6,7,3,5,1,4,2]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[6,7,3,5,2,1,4]=>[4,7,3,6,2,1,5]=>100011=>110001=>2
[6,7,3,5,2,4,1]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[6,7,3,5,4,1,2]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[6,7,3,5,4,2,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[6,7,4,1,2,3,5]=>[5,7,4,1,2,3,6]=>001001=>100100=>1
[6,7,4,1,2,5,3]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[6,7,4,1,3,2,5]=>[5,7,4,1,3,2,6]=>011001=>100110=>1
[6,7,4,1,3,5,2]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[6,7,4,1,5,2,3]=>[4,7,3,1,6,2,5]=>010011=>110010=>2
[6,7,4,1,5,3,2]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[6,7,4,2,1,3,5]=>[5,7,4,2,1,3,6]=>101001=>100101=>1
[6,7,4,2,1,5,3]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[6,7,4,2,3,1,5]=>[5,7,4,1,3,2,6]=>011001=>100110=>1
[6,7,4,2,3,5,1]=>[4,7,3,1,2,6,5]=>010011=>110010=>2
[6,7,4,2,5,1,3]=>[4,7,3,2,6,1,5]=>010011=>110010=>2
[6,7,4,2,5,3,1]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[6,7,4,3,1,2,5]=>[5,7,4,3,1,2,6]=>011001=>100110=>1
[6,7,4,3,1,5,2]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[6,7,4,3,2,1,5]=>[5,7,4,3,2,1,6]=>111001=>100111=>1
[6,7,4,3,2,5,1]=>[4,7,3,2,1,6,5]=>110011=>110011=>2
[6,7,4,3,5,1,2]=>[4,7,3,2,6,1,5]=>010011=>110010=>2
[6,7,4,3,5,2,1]=>[3,7,2,1,6,5,4]=>100111=>111001=>3
[6,7,4,5,1,2,3]=>[4,7,3,6,1,2,5]=>000011=>110000=>2
[6,7,4,5,1,3,2]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[6,7,4,5,2,1,3]=>[4,7,3,6,2,1,5]=>100011=>110001=>2
[6,7,4,5,2,3,1]=>[3,7,2,6,1,5,4]=>000111=>111000=>3
[6,7,4,5,3,1,2]=>[3,7,2,6,5,1,4]=>000111=>111000=>3
[6,7,4,5,3,2,1]=>[2,7,1,6,5,4,3]=>001111=>111100=>4
[6,7,5,1,2,3,4]=>[4,7,6,1,2,3,5]=>000011=>110000=>2
[6,7,5,1,2,4,3]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[6,7,5,1,3,2,4]=>[4,7,6,1,3,2,5]=>010011=>110010=>2
[6,7,5,1,3,4,2]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[6,7,5,1,4,2,3]=>[3,7,6,1,5,2,4]=>000111=>111000=>3
[6,7,5,1,4,3,2]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[6,7,5,2,1,3,4]=>[4,7,6,2,1,3,5]=>100011=>110001=>2
[6,7,5,2,1,4,3]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[6,7,5,2,3,1,4]=>[4,7,6,1,3,2,5]=>010011=>110010=>2
[6,7,5,2,3,4,1]=>[3,7,6,1,2,5,4]=>000111=>111000=>3
[6,7,5,2,4,1,3]=>[3,7,6,2,5,1,4]=>000111=>111000=>3
[6,7,5,2,4,3,1]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[6,7,5,3,1,2,4]=>[4,7,6,3,1,2,5]=>010011=>110010=>2
[6,7,5,3,1,4,2]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[6,7,5,3,2,1,4]=>[4,7,6,3,2,1,5]=>110011=>110011=>2
[6,7,5,3,2,4,1]=>[3,7,6,2,1,5,4]=>100111=>111001=>3
[6,7,5,3,4,1,2]=>[3,7,6,2,5,1,4]=>000111=>111000=>3
[6,7,5,3,4,2,1]=>[2,7,6,1,5,4,3]=>001111=>111100=>4
[6,7,5,4,1,2,3]=>[3,7,6,5,1,2,4]=>000111=>111000=>3
[6,7,5,4,1,3,2]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[6,7,5,4,2,1,3]=>[3,7,6,5,2,1,4]=>100111=>111001=>3
[6,7,5,4,2,3,1]=>[2,7,6,5,1,4,3]=>001111=>111100=>4
[6,7,5,4,3,1,2]=>[2,7,6,5,4,1,3]=>001111=>111100=>4
[6,7,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>011111=>111110=>5
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>000001=>100000=>1
[7,1,2,3,4,6,5]=>[7,1,2,3,4,6,5]=>000011=>110000=>2
[7,1,2,3,5,4,6]=>[7,1,2,3,5,4,6]=>000101=>101000=>1
[7,1,2,3,5,6,4]=>[7,1,2,3,4,6,5]=>000011=>110000=>2
[7,1,2,3,6,4,5]=>[7,1,2,3,6,4,5]=>000011=>110000=>2
[7,1,2,3,6,5,4]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,1,2,4,3,5,6]=>[7,1,2,4,3,5,6]=>001001=>100100=>1
[7,1,2,4,3,6,5]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,2,4,5,3,6]=>[7,1,2,3,5,4,6]=>000101=>101000=>1
[7,1,2,4,5,6,3]=>[7,1,2,3,4,6,5]=>000011=>110000=>2
[7,1,2,4,6,3,5]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,1,2,4,6,5,3]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,1,2,5,3,4,6]=>[7,1,2,5,3,4,6]=>000101=>101000=>1
[7,1,2,5,3,6,4]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,2,5,4,3,6]=>[7,1,2,5,4,3,6]=>001101=>101100=>1
[7,1,2,5,4,6,3]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,2,5,6,3,4]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,1,2,5,6,4,3]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,1,2,6,3,4,5]=>[7,1,2,6,3,4,5]=>000011=>110000=>2
[7,1,2,6,3,5,4]=>[7,1,2,6,3,5,4]=>000111=>111000=>3
[7,1,2,6,4,3,5]=>[7,1,2,6,4,3,5]=>001011=>110100=>2
[7,1,2,6,4,5,3]=>[7,1,2,6,3,5,4]=>000111=>111000=>3
[7,1,2,6,5,3,4]=>[7,1,2,6,5,3,4]=>000111=>111000=>3
[7,1,2,6,5,4,3]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,1,3,2,4,5,6]=>[7,1,3,2,4,5,6]=>010001=>100010=>1
[7,1,3,2,4,6,5]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,1,3,2,5,4,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,1,3,2,5,6,4]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,1,3,2,6,4,5]=>[7,1,3,2,6,4,5]=>010011=>110010=>2
[7,1,3,2,6,5,4]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,1,3,4,2,5,6]=>[7,1,2,4,3,5,6]=>001001=>100100=>1
[7,1,3,4,2,6,5]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,3,4,5,2,6]=>[7,1,2,3,5,4,6]=>000101=>101000=>1
[7,1,3,4,5,6,2]=>[7,1,2,3,4,6,5]=>000011=>110000=>2
[7,1,3,4,6,2,5]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,1,3,4,6,5,2]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,1,3,5,2,4,6]=>[7,1,3,5,2,4,6]=>000101=>101000=>1
[7,1,3,5,2,6,4]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,3,5,4,2,6]=>[7,1,2,5,4,3,6]=>001101=>101100=>1
[7,1,3,5,4,6,2]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,3,5,6,2,4]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,1,3,5,6,4,2]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,1,3,6,2,4,5]=>[7,1,3,6,2,4,5]=>000011=>110000=>2
[7,1,3,6,2,5,4]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,1,3,6,4,2,5]=>[7,1,2,6,4,3,5]=>001011=>110100=>2
[7,1,3,6,4,5,2]=>[7,1,2,6,3,5,4]=>000111=>111000=>3
[7,1,3,6,5,2,4]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,1,3,6,5,4,2]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,1,4,2,3,5,6]=>[7,1,4,2,3,5,6]=>001001=>100100=>1
[7,1,4,2,3,6,5]=>[7,1,4,2,3,6,5]=>001011=>110100=>2
[7,1,4,2,5,3,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,1,4,2,5,6,3]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,1,4,2,6,3,5]=>[7,1,4,2,6,3,5]=>001011=>110100=>2
[7,1,4,2,6,5,3]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,1,4,3,2,5,6]=>[7,1,4,3,2,5,6]=>011001=>100110=>1
[7,1,4,3,2,6,5]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,1,4,3,5,2,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,1,4,3,5,6,2]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,1,4,3,6,2,5]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,1,4,3,6,5,2]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,1,4,5,2,3,6]=>[7,1,3,5,2,4,6]=>000101=>101000=>1
[7,1,4,5,2,6,3]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,4,5,3,2,6]=>[7,1,2,5,4,3,6]=>001101=>101100=>1
[7,1,4,5,3,6,2]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,1,4,5,6,2,3]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,1,4,5,6,3,2]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,1,4,6,2,3,5]=>[7,1,4,6,2,3,5]=>000011=>110000=>2
[7,1,4,6,2,5,3]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,1,4,6,3,2,5]=>[7,1,4,6,3,2,5]=>010011=>110010=>2
[7,1,4,6,3,5,2]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,1,4,6,5,2,3]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,1,4,6,5,3,2]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,1,5,2,3,4,6]=>[7,1,5,2,3,4,6]=>000101=>101000=>1
[7,1,5,2,3,6,4]=>[7,1,4,2,3,6,5]=>001011=>110100=>2
[7,1,5,2,4,3,6]=>[7,1,5,2,4,3,6]=>001101=>101100=>1
[7,1,5,2,4,6,3]=>[7,1,4,2,3,6,5]=>001011=>110100=>2
[7,1,5,2,6,3,4]=>[7,1,4,2,6,3,5]=>001011=>110100=>2
[7,1,5,2,6,4,3]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,1,5,3,2,4,6]=>[7,1,5,3,2,4,6]=>010101=>101010=>1
[7,1,5,3,2,6,4]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,1,5,3,4,2,6]=>[7,1,5,2,4,3,6]=>001101=>101100=>1
[7,1,5,3,4,6,2]=>[7,1,4,2,3,6,5]=>001011=>110100=>2
[7,1,5,3,6,2,4]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,1,5,3,6,4,2]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,1,5,4,2,3,6]=>[7,1,5,4,2,3,6]=>001101=>101100=>1
[7,1,5,4,2,6,3]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,1,5,4,3,2,6]=>[7,1,5,4,3,2,6]=>011101=>101110=>1
[7,1,5,4,3,6,2]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,1,5,4,6,2,3]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,1,5,4,6,3,2]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,1,5,6,2,3,4]=>[7,1,4,6,2,3,5]=>000011=>110000=>2
[7,1,5,6,2,4,3]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,1,5,6,3,2,4]=>[7,1,4,6,3,2,5]=>010011=>110010=>2
[7,1,5,6,3,4,2]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,1,5,6,4,2,3]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,1,5,6,4,3,2]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,1,6,2,3,4,5]=>[7,1,6,2,3,4,5]=>000011=>110000=>2
[7,1,6,2,3,5,4]=>[7,1,6,2,3,5,4]=>000111=>111000=>3
[7,1,6,2,4,3,5]=>[7,1,6,2,4,3,5]=>001011=>110100=>2
[7,1,6,2,4,5,3]=>[7,1,6,2,3,5,4]=>000111=>111000=>3
[7,1,6,2,5,3,4]=>[7,1,6,2,5,3,4]=>000111=>111000=>3
[7,1,6,2,5,4,3]=>[7,1,6,2,5,4,3]=>001111=>111100=>4
[7,1,6,3,2,4,5]=>[7,1,6,3,2,4,5]=>010011=>110010=>2
[7,1,6,3,2,5,4]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,1,6,3,4,2,5]=>[7,1,6,2,4,3,5]=>001011=>110100=>2
[7,1,6,3,4,5,2]=>[7,1,6,2,3,5,4]=>000111=>111000=>3
[7,1,6,3,5,2,4]=>[7,1,6,3,5,2,4]=>000111=>111000=>3
[7,1,6,3,5,4,2]=>[7,1,6,2,5,4,3]=>001111=>111100=>4
[7,1,6,4,2,3,5]=>[7,1,6,4,2,3,5]=>001011=>110100=>2
[7,1,6,4,2,5,3]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,1,6,4,3,2,5]=>[7,1,6,4,3,2,5]=>011011=>110110=>2
[7,1,6,4,3,5,2]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,1,6,4,5,2,3]=>[7,1,6,3,5,2,4]=>000111=>111000=>3
[7,1,6,4,5,3,2]=>[7,1,6,2,5,4,3]=>001111=>111100=>4
[7,1,6,5,2,3,4]=>[7,1,6,5,2,3,4]=>000111=>111000=>3
[7,1,6,5,2,4,3]=>[7,1,6,5,2,4,3]=>001111=>111100=>4
[7,1,6,5,3,2,4]=>[7,1,6,5,3,2,4]=>010111=>111010=>3
[7,1,6,5,3,4,2]=>[7,1,6,5,2,4,3]=>001111=>111100=>4
[7,1,6,5,4,2,3]=>[7,1,6,5,4,2,3]=>001111=>111100=>4
[7,1,6,5,4,3,2]=>[7,1,6,5,4,3,2]=>011111=>111110=>5
[7,2,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>100001=>100001=>1
[7,2,1,3,4,6,5]=>[7,2,1,3,4,6,5]=>100011=>110001=>2
[7,2,1,3,5,4,6]=>[7,2,1,3,5,4,6]=>100101=>101001=>1
[7,2,1,3,5,6,4]=>[7,2,1,3,4,6,5]=>100011=>110001=>2
[7,2,1,3,6,4,5]=>[7,2,1,3,6,4,5]=>100011=>110001=>2
[7,2,1,3,6,5,4]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,2,1,4,3,5,6]=>[7,2,1,4,3,5,6]=>101001=>100101=>1
[7,2,1,4,3,6,5]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,2,1,4,5,3,6]=>[7,2,1,3,5,4,6]=>100101=>101001=>1
[7,2,1,4,5,6,3]=>[7,2,1,3,4,6,5]=>100011=>110001=>2
[7,2,1,4,6,3,5]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,2,1,4,6,5,3]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,2,1,5,3,4,6]=>[7,2,1,5,3,4,6]=>100101=>101001=>1
[7,2,1,5,3,6,4]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,2,1,5,4,3,6]=>[7,2,1,5,4,3,6]=>101101=>101101=>1
[7,2,1,5,4,6,3]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,2,1,5,6,3,4]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,2,1,5,6,4,3]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,2,1,6,3,4,5]=>[7,2,1,6,3,4,5]=>100011=>110001=>2
[7,2,1,6,3,5,4]=>[7,2,1,6,3,5,4]=>100111=>111001=>3
[7,2,1,6,4,3,5]=>[7,2,1,6,4,3,5]=>101011=>110101=>2
[7,2,1,6,4,5,3]=>[7,2,1,6,3,5,4]=>100111=>111001=>3
[7,2,1,6,5,3,4]=>[7,2,1,6,5,3,4]=>100111=>111001=>3
[7,2,1,6,5,4,3]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,2,3,1,4,5,6]=>[7,1,3,2,4,5,6]=>010001=>100010=>1
[7,2,3,1,4,6,5]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,2,3,1,5,4,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,2,3,1,5,6,4]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,2,3,1,6,4,5]=>[7,1,3,2,6,4,5]=>010011=>110010=>2
[7,2,3,1,6,5,4]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,2,3,4,1,5,6]=>[7,1,2,4,3,5,6]=>001001=>100100=>1
[7,2,3,4,1,6,5]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,2,3,4,5,1,6]=>[7,1,2,3,5,4,6]=>000101=>101000=>1
[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>000011=>110000=>2
[7,2,3,4,6,1,5]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,2,3,4,6,5,1]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,2,3,5,1,4,6]=>[7,1,3,5,2,4,6]=>000101=>101000=>1
[7,2,3,5,1,6,4]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,2,3,5,4,1,6]=>[7,1,2,5,4,3,6]=>001101=>101100=>1
[7,2,3,5,4,6,1]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,2,3,5,6,1,4]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,2,3,5,6,4,1]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,2,3,6,1,4,5]=>[7,1,3,6,2,4,5]=>000011=>110000=>2
[7,2,3,6,1,5,4]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,2,3,6,4,1,5]=>[7,1,2,6,4,3,5]=>001011=>110100=>2
[7,2,3,6,4,5,1]=>[7,1,2,6,3,5,4]=>000111=>111000=>3
[7,2,3,6,5,1,4]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,2,3,6,5,4,1]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,2,4,1,3,5,6]=>[7,2,4,1,3,5,6]=>001001=>100100=>1
[7,2,4,1,3,6,5]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,2,4,1,5,3,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,2,4,1,5,6,3]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,2,4,1,6,3,5]=>[7,2,4,1,6,3,5]=>001011=>110100=>2
[7,2,4,1,6,5,3]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,2,4,3,1,5,6]=>[7,1,4,3,2,5,6]=>011001=>100110=>1
[7,2,4,3,1,6,5]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,2,4,3,5,1,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,2,4,3,5,6,1]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,2,4,3,6,1,5]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,2,4,3,6,5,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,2,4,5,1,3,6]=>[7,1,3,5,2,4,6]=>000101=>101000=>1
[7,2,4,5,1,6,3]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,2,4,5,3,1,6]=>[7,1,2,5,4,3,6]=>001101=>101100=>1
[7,2,4,5,3,6,1]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,2,4,5,6,1,3]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,2,4,5,6,3,1]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,2,4,6,1,3,5]=>[7,2,4,6,1,3,5]=>000011=>110000=>2
[7,2,4,6,1,5,3]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,2,4,6,3,1,5]=>[7,1,4,6,3,2,5]=>010011=>110010=>2
[7,2,4,6,3,5,1]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,2,4,6,5,1,3]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,2,4,6,5,3,1]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,2,5,1,3,4,6]=>[7,2,5,1,3,4,6]=>000101=>101000=>1
[7,2,5,1,3,6,4]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,2,5,1,4,3,6]=>[7,2,5,1,4,3,6]=>001101=>101100=>1
[7,2,5,1,4,6,3]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,2,5,1,6,3,4]=>[7,2,4,1,6,3,5]=>001011=>110100=>2
[7,2,5,1,6,4,3]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,2,5,3,1,4,6]=>[7,1,5,3,2,4,6]=>010101=>101010=>1
[7,2,5,3,1,6,4]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,2,5,3,4,1,6]=>[7,1,5,2,4,3,6]=>001101=>101100=>1
[7,2,5,3,4,6,1]=>[7,1,4,2,3,6,5]=>001011=>110100=>2
[7,2,5,3,6,1,4]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,2,5,3,6,4,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,2,5,4,1,3,6]=>[7,2,5,4,1,3,6]=>001101=>101100=>1
[7,2,5,4,1,6,3]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,2,5,4,3,1,6]=>[7,1,5,4,3,2,6]=>011101=>101110=>1
[7,2,5,4,3,6,1]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,2,5,4,6,1,3]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,2,5,4,6,3,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,2,5,6,1,3,4]=>[7,2,4,6,1,3,5]=>000011=>110000=>2
[7,2,5,6,1,4,3]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,2,5,6,3,1,4]=>[7,1,4,6,3,2,5]=>010011=>110010=>2
[7,2,5,6,3,4,1]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,2,5,6,4,1,3]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,2,5,6,4,3,1]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,2,6,1,3,4,5]=>[7,2,6,1,3,4,5]=>000011=>110000=>2
[7,2,6,1,3,5,4]=>[7,2,6,1,3,5,4]=>000111=>111000=>3
[7,2,6,1,4,3,5]=>[7,2,6,1,4,3,5]=>001011=>110100=>2
[7,2,6,1,4,5,3]=>[7,2,6,1,3,5,4]=>000111=>111000=>3
[7,2,6,1,5,3,4]=>[7,2,6,1,5,3,4]=>000111=>111000=>3
[7,2,6,1,5,4,3]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,2,6,3,1,4,5]=>[7,1,6,3,2,4,5]=>010011=>110010=>2
[7,2,6,3,1,5,4]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,2,6,3,4,1,5]=>[7,1,6,2,4,3,5]=>001011=>110100=>2
[7,2,6,3,4,5,1]=>[7,1,6,2,3,5,4]=>000111=>111000=>3
[7,2,6,3,5,1,4]=>[7,1,6,3,5,2,4]=>000111=>111000=>3
[7,2,6,3,5,4,1]=>[7,1,6,2,5,4,3]=>001111=>111100=>4
[7,2,6,4,1,3,5]=>[7,2,6,4,1,3,5]=>001011=>110100=>2
[7,2,6,4,1,5,3]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,2,6,4,3,1,5]=>[7,1,6,4,3,2,5]=>011011=>110110=>2
[7,2,6,4,3,5,1]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,2,6,4,5,1,3]=>[7,1,6,3,5,2,4]=>000111=>111000=>3
[7,2,6,4,5,3,1]=>[7,1,6,2,5,4,3]=>001111=>111100=>4
[7,2,6,5,1,3,4]=>[7,2,6,5,1,3,4]=>000111=>111000=>3
[7,2,6,5,1,4,3]=>[7,2,6,5,1,4,3]=>001111=>111100=>4
[7,2,6,5,3,1,4]=>[7,1,6,5,3,2,4]=>010111=>111010=>3
[7,2,6,5,3,4,1]=>[7,1,6,5,2,4,3]=>001111=>111100=>4
[7,2,6,5,4,1,3]=>[7,2,6,5,4,1,3]=>001111=>111100=>4
[7,2,6,5,4,3,1]=>[7,1,6,5,4,3,2]=>011111=>111110=>5
[7,3,1,2,4,5,6]=>[7,3,1,2,4,5,6]=>010001=>100010=>1
[7,3,1,2,4,6,5]=>[7,3,1,2,4,6,5]=>010011=>110010=>2
[7,3,1,2,5,4,6]=>[7,3,1,2,5,4,6]=>010101=>101010=>1
[7,3,1,2,5,6,4]=>[7,3,1,2,4,6,5]=>010011=>110010=>2
[7,3,1,2,6,4,5]=>[7,3,1,2,6,4,5]=>010011=>110010=>2
[7,3,1,2,6,5,4]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,3,1,4,2,5,6]=>[7,2,1,4,3,5,6]=>101001=>100101=>1
[7,3,1,4,2,6,5]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,3,1,4,5,2,6]=>[7,2,1,3,5,4,6]=>100101=>101001=>1
[7,3,1,4,5,6,2]=>[7,2,1,3,4,6,5]=>100011=>110001=>2
[7,3,1,4,6,2,5]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,3,1,4,6,5,2]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,3,1,5,2,4,6]=>[7,3,1,5,2,4,6]=>010101=>101010=>1
[7,3,1,5,2,6,4]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,3,1,5,4,2,6]=>[7,2,1,5,4,3,6]=>101101=>101101=>1
[7,3,1,5,4,6,2]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,3,1,5,6,2,4]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,3,1,5,6,4,2]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,3,1,6,2,4,5]=>[7,3,1,6,2,4,5]=>010011=>110010=>2
[7,3,1,6,2,5,4]=>[7,3,1,6,2,5,4]=>010111=>111010=>3
[7,3,1,6,4,2,5]=>[7,2,1,6,4,3,5]=>101011=>110101=>2
[7,3,1,6,4,5,2]=>[7,2,1,6,3,5,4]=>100111=>111001=>3
[7,3,1,6,5,2,4]=>[7,3,1,6,5,2,4]=>010111=>111010=>3
[7,3,1,6,5,4,2]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,3,2,1,4,5,6]=>[7,3,2,1,4,5,6]=>110001=>100011=>1
[7,3,2,1,4,6,5]=>[7,3,2,1,4,6,5]=>110011=>110011=>2
[7,3,2,1,5,4,6]=>[7,3,2,1,5,4,6]=>110101=>101011=>1
[7,3,2,1,5,6,4]=>[7,3,2,1,4,6,5]=>110011=>110011=>2
[7,3,2,1,6,4,5]=>[7,3,2,1,6,4,5]=>110011=>110011=>2
[7,3,2,1,6,5,4]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,3,2,4,1,5,6]=>[7,2,1,4,3,5,6]=>101001=>100101=>1
[7,3,2,4,1,6,5]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,3,2,4,5,1,6]=>[7,2,1,3,5,4,6]=>100101=>101001=>1
[7,3,2,4,5,6,1]=>[7,2,1,3,4,6,5]=>100011=>110001=>2
[7,3,2,4,6,1,5]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,3,2,4,6,5,1]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,3,2,5,1,4,6]=>[7,3,2,5,1,4,6]=>010101=>101010=>1
[7,3,2,5,1,6,4]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,3,2,5,4,1,6]=>[7,2,1,5,4,3,6]=>101101=>101101=>1
[7,3,2,5,4,6,1]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,3,2,5,6,1,4]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,3,2,5,6,4,1]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,3,2,6,1,4,5]=>[7,3,2,6,1,4,5]=>010011=>110010=>2
[7,3,2,6,1,5,4]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,3,2,6,4,1,5]=>[7,2,1,6,4,3,5]=>101011=>110101=>2
[7,3,2,6,4,5,1]=>[7,2,1,6,3,5,4]=>100111=>111001=>3
[7,3,2,6,5,1,4]=>[7,3,2,6,5,1,4]=>010111=>111010=>3
[7,3,2,6,5,4,1]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,3,4,1,2,5,6]=>[7,2,4,1,3,5,6]=>001001=>100100=>1
[7,3,4,1,2,6,5]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,3,4,1,5,2,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,3,4,1,5,6,2]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,3,4,1,6,2,5]=>[7,2,4,1,6,3,5]=>001011=>110100=>2
[7,3,4,1,6,5,2]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,3,4,2,1,5,6]=>[7,1,4,3,2,5,6]=>011001=>100110=>1
[7,3,4,2,1,6,5]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,3,4,2,5,1,6]=>[7,1,3,2,5,4,6]=>010101=>101010=>1
[7,3,4,2,5,6,1]=>[7,1,3,2,4,6,5]=>010011=>110010=>2
[7,3,4,2,6,1,5]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,3,4,2,6,5,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,3,4,5,1,2,6]=>[7,1,3,5,2,4,6]=>000101=>101000=>1
[7,3,4,5,1,6,2]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,3,4,5,2,1,6]=>[7,1,2,5,4,3,6]=>001101=>101100=>1
[7,3,4,5,2,6,1]=>[7,1,2,4,3,6,5]=>001011=>110100=>2
[7,3,4,5,6,1,2]=>[7,1,2,4,6,3,5]=>000011=>110000=>2
[7,3,4,5,6,2,1]=>[7,1,2,3,6,5,4]=>000111=>111000=>3
[7,3,4,6,1,2,5]=>[7,2,4,6,1,3,5]=>000011=>110000=>2
[7,3,4,6,1,5,2]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,3,4,6,2,1,5]=>[7,1,4,6,3,2,5]=>010011=>110010=>2
[7,3,4,6,2,5,1]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,3,4,6,5,1,2]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,3,4,6,5,2,1]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,3,5,1,2,4,6]=>[7,3,5,1,2,4,6]=>000101=>101000=>1
[7,3,5,1,2,6,4]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,3,5,1,4,2,6]=>[7,2,5,1,4,3,6]=>001101=>101100=>1
[7,3,5,1,4,6,2]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,3,5,1,6,2,4]=>[7,2,4,1,6,3,5]=>001011=>110100=>2
[7,3,5,1,6,4,2]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,3,5,2,1,4,6]=>[7,3,5,2,1,4,6]=>100101=>101001=>1
[7,3,5,2,1,6,4]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,3,5,2,4,1,6]=>[7,2,5,1,4,3,6]=>001101=>101100=>1
[7,3,5,2,4,6,1]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,3,5,2,6,1,4]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,3,5,2,6,4,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,3,5,4,1,2,6]=>[7,2,5,4,1,3,6]=>001101=>101100=>1
[7,3,5,4,1,6,2]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,3,5,4,2,1,6]=>[7,1,5,4,3,2,6]=>011101=>101110=>1
[7,3,5,4,2,6,1]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,3,5,4,6,1,2]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,3,5,4,6,2,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,3,5,6,1,2,4]=>[7,2,4,6,1,3,5]=>000011=>110000=>2
[7,3,5,6,1,4,2]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,3,5,6,2,1,4]=>[7,1,4,6,3,2,5]=>010011=>110010=>2
[7,3,5,6,2,4,1]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,3,5,6,4,1,2]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,3,5,6,4,2,1]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,3,6,1,2,4,5]=>[7,3,6,1,2,4,5]=>000011=>110000=>2
[7,3,6,1,2,5,4]=>[7,3,6,1,2,5,4]=>000111=>111000=>3
[7,3,6,1,4,2,5]=>[7,2,6,1,4,3,5]=>001011=>110100=>2
[7,3,6,1,4,5,2]=>[7,2,6,1,3,5,4]=>000111=>111000=>3
[7,3,6,1,5,2,4]=>[7,3,6,1,5,2,4]=>000111=>111000=>3
[7,3,6,1,5,4,2]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,3,6,2,1,4,5]=>[7,3,6,2,1,4,5]=>100011=>110001=>2
[7,3,6,2,1,5,4]=>[7,3,6,2,1,5,4]=>100111=>111001=>3
[7,3,6,2,4,1,5]=>[7,2,6,1,4,3,5]=>001011=>110100=>2
[7,3,6,2,4,5,1]=>[7,2,6,1,3,5,4]=>000111=>111000=>3
[7,3,6,2,5,1,4]=>[7,3,6,2,5,1,4]=>000111=>111000=>3
[7,3,6,2,5,4,1]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,3,6,4,1,2,5]=>[7,2,6,4,1,3,5]=>001011=>110100=>2
[7,3,6,4,1,5,2]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,3,6,4,2,1,5]=>[7,1,6,4,3,2,5]=>011011=>110110=>2
[7,3,6,4,2,5,1]=>[7,1,6,3,2,5,4]=>010111=>111010=>3
[7,3,6,4,5,1,2]=>[7,1,6,3,5,2,4]=>000111=>111000=>3
[7,3,6,4,5,2,1]=>[7,1,6,2,5,4,3]=>001111=>111100=>4
[7,3,6,5,1,2,4]=>[7,3,6,5,1,2,4]=>000111=>111000=>3
[7,3,6,5,1,4,2]=>[7,2,6,5,1,4,3]=>001111=>111100=>4
[7,3,6,5,2,1,4]=>[7,3,6,5,2,1,4]=>100111=>111001=>3
[7,3,6,5,2,4,1]=>[7,2,6,5,1,4,3]=>001111=>111100=>4
[7,3,6,5,4,1,2]=>[7,2,6,5,4,1,3]=>001111=>111100=>4
[7,3,6,5,4,2,1]=>[7,1,6,5,4,3,2]=>011111=>111110=>5
[7,4,1,2,3,5,6]=>[7,4,1,2,3,5,6]=>001001=>100100=>1
[7,4,1,2,3,6,5]=>[7,4,1,2,3,6,5]=>001011=>110100=>2
[7,4,1,2,5,3,6]=>[7,3,1,2,5,4,6]=>010101=>101010=>1
[7,4,1,2,5,6,3]=>[7,3,1,2,4,6,5]=>010011=>110010=>2
[7,4,1,2,6,3,5]=>[7,4,1,2,6,3,5]=>001011=>110100=>2
[7,4,1,2,6,5,3]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,4,1,3,2,5,6]=>[7,4,1,3,2,5,6]=>011001=>100110=>1
[7,4,1,3,2,6,5]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,4,1,3,5,2,6]=>[7,3,1,2,5,4,6]=>010101=>101010=>1
[7,4,1,3,5,6,2]=>[7,3,1,2,4,6,5]=>010011=>110010=>2
[7,4,1,3,6,2,5]=>[7,4,1,3,6,2,5]=>001011=>110100=>2
[7,4,1,3,6,5,2]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,4,1,5,2,3,6]=>[7,3,1,5,2,4,6]=>010101=>101010=>1
[7,4,1,5,2,6,3]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,4,1,5,3,2,6]=>[7,2,1,5,4,3,6]=>101101=>101101=>1
[7,4,1,5,3,6,2]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,4,1,5,6,2,3]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,4,1,5,6,3,2]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,4,1,6,2,3,5]=>[7,4,1,6,2,3,5]=>001011=>110100=>2
[7,4,1,6,2,5,3]=>[7,3,1,6,2,5,4]=>010111=>111010=>3
[7,4,1,6,3,2,5]=>[7,4,1,6,3,2,5]=>011011=>110110=>2
[7,4,1,6,3,5,2]=>[7,3,1,6,2,5,4]=>010111=>111010=>3
[7,4,1,6,5,2,3]=>[7,3,1,6,5,2,4]=>010111=>111010=>3
[7,4,1,6,5,3,2]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,4,2,1,3,5,6]=>[7,4,2,1,3,5,6]=>101001=>100101=>1
[7,4,2,1,3,6,5]=>[7,4,2,1,3,6,5]=>101011=>110101=>2
[7,4,2,1,5,3,6]=>[7,3,2,1,5,4,6]=>110101=>101011=>1
[7,4,2,1,5,6,3]=>[7,3,2,1,4,6,5]=>110011=>110011=>2
[7,4,2,1,6,3,5]=>[7,4,2,1,6,3,5]=>101011=>110101=>2
[7,4,2,1,6,5,3]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,4,2,3,1,5,6]=>[7,4,1,3,2,5,6]=>011001=>100110=>1
[7,4,2,3,1,6,5]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,4,2,3,5,1,6]=>[7,3,1,2,5,4,6]=>010101=>101010=>1
[7,4,2,3,5,6,1]=>[7,3,1,2,4,6,5]=>010011=>110010=>2
[7,4,2,3,6,1,5]=>[7,4,1,3,6,2,5]=>001011=>110100=>2
[7,4,2,3,6,5,1]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,4,2,5,1,3,6]=>[7,3,2,5,1,4,6]=>010101=>101010=>1
[7,4,2,5,1,6,3]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,4,2,5,3,1,6]=>[7,2,1,5,4,3,6]=>101101=>101101=>1
[7,4,2,5,3,6,1]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,4,2,5,6,1,3]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,4,2,5,6,3,1]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,4,2,6,1,3,5]=>[7,4,2,6,1,3,5]=>001011=>110100=>2
[7,4,2,6,1,5,3]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,4,2,6,3,1,5]=>[7,4,1,6,3,2,5]=>011011=>110110=>2
[7,4,2,6,3,5,1]=>[7,3,1,6,2,5,4]=>010111=>111010=>3
[7,4,2,6,5,1,3]=>[7,3,2,6,5,1,4]=>010111=>111010=>3
[7,4,2,6,5,3,1]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,4,3,1,2,5,6]=>[7,4,3,1,2,5,6]=>011001=>100110=>1
[7,4,3,1,2,6,5]=>[7,4,3,1,2,6,5]=>011011=>110110=>2
[7,4,3,1,5,2,6]=>[7,3,2,1,5,4,6]=>110101=>101011=>1
[7,4,3,1,5,6,2]=>[7,3,2,1,4,6,5]=>110011=>110011=>2
[7,4,3,1,6,2,5]=>[7,4,3,1,6,2,5]=>011011=>110110=>2
[7,4,3,1,6,5,2]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,4,3,2,1,5,6]=>[7,4,3,2,1,5,6]=>111001=>100111=>1
[7,4,3,2,1,6,5]=>[7,4,3,2,1,6,5]=>111011=>110111=>2
[7,4,3,2,5,1,6]=>[7,3,2,1,5,4,6]=>110101=>101011=>1
[7,4,3,2,5,6,1]=>[7,3,2,1,4,6,5]=>110011=>110011=>2
[7,4,3,2,6,1,5]=>[7,4,3,2,6,1,5]=>011011=>110110=>2
[7,4,3,2,6,5,1]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,4,3,5,1,2,6]=>[7,3,2,5,1,4,6]=>010101=>101010=>1
[7,4,3,5,1,6,2]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,4,3,5,2,1,6]=>[7,2,1,5,4,3,6]=>101101=>101101=>1
[7,4,3,5,2,6,1]=>[7,2,1,4,3,6,5]=>101011=>110101=>2
[7,4,3,5,6,1,2]=>[7,2,1,4,6,3,5]=>100011=>110001=>2
[7,4,3,5,6,2,1]=>[7,2,1,3,6,5,4]=>100111=>111001=>3
[7,4,3,6,1,2,5]=>[7,4,3,6,1,2,5]=>001011=>110100=>2
[7,4,3,6,1,5,2]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,4,3,6,2,1,5]=>[7,4,3,6,2,1,5]=>101011=>110101=>2
[7,4,3,6,2,5,1]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,4,3,6,5,1,2]=>[7,3,2,6,5,1,4]=>010111=>111010=>3
[7,4,3,6,5,2,1]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,4,5,1,2,3,6]=>[7,3,5,1,2,4,6]=>000101=>101000=>1
[7,4,5,1,2,6,3]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,4,5,1,3,2,6]=>[7,2,5,1,4,3,6]=>001101=>101100=>1
[7,4,5,1,3,6,2]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,4,5,1,6,2,3]=>[7,2,4,1,6,3,5]=>001011=>110100=>2
[7,4,5,1,6,3,2]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,4,5,2,1,3,6]=>[7,3,5,2,1,4,6]=>100101=>101001=>1
[7,4,5,2,1,6,3]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,4,5,2,3,1,6]=>[7,2,5,1,4,3,6]=>001101=>101100=>1
[7,4,5,2,3,6,1]=>[7,2,4,1,3,6,5]=>001011=>110100=>2
[7,4,5,2,6,1,3]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,4,5,2,6,3,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,4,5,3,1,2,6]=>[7,2,5,4,1,3,6]=>001101=>101100=>1
[7,4,5,3,1,6,2]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,4,5,3,2,1,6]=>[7,1,5,4,3,2,6]=>011101=>101110=>1
[7,4,5,3,2,6,1]=>[7,1,4,3,2,6,5]=>011011=>110110=>2
[7,4,5,3,6,1,2]=>[7,1,4,3,6,2,5]=>001011=>110100=>2
[7,4,5,3,6,2,1]=>[7,1,3,2,6,5,4]=>010111=>111010=>3
[7,4,5,6,1,2,3]=>[7,2,4,6,1,3,5]=>000011=>110000=>2
[7,4,5,6,1,3,2]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,4,5,6,2,1,3]=>[7,1,4,6,3,2,5]=>010011=>110010=>2
[7,4,5,6,2,3,1]=>[7,1,3,6,2,5,4]=>000111=>111000=>3
[7,4,5,6,3,1,2]=>[7,1,3,6,5,2,4]=>000111=>111000=>3
[7,4,5,6,3,2,1]=>[7,1,2,6,5,4,3]=>001111=>111100=>4
[7,4,6,1,2,3,5]=>[7,4,6,1,2,3,5]=>000011=>110000=>2
[7,4,6,1,2,5,3]=>[7,3,6,1,2,5,4]=>000111=>111000=>3
[7,4,6,1,3,2,5]=>[7,4,6,1,3,2,5]=>010011=>110010=>2
[7,4,6,1,3,5,2]=>[7,3,6,1,2,5,4]=>000111=>111000=>3
[7,4,6,1,5,2,3]=>[7,3,6,1,5,2,4]=>000111=>111000=>3
[7,4,6,1,5,3,2]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,4,6,2,1,3,5]=>[7,4,6,2,1,3,5]=>100011=>110001=>2
[7,4,6,2,1,5,3]=>[7,3,6,2,1,5,4]=>100111=>111001=>3
[7,4,6,2,3,1,5]=>[7,4,6,1,3,2,5]=>010011=>110010=>2
[7,4,6,2,3,5,1]=>[7,3,6,1,2,5,4]=>000111=>111000=>3
[7,4,6,2,5,1,3]=>[7,3,6,2,5,1,4]=>000111=>111000=>3
[7,4,6,2,5,3,1]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,4,6,3,1,2,5]=>[7,4,6,3,1,2,5]=>010011=>110010=>2
[7,4,6,3,1,5,2]=>[7,3,6,2,1,5,4]=>100111=>111001=>3
[7,4,6,3,2,1,5]=>[7,4,6,3,2,1,5]=>110011=>110011=>2
[7,4,6,3,2,5,1]=>[7,3,6,2,1,5,4]=>100111=>111001=>3
[7,4,6,3,5,1,2]=>[7,3,6,2,5,1,4]=>000111=>111000=>3
[7,4,6,3,5,2,1]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,4,6,5,1,2,3]=>[7,3,6,5,1,2,4]=>000111=>111000=>3
[7,4,6,5,1,3,2]=>[7,2,6,5,1,4,3]=>001111=>111100=>4
[7,4,6,5,2,1,3]=>[7,3,6,5,2,1,4]=>100111=>111001=>3
[7,4,6,5,2,3,1]=>[7,2,6,5,1,4,3]=>001111=>111100=>4
[7,4,6,5,3,1,2]=>[7,2,6,5,4,1,3]=>001111=>111100=>4
[7,4,6,5,3,2,1]=>[7,1,6,5,4,3,2]=>011111=>111110=>5
[7,5,1,2,3,4,6]=>[7,5,1,2,3,4,6]=>000101=>101000=>1
[7,5,1,2,3,6,4]=>[7,4,1,2,3,6,5]=>001011=>110100=>2
[7,5,1,2,4,3,6]=>[7,5,1,2,4,3,6]=>001101=>101100=>1
[7,5,1,2,4,6,3]=>[7,4,1,2,3,6,5]=>001011=>110100=>2
[7,5,1,2,6,3,4]=>[7,4,1,2,6,3,5]=>001011=>110100=>2
[7,5,1,2,6,4,3]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,5,1,3,2,4,6]=>[7,5,1,3,2,4,6]=>010101=>101010=>1
[7,5,1,3,2,6,4]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,1,3,4,2,6]=>[7,5,1,2,4,3,6]=>001101=>101100=>1
[7,5,1,3,4,6,2]=>[7,4,1,2,3,6,5]=>001011=>110100=>2
[7,5,1,3,6,2,4]=>[7,4,1,3,6,2,5]=>001011=>110100=>2
[7,5,1,3,6,4,2]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,5,1,4,2,3,6]=>[7,5,1,4,2,3,6]=>001101=>101100=>1
[7,5,1,4,2,6,3]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,1,4,3,2,6]=>[7,5,1,4,3,2,6]=>011101=>101110=>1
[7,5,1,4,3,6,2]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,1,4,6,2,3]=>[7,4,1,3,6,2,5]=>001011=>110100=>2
[7,5,1,4,6,3,2]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,5,1,6,2,3,4]=>[7,4,1,6,2,3,5]=>001011=>110100=>2
[7,5,1,6,2,4,3]=>[7,3,1,6,2,5,4]=>010111=>111010=>3
[7,5,1,6,3,2,4]=>[7,4,1,6,3,2,5]=>011011=>110110=>2
[7,5,1,6,3,4,2]=>[7,3,1,6,2,5,4]=>010111=>111010=>3
[7,5,1,6,4,2,3]=>[7,3,1,6,5,2,4]=>010111=>111010=>3
[7,5,1,6,4,3,2]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,5,2,1,3,4,6]=>[7,5,2,1,3,4,6]=>100101=>101001=>1
[7,5,2,1,3,6,4]=>[7,4,2,1,3,6,5]=>101011=>110101=>2
[7,5,2,1,4,3,6]=>[7,5,2,1,4,3,6]=>101101=>101101=>1
[7,5,2,1,4,6,3]=>[7,4,2,1,3,6,5]=>101011=>110101=>2
[7,5,2,1,6,3,4]=>[7,4,2,1,6,3,5]=>101011=>110101=>2
[7,5,2,1,6,4,3]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,5,2,3,1,4,6]=>[7,5,1,3,2,4,6]=>010101=>101010=>1
[7,5,2,3,1,6,4]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,2,3,4,1,6]=>[7,5,1,2,4,3,6]=>001101=>101100=>1
[7,5,2,3,4,6,1]=>[7,4,1,2,3,6,5]=>001011=>110100=>2
[7,5,2,3,6,1,4]=>[7,4,1,3,6,2,5]=>001011=>110100=>2
[7,5,2,3,6,4,1]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,5,2,4,1,3,6]=>[7,5,2,4,1,3,6]=>001101=>101100=>1
[7,5,2,4,1,6,3]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,2,4,3,1,6]=>[7,5,1,4,3,2,6]=>011101=>101110=>1
[7,5,2,4,3,6,1]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,2,4,6,1,3]=>[7,4,1,3,6,2,5]=>001011=>110100=>2
[7,5,2,4,6,3,1]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,5,2,6,1,3,4]=>[7,4,2,6,1,3,5]=>001011=>110100=>2
[7,5,2,6,1,4,3]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,5,2,6,3,1,4]=>[7,4,1,6,3,2,5]=>011011=>110110=>2
[7,5,2,6,3,4,1]=>[7,3,1,6,2,5,4]=>010111=>111010=>3
[7,5,2,6,4,1,3]=>[7,3,2,6,5,1,4]=>010111=>111010=>3
[7,5,2,6,4,3,1]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,5,3,1,2,4,6]=>[7,5,3,1,2,4,6]=>010101=>101010=>1
[7,5,3,1,2,6,4]=>[7,4,3,1,2,6,5]=>011011=>110110=>2
[7,5,3,1,4,2,6]=>[7,5,2,1,4,3,6]=>101101=>101101=>1
[7,5,3,1,4,6,2]=>[7,4,2,1,3,6,5]=>101011=>110101=>2
[7,5,3,1,6,2,4]=>[7,4,3,1,6,2,5]=>011011=>110110=>2
[7,5,3,1,6,4,2]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,5,3,2,1,4,6]=>[7,5,3,2,1,4,6]=>110101=>101011=>1
[7,5,3,2,1,6,4]=>[7,4,3,2,1,6,5]=>111011=>110111=>2
[7,5,3,2,4,1,6]=>[7,5,2,1,4,3,6]=>101101=>101101=>1
[7,5,3,2,4,6,1]=>[7,4,2,1,3,6,5]=>101011=>110101=>2
[7,5,3,2,6,1,4]=>[7,4,3,2,6,1,5]=>011011=>110110=>2
[7,5,3,2,6,4,1]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,5,3,4,1,2,6]=>[7,5,2,4,1,3,6]=>001101=>101100=>1
[7,5,3,4,1,6,2]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,3,4,2,1,6]=>[7,5,1,4,3,2,6]=>011101=>101110=>1
[7,5,3,4,2,6,1]=>[7,4,1,3,2,6,5]=>011011=>110110=>2
[7,5,3,4,6,1,2]=>[7,4,1,3,6,2,5]=>001011=>110100=>2
[7,5,3,4,6,2,1]=>[7,3,1,2,6,5,4]=>010111=>111010=>3
[7,5,3,6,1,2,4]=>[7,4,3,6,1,2,5]=>001011=>110100=>2
[7,5,3,6,1,4,2]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,5,3,6,2,1,4]=>[7,4,3,6,2,1,5]=>101011=>110101=>2
[7,5,3,6,2,4,1]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,5,3,6,4,1,2]=>[7,3,2,6,5,1,4]=>010111=>111010=>3
[7,5,3,6,4,2,1]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,5,4,1,2,3,6]=>[7,5,4,1,2,3,6]=>001101=>101100=>1
[7,5,4,1,2,6,3]=>[7,4,3,1,2,6,5]=>011011=>110110=>2
[7,5,4,1,3,2,6]=>[7,5,4,1,3,2,6]=>011101=>101110=>1
[7,5,4,1,3,6,2]=>[7,4,3,1,2,6,5]=>011011=>110110=>2
[7,5,4,1,6,2,3]=>[7,4,3,1,6,2,5]=>011011=>110110=>2
[7,5,4,1,6,3,2]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,5,4,2,1,3,6]=>[7,5,4,2,1,3,6]=>101101=>101101=>1
[7,5,4,2,1,6,3]=>[7,4,3,2,1,6,5]=>111011=>110111=>2
[7,5,4,2,3,1,6]=>[7,5,4,1,3,2,6]=>011101=>101110=>1
[7,5,4,2,3,6,1]=>[7,4,3,1,2,6,5]=>011011=>110110=>2
[7,5,4,2,6,1,3]=>[7,4,3,2,6,1,5]=>011011=>110110=>2
[7,5,4,2,6,3,1]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,5,4,3,1,2,6]=>[7,5,4,3,1,2,6]=>011101=>101110=>1
[7,5,4,3,1,6,2]=>[7,4,3,2,1,6,5]=>111011=>110111=>2
[7,5,4,3,2,1,6]=>[7,5,4,3,2,1,6]=>111101=>101111=>1
[7,5,4,3,2,6,1]=>[7,4,3,2,1,6,5]=>111011=>110111=>2
[7,5,4,3,6,1,2]=>[7,4,3,2,6,1,5]=>011011=>110110=>2
[7,5,4,3,6,2,1]=>[7,3,2,1,6,5,4]=>110111=>111011=>3
[7,5,4,6,1,2,3]=>[7,4,3,6,1,2,5]=>001011=>110100=>2
[7,5,4,6,1,3,2]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,5,4,6,2,1,3]=>[7,4,3,6,2,1,5]=>101011=>110101=>2
[7,5,4,6,2,3,1]=>[7,3,2,6,1,5,4]=>010111=>111010=>3
[7,5,4,6,3,1,2]=>[7,3,2,6,5,1,4]=>010111=>111010=>3
[7,5,4,6,3,2,1]=>[7,2,1,6,5,4,3]=>101111=>111101=>4
[7,5,6,1,2,3,4]=>[7,4,6,1,2,3,5]=>000011=>110000=>2
[7,5,6,1,2,4,3]=>[7,3,6,1,2,5,4]=>000111=>111000=>3
[7,5,6,1,3,2,4]=>[7,4,6,1,3,2,5]=>010011=>110010=>2
[7,5,6,1,3,4,2]=>[7,3,6,1,2,5,4]=>000111=>111000=>3
[7,5,6,1,4,2,3]=>[7,3,6,1,5,2,4]=>000111=>111000=>3
[7,5,6,1,4,3,2]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,5,6,2,1,3,4]=>[7,4,6,2,1,3,5]=>100011=>110001=>2
[7,5,6,2,1,4,3]=>[7,3,6,2,1,5,4]=>100111=>111001=>3
[7,5,6,2,3,1,4]=>[7,4,6,1,3,2,5]=>010011=>110010=>2
[7,5,6,2,3,4,1]=>[7,3,6,1,2,5,4]=>000111=>111000=>3
[7,5,6,2,4,1,3]=>[7,3,6,2,5,1,4]=>000111=>111000=>3
[7,5,6,2,4,3,1]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,5,6,3,1,2,4]=>[7,4,6,3,1,2,5]=>010011=>110010=>2
[7,5,6,3,1,4,2]=>[7,3,6,2,1,5,4]=>100111=>111001=>3
[7,5,6,3,2,1,4]=>[7,4,6,3,2,1,5]=>110011=>110011=>2
[7,5,6,3,2,4,1]=>[7,3,6,2,1,5,4]=>100111=>111001=>3
[7,5,6,3,4,1,2]=>[7,3,6,2,5,1,4]=>000111=>111000=>3
[7,5,6,3,4,2,1]=>[7,2,6,1,5,4,3]=>001111=>111100=>4
[7,5,6,4,1,2,3]=>[7,3,6,5,1,2,4]=>000111=>111000=>3
[7,5,6,4,1,3,2]=>[7,2,6,5,1,4,3]=>001111=>111100=>4
[7,5,6,4,2,1,3]=>[7,3,6,5,2,1,4]=>100111=>111001=>3
[7,5,6,4,2,3,1]=>[7,2,6,5,1,4,3]=>001111=>111100=>4
[7,5,6,4,3,1,2]=>[7,2,6,5,4,1,3]=>001111=>111100=>4
[7,5,6,4,3,2,1]=>[7,1,6,5,4,3,2]=>011111=>111110=>5
[7,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>000011=>110000=>2
[7,6,1,2,3,5,4]=>[7,6,1,2,3,5,4]=>000111=>111000=>3
[7,6,1,2,4,3,5]=>[7,6,1,2,4,3,5]=>001011=>110100=>2
[7,6,1,2,4,5,3]=>[7,6,1,2,3,5,4]=>000111=>111000=>3
[7,6,1,2,5,3,4]=>[7,6,1,2,5,3,4]=>000111=>111000=>3
[7,6,1,2,5,4,3]=>[7,6,1,2,5,4,3]=>001111=>111100=>4
[7,6,1,3,2,4,5]=>[7,6,1,3,2,4,5]=>010011=>110010=>2
[7,6,1,3,2,5,4]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,1,3,4,2,5]=>[7,6,1,2,4,3,5]=>001011=>110100=>2
[7,6,1,3,4,5,2]=>[7,6,1,2,3,5,4]=>000111=>111000=>3
[7,6,1,3,5,2,4]=>[7,6,1,3,5,2,4]=>000111=>111000=>3
[7,6,1,3,5,4,2]=>[7,6,1,2,5,4,3]=>001111=>111100=>4
[7,6,1,4,2,3,5]=>[7,6,1,4,2,3,5]=>001011=>110100=>2
[7,6,1,4,2,5,3]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,1,4,3,2,5]=>[7,6,1,4,3,2,5]=>011011=>110110=>2
[7,6,1,4,3,5,2]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,1,4,5,2,3]=>[7,6,1,3,5,2,4]=>000111=>111000=>3
[7,6,1,4,5,3,2]=>[7,6,1,2,5,4,3]=>001111=>111100=>4
[7,6,1,5,2,3,4]=>[7,6,1,5,2,3,4]=>000111=>111000=>3
[7,6,1,5,2,4,3]=>[7,6,1,5,2,4,3]=>001111=>111100=>4
[7,6,1,5,3,2,4]=>[7,6,1,5,3,2,4]=>010111=>111010=>3
[7,6,1,5,3,4,2]=>[7,6,1,5,2,4,3]=>001111=>111100=>4
[7,6,1,5,4,2,3]=>[7,6,1,5,4,2,3]=>001111=>111100=>4
[7,6,1,5,4,3,2]=>[7,6,1,5,4,3,2]=>011111=>111110=>5
[7,6,2,1,3,4,5]=>[7,6,2,1,3,4,5]=>100011=>110001=>2
[7,6,2,1,3,5,4]=>[7,6,2,1,3,5,4]=>100111=>111001=>3
[7,6,2,1,4,3,5]=>[7,6,2,1,4,3,5]=>101011=>110101=>2
[7,6,2,1,4,5,3]=>[7,6,2,1,3,5,4]=>100111=>111001=>3
[7,6,2,1,5,3,4]=>[7,6,2,1,5,3,4]=>100111=>111001=>3
[7,6,2,1,5,4,3]=>[7,6,2,1,5,4,3]=>101111=>111101=>4
[7,6,2,3,1,4,5]=>[7,6,1,3,2,4,5]=>010011=>110010=>2
[7,6,2,3,1,5,4]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,2,3,4,1,5]=>[7,6,1,2,4,3,5]=>001011=>110100=>2
[7,6,2,3,4,5,1]=>[7,6,1,2,3,5,4]=>000111=>111000=>3
[7,6,2,3,5,1,4]=>[7,6,1,3,5,2,4]=>000111=>111000=>3
[7,6,2,3,5,4,1]=>[7,6,1,2,5,4,3]=>001111=>111100=>4
[7,6,2,4,1,3,5]=>[7,6,2,4,1,3,5]=>001011=>110100=>2
[7,6,2,4,1,5,3]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,2,4,3,1,5]=>[7,6,1,4,3,2,5]=>011011=>110110=>2
[7,6,2,4,3,5,1]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,2,4,5,1,3]=>[7,6,1,3,5,2,4]=>000111=>111000=>3
[7,6,2,4,5,3,1]=>[7,6,1,2,5,4,3]=>001111=>111100=>4
[7,6,2,5,1,3,4]=>[7,6,2,5,1,3,4]=>000111=>111000=>3
[7,6,2,5,1,4,3]=>[7,6,2,5,1,4,3]=>001111=>111100=>4
[7,6,2,5,3,1,4]=>[7,6,1,5,3,2,4]=>010111=>111010=>3
[7,6,2,5,3,4,1]=>[7,6,1,5,2,4,3]=>001111=>111100=>4
[7,6,2,5,4,1,3]=>[7,6,2,5,4,1,3]=>001111=>111100=>4
[7,6,2,5,4,3,1]=>[7,6,1,5,4,3,2]=>011111=>111110=>5
[7,6,3,1,2,4,5]=>[7,6,3,1,2,4,5]=>010011=>110010=>2
[7,6,3,1,2,5,4]=>[7,6,3,1,2,5,4]=>010111=>111010=>3
[7,6,3,1,4,2,5]=>[7,6,2,1,4,3,5]=>101011=>110101=>2
[7,6,3,1,4,5,2]=>[7,6,2,1,3,5,4]=>100111=>111001=>3
[7,6,3,1,5,2,4]=>[7,6,3,1,5,2,4]=>010111=>111010=>3
[7,6,3,1,5,4,2]=>[7,6,2,1,5,4,3]=>101111=>111101=>4
[7,6,3,2,1,4,5]=>[7,6,3,2,1,4,5]=>110011=>110011=>2
[7,6,3,2,1,5,4]=>[7,6,3,2,1,5,4]=>110111=>111011=>3
[7,6,3,2,4,1,5]=>[7,6,2,1,4,3,5]=>101011=>110101=>2
[7,6,3,2,4,5,1]=>[7,6,2,1,3,5,4]=>100111=>111001=>3
[7,6,3,2,5,1,4]=>[7,6,3,2,5,1,4]=>010111=>111010=>3
[7,6,3,2,5,4,1]=>[7,6,2,1,5,4,3]=>101111=>111101=>4
[7,6,3,4,1,2,5]=>[7,6,2,4,1,3,5]=>001011=>110100=>2
[7,6,3,4,1,5,2]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,3,4,2,1,5]=>[7,6,1,4,3,2,5]=>011011=>110110=>2
[7,6,3,4,2,5,1]=>[7,6,1,3,2,5,4]=>010111=>111010=>3
[7,6,3,4,5,1,2]=>[7,6,1,3,5,2,4]=>000111=>111000=>3
[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>001111=>111100=>4
[7,6,3,5,1,2,4]=>[7,6,3,5,1,2,4]=>000111=>111000=>3
[7,6,3,5,1,4,2]=>[7,6,2,5,1,4,3]=>001111=>111100=>4
[7,6,3,5,2,1,4]=>[7,6,3,5,2,1,4]=>100111=>111001=>3
[7,6,3,5,2,4,1]=>[7,6,2,5,1,4,3]=>001111=>111100=>4
[7,6,3,5,4,1,2]=>[7,6,2,5,4,1,3]=>001111=>111100=>4
[7,6,3,5,4,2,1]=>[7,6,1,5,4,3,2]=>011111=>111110=>5
[7,6,4,1,2,3,5]=>[7,6,4,1,2,3,5]=>001011=>110100=>2
[7,6,4,1,2,5,3]=>[7,6,3,1,2,5,4]=>010111=>111010=>3
[7,6,4,1,3,2,5]=>[7,6,4,1,3,2,5]=>011011=>110110=>2
[7,6,4,1,3,5,2]=>[7,6,3,1,2,5,4]=>010111=>111010=>3
[7,6,4,1,5,2,3]=>[7,6,3,1,5,2,4]=>010111=>111010=>3
[7,6,4,1,5,3,2]=>[7,6,2,1,5,4,3]=>101111=>111101=>4
[7,6,4,2,1,3,5]=>[7,6,4,2,1,3,5]=>101011=>110101=>2
[7,6,4,2,1,5,3]=>[7,6,3,2,1,5,4]=>110111=>111011=>3
[7,6,4,2,3,1,5]=>[7,6,4,1,3,2,5]=>011011=>110110=>2
[7,6,4,2,3,5,1]=>[7,6,3,1,2,5,4]=>010111=>111010=>3
[7,6,4,2,5,1,3]=>[7,6,3,2,5,1,4]=>010111=>111010=>3
[7,6,4,2,5,3,1]=>[7,6,2,1,5,4,3]=>101111=>111101=>4
[7,6,4,3,1,2,5]=>[7,6,4,3,1,2,5]=>011011=>110110=>2
[7,6,4,3,1,5,2]=>[7,6,3,2,1,5,4]=>110111=>111011=>3
[7,6,4,3,2,1,5]=>[7,6,4,3,2,1,5]=>111011=>110111=>2
[7,6,4,3,2,5,1]=>[7,6,3,2,1,5,4]=>110111=>111011=>3
[7,6,4,3,5,1,2]=>[7,6,3,2,5,1,4]=>010111=>111010=>3
[7,6,4,3,5,2,1]=>[7,6,2,1,5,4,3]=>101111=>111101=>4
[7,6,4,5,1,2,3]=>[7,6,3,5,1,2,4]=>000111=>111000=>3
[7,6,4,5,1,3,2]=>[7,6,2,5,1,4,3]=>001111=>111100=>4
[7,6,4,5,2,1,3]=>[7,6,3,5,2,1,4]=>100111=>111001=>3
[7,6,4,5,2,3,1]=>[7,6,2,5,1,4,3]=>001111=>111100=>4
[7,6,4,5,3,1,2]=>[7,6,2,5,4,1,3]=>001111=>111100=>4
[7,6,4,5,3,2,1]=>[7,6,1,5,4,3,2]=>011111=>111110=>5
[7,6,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111=>111000=>3
[7,6,5,1,2,4,3]=>[7,6,5,1,2,4,3]=>001111=>111100=>4
[7,6,5,1,3,2,4]=>[7,6,5,1,3,2,4]=>010111=>111010=>3
[7,6,5,1,3,4,2]=>[7,6,5,1,2,4,3]=>001111=>111100=>4
[7,6,5,1,4,2,3]=>[7,6,5,1,4,2,3]=>001111=>111100=>4
[7,6,5,1,4,3,2]=>[7,6,5,1,4,3,2]=>011111=>111110=>5
[7,6,5,2,1,3,4]=>[7,6,5,2,1,3,4]=>100111=>111001=>3
[7,6,5,2,1,4,3]=>[7,6,5,2,1,4,3]=>101111=>111101=>4
[7,6,5,2,3,1,4]=>[7,6,5,1,3,2,4]=>010111=>111010=>3
[7,6,5,2,3,4,1]=>[7,6,5,1,2,4,3]=>001111=>111100=>4
[7,6,5,2,4,1,3]=>[7,6,5,2,4,1,3]=>001111=>111100=>4
[7,6,5,2,4,3,1]=>[7,6,5,1,4,3,2]=>011111=>111110=>5
[7,6,5,3,1,2,4]=>[7,6,5,3,1,2,4]=>010111=>111010=>3
[7,6,5,3,1,4,2]=>[7,6,5,2,1,4,3]=>101111=>111101=>4
[7,6,5,3,2,1,4]=>[7,6,5,3,2,1,4]=>110111=>111011=>3
[7,6,5,3,2,4,1]=>[7,6,5,2,1,4,3]=>101111=>111101=>4
[7,6,5,3,4,1,2]=>[7,6,5,2,4,1,3]=>001111=>111100=>4
[7,6,5,3,4,2,1]=>[7,6,5,1,4,3,2]=>011111=>111110=>5
[7,6,5,4,1,2,3]=>[7,6,5,4,1,2,3]=>001111=>111100=>4
[7,6,5,4,1,3,2]=>[7,6,5,4,1,3,2]=>011111=>111110=>5
[7,6,5,4,2,1,3]=>[7,6,5,4,2,1,3]=>101111=>111101=>4
[7,6,5,4,2,3,1]=>[7,6,5,4,1,3,2]=>011111=>111110=>5
[7,6,5,4,3,1,2]=>[7,6,5,4,3,1,2]=>011111=>111110=>5
[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111=>111111=>6
[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111=>1111111=>7
[5,6,7,8,4,3,2,1]=>[1,2,3,8,7,6,5,4]=>0001111=>1111000=>4
[8,7,5,6,3,4,2,1]=>[8,7,2,6,1,5,4,3]=>0011111=>1111100=>5
[5,6,7,8,3,4,2,1]=>[1,2,4,8,3,7,6,5]=>0000111=>1110000=>3
[8,6,7,5,4,2,3,1]=>[8,2,7,6,5,1,4,3]=>0011111=>1111100=>5
[5,6,7,8,4,2,3,1]=>[1,2,4,8,7,3,6,5]=>0000111=>1110000=>3
[8,6,5,7,3,2,4,1]=>[8,4,3,7,2,1,6,5]=>1010111=>1110101=>3
[5,6,7,8,3,2,4,1]=>[1,2,5,8,4,3,7,6]=>0010011=>1100100=>2
[8,5,6,7,2,3,4,1]=>[8,2,4,7,1,3,6,5]=>0000111=>1110000=>3
[5,6,7,8,2,3,4,1]=>[1,3,5,8,2,4,7,6]=>0000011=>1100000=>2
[5,4,6,3,7,2,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,8,7]=>0000001=>1000000=>1
[7,8,6,5,4,3,1,2]=>[2,8,7,6,5,4,1,3]=>0011111=>1111100=>5
[5,6,7,8,4,3,1,2]=>[1,2,4,8,7,6,3,5]=>0000111=>1110000=>3
[7,8,5,6,3,4,1,2]=>[4,8,3,7,2,6,1,5]=>0000111=>1110000=>3
[6,5,7,8,3,4,1,2]=>[2,1,5,8,4,7,3,6]=>1000011=>1100001=>2
[5,6,7,8,3,4,1,2]=>[1,2,5,8,4,7,3,6]=>0000011=>1100000=>2
[7,8,4,3,5,6,1,2]=>[5,8,2,1,4,7,3,6]=>1000011=>1100001=>2
[7,8,3,4,5,6,1,2]=>[5,8,1,2,4,7,3,6]=>0000011=>1100000=>2
[8,4,3,5,6,7,1,2]=>[8,2,1,3,5,7,4,6]=>1000011=>1100001=>2
[6,3,4,5,7,8,1,2]=>[4,1,2,3,6,8,5,7]=>0010001=>1000100=>1
[5,4,3,6,7,8,1,2]=>[3,2,1,4,6,8,5,7]=>1100001=>1000011=>1
[3,4,5,6,7,8,1,2]=>[1,2,3,4,6,8,5,7]=>0000001=>1000000=>1
[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,2,1,3]=>1011111=>1111101=>5
[7,6,8,5,4,2,1,3]=>[4,3,8,7,6,2,1,5]=>1010111=>1110101=>3
[5,6,7,8,4,2,1,3]=>[1,2,5,8,7,4,3,6]=>0010011=>1100100=>2
[6,7,8,5,4,1,2,3]=>[2,4,8,7,6,1,3,5]=>0000111=>1110000=>3
[5,6,7,8,4,1,2,3]=>[1,3,5,8,7,2,4,6]=>0000011=>1100000=>2
[7,6,5,8,3,2,1,4]=>[6,5,4,8,3,2,1,7]=>1101101=>1011011=>1
[5,6,7,8,3,2,1,4]=>[1,2,6,8,5,4,3,7]=>0011001=>1001100=>1
[7,5,6,8,2,3,1,4]=>[6,2,5,8,1,4,3,7]=>0010101=>1010100=>1
[5,6,7,8,2,3,1,4]=>[1,3,6,8,2,5,4,7]=>0001001=>1001000=>1
[6,7,5,8,3,1,2,4]=>[2,6,5,8,4,1,3,7]=>0010101=>1010100=>1
[5,6,7,8,3,1,2,4]=>[1,3,6,8,5,2,4,7]=>0001001=>1001000=>1
[7,8,6,5,2,1,3,4]=>[4,8,7,6,2,1,3,5]=>1000111=>1110001=>3
[7,8,5,6,2,1,3,4]=>[5,8,4,7,2,1,3,6]=>1000011=>1100001=>2
[6,5,7,8,2,1,3,4]=>[4,3,6,8,2,1,5,7]=>1010001=>1000101=>1
[5,6,7,8,2,1,3,4]=>[1,4,6,8,3,2,5,7]=>0100001=>1000010=>1
[8,7,6,5,1,2,3,4]=>[8,7,6,5,1,2,3,4]=>0001111=>1111000=>4
[7,8,6,5,1,2,3,4]=>[4,8,7,6,1,2,3,5]=>0000111=>1110000=>3
[8,6,7,5,1,2,3,4]=>[8,4,7,6,1,2,3,5]=>0000111=>1110000=>3
[7,6,8,5,1,2,3,4]=>[5,4,8,7,1,2,3,6]=>0001011=>1101000=>2
[6,7,8,5,1,2,3,4]=>[3,5,8,7,1,2,4,6]=>0000011=>1100000=>2
[8,7,5,6,1,2,3,4]=>[8,7,4,6,1,2,3,5]=>0000111=>1110000=>3
[7,8,5,6,1,2,3,4]=>[5,8,4,7,1,2,3,6]=>0000011=>1100000=>2
[8,6,5,7,1,2,3,4]=>[8,5,4,7,1,2,3,6]=>0001011=>1101000=>2
[8,5,6,7,1,2,3,4]=>[8,3,5,7,1,2,4,6]=>0000011=>1100000=>2
[7,6,5,8,1,2,3,4]=>[6,5,4,8,1,2,3,7]=>0001101=>1011000=>1
[6,7,5,8,1,2,3,4]=>[3,6,5,8,1,2,4,7]=>0000101=>1010000=>1
[7,5,6,8,1,2,3,4]=>[6,3,5,8,1,2,4,7]=>0000101=>1010000=>1
[6,5,7,8,1,2,3,4]=>[4,3,6,8,1,2,5,7]=>0010001=>1000100=>1
[5,6,7,8,1,2,3,4]=>[2,4,6,8,1,3,5,7]=>0000001=>1000000=>1
[8,7,6,4,3,2,1,5]=>[8,7,6,4,3,2,1,5]=>1110111=>1110111=>3
[8,7,6,4,2,1,3,5]=>[8,7,6,4,2,1,3,5]=>1010111=>1110101=>3
[8,7,6,1,2,3,4,5]=>[8,7,6,1,2,3,4,5]=>0000111=>1110000=>3
[7,8,6,1,2,3,4,5]=>[5,8,7,1,2,3,4,6]=>0000011=>1100000=>2
[8,6,7,1,2,3,4,5]=>[8,5,7,1,2,3,4,6]=>0000011=>1100000=>2
[7,6,8,1,2,3,4,5]=>[6,5,8,1,2,3,4,7]=>0000101=>1010000=>1
[6,7,8,1,2,3,4,5]=>[4,6,8,1,2,3,5,7]=>0000001=>1000000=>1
[7,8,5,4,2,1,3,6]=>[6,8,5,4,2,1,3,7]=>1011001=>1001101=>1
[8,7,5,2,1,3,4,6]=>[8,7,5,2,1,3,4,6]=>1001011=>1101001=>2
[7,8,5,2,1,3,4,6]=>[6,8,5,2,1,3,4,7]=>1001001=>1001001=>1
[8,7,5,1,2,3,4,6]=>[8,7,5,1,2,3,4,6]=>0001011=>1101000=>2
[7,8,5,1,2,3,4,6]=>[6,8,5,1,2,3,4,7]=>0001001=>1001000=>1
[7,8,3,2,1,4,5,6]=>[6,8,3,2,1,4,5,7]=>1100001=>1000011=>1
[7,8,1,2,3,4,5,6]=>[6,8,1,2,3,4,5,7]=>0000001=>1000000=>1
[8,6,5,4,3,2,1,7]=>[8,6,5,4,3,2,1,7]=>1111101=>1011111=>1
[8,4,5,6,3,2,1,7]=>[8,1,2,6,5,4,3,7]=>0011101=>1011100=>1
[8,6,5,4,3,1,2,7]=>[8,6,5,4,3,1,2,7]=>0111101=>1011110=>1
[8,5,6,3,4,1,2,7]=>[8,3,6,2,5,1,4,7]=>0001101=>1011000=>1
[8,6,5,4,2,1,3,7]=>[8,6,5,4,2,1,3,7]=>1011101=>1011101=>1
[8,6,5,2,3,1,4,7]=>[8,6,5,1,3,2,4,7]=>0101101=>1011010=>1
[8,5,6,2,3,1,4,7]=>[8,4,6,1,3,2,5,7]=>0100101=>1010010=>1
[8,6,5,1,2,3,4,7]=>[8,6,5,1,2,3,4,7]=>0001101=>1011000=>1
[8,6,4,3,2,1,5,7]=>[8,6,4,3,2,1,5,7]=>1110101=>1010111=>1
[8,6,3,4,2,1,5,7]=>[8,6,1,4,3,2,5,7]=>0110101=>1010110=>1
[8,6,4,2,1,3,5,7]=>[8,6,4,2,1,3,5,7]=>1010101=>1010101=>1
[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0000001=>1000000=>1
[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110=>0111111=>0
[7,5,6,3,4,2,1,8]=>[7,2,6,1,5,4,3,8]=>0011110=>0111100=>0
[6,7,5,4,2,3,1,8]=>[2,7,6,5,1,4,3,8]=>0011110=>0111100=>0
[6,5,7,3,2,4,1,8]=>[4,3,7,2,1,6,5,8]=>1010110=>0110101=>0
[7,6,5,2,3,4,1,8]=>[7,6,5,1,2,4,3,8]=>0011110=>0111100=>0
[7,5,6,2,3,4,1,8]=>[7,3,6,1,2,5,4,8]=>0001110=>0111000=>0
[5,6,7,2,3,4,1,8]=>[2,4,7,1,3,6,5,8]=>0000110=>0110000=>0
[7,6,5,1,2,3,4,8]=>[7,6,5,1,2,3,4,8]=>0001110=>0111000=>0
[6,7,5,1,2,3,4,8]=>[4,7,6,1,2,3,5,8]=>0000110=>0110000=>0
[7,5,6,1,2,3,4,8]=>[7,4,6,1,2,3,5,8]=>0000110=>0110000=>0
[6,5,7,1,2,3,4,8]=>[5,4,7,1,2,3,6,8]=>0001010=>0101000=>0
[5,6,7,1,2,3,4,8]=>[3,5,7,1,2,4,6,8]=>0000010=>0100000=>0
[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000=>0000111=>0
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000=>0000000=>0
[3,5,8,7,6,4,2,1]=>[1,2,8,7,6,5,4,3]=>0011111=>1111100=>5
[3,5,6,7,8,4,2,1]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000=>3
[2,6,8,7,5,4,3,1]=>[1,2,8,7,6,5,4,3]=>0011111=>1111100=>5
[2,5,6,7,8,4,3,1]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000=>3
[2,3,5,6,8,7,4,1]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000=>3
[2,3,5,6,7,8,4,1]=>[1,2,3,4,5,8,7,6]=>0000011=>1100000=>2
[3,4,2,5,7,8,6,1]=>[1,3,2,4,5,8,7,6]=>0100011=>1100010=>2
[4,3,6,5,7,2,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,6,5,7,4,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,5,2,7,6,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,5,4,7,6,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>0111111=>1111110=>6
[1,7,8,6,5,4,3,2]=>[1,2,8,7,6,5,4,3]=>0011111=>1111100=>5
[1,5,6,7,8,4,3,2]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000=>3
[1,3,5,7,8,6,4,2]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000=>3
[1,3,5,6,7,8,4,2]=>[1,2,3,4,5,8,7,6]=>0000011=>1100000=>2
[1,4,3,8,7,6,5,2]=>[1,3,2,8,7,6,5,4]=>0101111=>1111010=>4
[1,6,5,4,3,8,7,2]=>[1,5,4,3,2,8,7,6]=>0111011=>1101110=>2
[1,4,3,6,5,8,7,2]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101=>5
[2,1,6,7,8,5,4,3]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001=>3
[2,1,6,7,5,8,4,3]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[2,1,5,6,7,8,4,3]=>[2,1,3,4,5,8,7,6]=>1000011=>1100001=>2
[2,1,6,5,7,4,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,5,4,7,6,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,4,5,6,7,8,3]=>[2,1,3,4,5,6,8,7]=>1000001=>1000001=>1
[1,2,6,7,8,5,4,3]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000=>3
[1,2,5,6,7,8,4,3]=>[1,2,3,4,5,8,7,6]=>0000011=>1100000=>2
[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>1101111=>1111011=>4
[1,2,3,5,6,7,8,4]=>[1,2,3,4,5,6,8,7]=>0000001=>1000000=>1
[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111=>3
[4,3,2,1,7,8,6,5]=>[4,3,2,1,5,8,7,6]=>1110011=>1100111=>2
[4,3,2,1,6,8,7,5]=>[4,3,2,1,5,8,7,6]=>1110011=>1100111=>2
[4,3,2,1,7,6,8,5]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111=>1
[4,3,2,1,6,7,8,5]=>[4,3,2,1,5,6,8,7]=>1110001=>1000111=>1
[3,4,2,1,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110=>3
[3,4,2,1,7,8,6,5]=>[1,4,3,2,5,8,7,6]=>0110011=>1100110=>2
[2,4,3,1,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110=>3
[2,4,3,1,6,8,7,5]=>[1,4,3,2,5,8,7,6]=>0110011=>1100110=>2
[3,2,4,1,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[3,2,4,1,6,8,7,5]=>[2,1,4,3,5,8,7,6]=>1010011=>1100101=>2
[3,2,4,1,7,6,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,3,4,1,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[2,3,4,1,6,7,8,5]=>[1,2,4,3,5,6,8,7]=>0010001=>1000100=>1
[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110=>3
[1,3,4,2,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[2,1,4,3,7,8,6,5]=>[2,1,4,3,5,8,7,6]=>1010011=>1100101=>2
[2,1,4,3,6,8,7,5]=>[2,1,4,3,5,8,7,6]=>1010011=>1100101=>2
[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,4,3,6,7,8,5]=>[2,1,4,3,5,6,8,7]=>1010001=>1000101=>1
[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>1100111=>1110011=>3
[2,3,1,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010=>3
[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010=>3
[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001=>3
[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000=>3
[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>1111011=>1101111=>2
[3,2,5,4,1,8,7,6]=>[2,1,5,4,3,8,7,6]=>1011011=>1101101=>2
[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>1110011=>1100111=>2
[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,6,8,7]=>1110001=>1000111=>1
[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>1100011=>1100011=>2
[2,3,1,4,5,7,8,6]=>[1,3,2,4,5,6,8,7]=>0100001=>1000010=>1
[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>1111101=>1011111=>1
[4,5,3,6,2,1,8,7]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[4,3,5,2,6,1,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,5,4,6,1,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,3,4,5,6,1,8,7]=>[1,2,3,4,6,5,8,7]=>0000101=>1010000=>1
[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101=>1
[2,1,5,6,4,3,8,7]=>[2,1,3,6,5,4,8,7]=>1001101=>1011001=>1
[2,1,4,6,5,3,8,7]=>[2,1,3,6,5,4,8,7]=>1001101=>1011001=>1
[2,1,5,4,6,3,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,4,5,6,3,8,7]=>[2,1,3,4,6,5,8,7]=>1000101=>1010001=>1
[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111=>1
[3,2,4,1,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,3,4,1,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100=>1
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>1110001=>1000111=>1
[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>1000001=>1000001=>1
[3,2,7,6,5,4,1,8]=>[2,1,7,6,5,4,3,8]=>1011110=>0111101=>0
[5,4,3,2,7,6,1,8]=>[4,3,2,1,7,6,5,8]=>1110110=>0110111=>0
[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>1110110=>0110111=>0
[4,3,2,1,6,7,5,8]=>[4,3,2,1,5,7,6,8]=>1110010=>0100111=>0
[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>0110110=>0110110=>0
[1,3,4,2,6,7,5,8]=>[1,2,4,3,5,7,6,8]=>0010010=>0100100=>0
[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>1110010=>0100111=>0
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>0100010=>0100010=>0
[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100=>0010111=>0
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>0010100=>0010100=>0
[1,8,5,4,7,6,3,2]=>[1,8,3,2,7,6,5,4]=>0101111=>1111010=>4
[2,1,4,5,8,6,7,3]=>[2,1,3,4,8,5,7,6]=>1000011=>1100001=>2
[2,1,8,5,4,7,6,3]=>[2,1,8,4,3,7,6,5]=>1010111=>1110101=>3
[2,3,4,8,5,6,7,1]=>[1,2,3,8,4,5,7,6]=>0000011=>1100000=>2
[4,2,3,1,8,6,7,5]=>[4,1,3,2,8,5,7,6]=>0110011=>1100110=>2
[4,2,3,1,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>0110111=>1110110=>3
[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,5,7,6]=>1110011=>1100111=>2
[6,3,2,5,4,1,8,7]=>[6,2,1,5,4,3,8,7]=>1011101=>1011101=>1
[8,3,2,5,4,7,6,1]=>[8,2,1,4,3,7,6,5]=>1010111=>1110101=>3
[8,3,2,7,6,5,4,1]=>[8,2,1,7,6,5,4,3]=>1011111=>1111101=>5
[7,4,3,6,5,2,1,8]=>[7,2,1,6,5,4,3,8]=>1011110=>0111101=>0
[8,5,4,3,2,7,6,1]=>[8,4,3,2,1,7,6,5]=>1110111=>1110111=>3
[8,7,4,3,6,5,2,1]=>[8,7,2,1,6,5,4,3]=>1011111=>1111101=>5
[2,4,6,8,1,3,5,7]=>[2,4,6,8,1,3,5,7]=>0000001=>1000000=>1
[2,4,1,6,7,3,8,5]=>[1,3,2,4,6,5,8,7]=>0100101=>1010010=>1
[2,4,6,1,7,3,8,5]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100=>1
[2,1,4,3,7,5,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,4,1,3,7,5,8,6]=>[2,4,1,3,6,5,8,7]=>0010101=>1010100=>1
[2,1,4,3,7,8,5,6]=>[2,1,4,3,6,8,5,7]=>1010001=>1000101=>1
[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>1010001=>1000101=>1
[2,4,5,6,7,1,8,3]=>[1,2,3,4,6,5,8,7]=>0000101=>1010000=>1
[2,1,5,3,6,4,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,5,6,3,4,8,7]=>[2,1,4,6,3,5,8,7]=>1000101=>1010001=>1
[2,1,5,3,7,4,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,5,1,7,3,4,8,6]=>[2,4,1,6,3,5,8,7]=>0010101=>1010100=>1
[2,1,5,7,3,8,4,6]=>[2,1,4,6,3,8,5,7]=>1000101=>1010001=>1
[2,3,5,6,1,7,8,4]=>[1,2,3,5,4,6,8,7]=>0001001=>1001000=>1
[2,3,5,6,7,8,1,4]=>[1,2,3,4,6,8,5,7]=>0000001=>1000000=>1
[2,1,6,3,7,4,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,6,7,1,3,4,8,5]=>[2,4,6,1,3,5,8,7]=>0000101=>1010000=>1
[2,1,6,7,8,3,4,5]=>[2,1,4,6,8,3,5,7]=>1000001=>1000001=>1
[2,1,6,3,4,7,8,5]=>[2,1,5,3,4,6,8,7]=>1001001=>1001001=>1
[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>1000101=>1010001=>1
[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>1000001=>1000001=>1
[3,1,4,2,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,4,1,2,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>0010101=>1010100=>1
[3,1,4,2,6,8,5,7]=>[2,1,4,3,6,8,5,7]=>1010001=>1000101=>1
[3,1,4,6,8,2,5,7]=>[2,1,4,6,8,3,5,7]=>1000001=>1000001=>1
[3,4,6,1,7,8,2,5]=>[1,2,4,3,6,8,5,7]=>0010001=>1000100=>1
[3,1,4,2,7,5,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,4,1,2,7,8,5,6]=>[2,4,1,3,6,8,5,7]=>0010001=>1000100=>1
[3,4,7,1,8,2,5,6]=>[2,4,6,1,8,3,5,7]=>0000101=>1010000=>1
[3,1,5,2,6,4,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,5,1,6,2,4,8,7]=>[2,4,1,6,3,5,8,7]=>0010101=>1010100=>1
[3,1,5,6,2,8,4,7]=>[2,1,4,6,3,8,5,7]=>1000101=>1010001=>1
[3,1,5,2,7,4,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,5,1,7,2,8,4,6]=>[2,4,1,6,3,8,5,7]=>0010101=>1010100=>1
[3,1,5,2,7,4,6,8]=>[3,1,5,2,7,4,6,8]=>0101010=>0101010=>0
[3,1,5,2,8,4,6,7]=>[3,1,5,2,8,4,6,7]=>0101001=>1001010=>1
[1,3,5,6,2,7,4,8]=>[1,2,3,5,4,7,6,8]=>0001010=>0101000=>0
[1,3,5,6,7,8,2,4]=>[1,2,3,4,6,8,5,7]=>0000001=>1000000=>1
[3,1,6,2,7,4,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,6,1,7,2,8,4,5]=>[2,4,1,6,3,8,5,7]=>0010101=>1010100=>1
[3,6,7,1,2,8,4,5]=>[2,4,6,1,3,8,5,7]=>0000101=>1010000=>1
[3,6,1,7,8,2,4,5]=>[2,4,1,6,8,3,5,7]=>0010001=>1000100=>1
[3,1,6,7,2,4,5,8]=>[3,1,5,7,2,4,6,8]=>0100010=>0100010=>0
[3,1,2,6,7,4,8,5]=>[3,1,2,4,6,5,8,7]=>0100101=>1010010=>1
[3,1,6,8,2,4,5,7]=>[3,1,6,8,2,4,5,7]=>0100001=>1000010=>1
[3,1,7,8,2,4,5,6]=>[3,1,6,8,2,4,5,7]=>0100001=>1000010=>1
[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>0100001=>1000010=>1
[4,1,5,2,6,3,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,5,6,1,2,3,8,7]=>[2,4,6,1,3,5,8,7]=>0000101=>1010000=>1
[4,1,5,2,6,8,3,7]=>[2,1,4,3,6,8,5,7]=>1010001=>1000101=>1
[4,1,5,6,8,2,3,7]=>[2,1,4,6,8,3,5,7]=>1000001=>1000001=>1
[4,1,5,2,7,3,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,5,2,7,8,3,6]=>[2,1,4,3,6,8,5,7]=>1010001=>1000101=>1
[4,5,7,1,2,8,3,6]=>[2,4,6,1,3,8,5,7]=>0000101=>1010000=>1
[4,5,1,7,8,2,3,6]=>[2,4,1,6,8,3,5,7]=>0010001=>1000100=>1
[4,5,1,2,7,3,6,8]=>[3,5,1,2,7,4,6,8]=>0001010=>0101000=>0
[4,5,1,2,8,3,6,7]=>[3,5,1,2,8,4,6,7]=>0001001=>1001000=>1
[1,4,5,6,7,2,3,8]=>[1,2,3,5,7,4,6,8]=>0000010=>0100000=>0
[4,1,6,2,7,3,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,6,7,1,8,2,3,5]=>[2,4,6,1,8,3,5,7]=>0000101=>1010000=>1
[4,6,1,7,2,3,5,8]=>[3,5,1,7,2,4,6,8]=>0001010=>0101000=>0
[1,4,2,6,7,8,3,5]=>[1,3,2,4,6,8,5,7]=>0100001=>1000010=>1
[4,6,1,8,2,3,5,7]=>[4,6,1,8,2,3,5,7]=>0000101=>1010000=>1
[4,1,2,6,3,8,5,7]=>[4,1,2,6,3,8,5,7]=>0010101=>1010100=>1
[1,4,2,6,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>0010101=>1010100=>1
[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>0010101=>1010100=>1
[4,7,1,8,2,3,5,6]=>[4,6,1,8,2,3,5,7]=>0000101=>1010000=>1
[1,4,2,7,8,3,5,6]=>[1,4,2,6,8,3,5,7]=>0010001=>1000100=>1
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>0010010=>0100100=>0
[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>0010001=>1000100=>1
[5,1,6,2,7,3,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,6,8,1,2,3,4,7]=>[4,6,8,1,2,3,5,7]=>0000001=>1000000=>1
[5,1,6,2,3,8,4,7]=>[4,1,6,2,3,8,5,7]=>0010101=>1010100=>1
[5,6,1,2,3,8,4,7]=>[4,6,1,2,3,8,5,7]=>0000101=>1010000=>1
[1,5,6,2,3,8,4,7]=>[1,4,6,2,3,8,5,7]=>0000101=>1010000=>1
[1,2,5,6,3,4,7,8]=>[1,2,4,6,3,5,7,8]=>0000100=>0010000=>0
[5,1,7,2,8,3,4,6]=>[4,1,6,2,8,3,5,7]=>0010101=>1010100=>1
[5,7,1,2,8,3,4,6]=>[4,6,1,2,8,3,5,7]=>0000101=>1010000=>1
[5,7,8,1,2,3,4,6]=>[4,6,8,1,2,3,5,7]=>0000001=>1000000=>1
[1,5,7,2,8,3,4,6]=>[1,4,6,2,8,3,5,7]=>0000101=>1010000=>1
[1,5,2,7,3,4,6,8]=>[1,5,2,7,3,4,6,8]=>0001010=>0101000=>0
[5,1,2,8,3,4,6,7]=>[5,1,2,8,3,4,6,7]=>0001001=>1001000=>1
[6,1,7,8,2,3,4,5]=>[4,1,6,8,2,3,5,7]=>0010001=>1000100=>1
[6,7,1,8,2,3,4,5]=>[4,6,1,8,2,3,5,7]=>0000101=>1010000=>1
[1,6,7,8,2,3,4,5]=>[1,4,6,8,2,3,5,7]=>0000001=>1000000=>1
[1,6,7,2,3,4,5,8]=>[1,5,7,2,3,4,6,8]=>0000010=>0100000=>0
[6,1,8,2,3,4,5,7]=>[6,1,8,2,3,4,5,7]=>0000101=>1010000=>1
[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>0000101=>1010000=>1
[5,3,2,6,1,4,8,7]=>[4,3,2,6,1,5,8,7]=>0110101=>1010110=>1
[8,4,5,2,3,7,6,1]=>[8,2,4,1,3,7,6,5]=>0010111=>1110100=>3
[7,4,5,2,3,8,1,6]=>[6,2,5,1,4,8,3,7]=>0001101=>1011000=>1
[6,4,5,2,3,1,8,7]=>[6,2,5,1,4,3,8,7]=>0011101=>1011100=>1
[3,6,1,5,4,2,8,7]=>[2,6,1,5,4,3,8,7]=>0011101=>1011100=>1
[4,6,5,1,3,2,8,7]=>[2,6,5,1,4,3,8,7]=>0011101=>1011100=>1
[5,6,4,3,1,2,8,7]=>[2,6,5,4,1,3,8,7]=>0011101=>1011100=>1
[7,5,4,3,2,8,1,6]=>[6,5,4,3,2,8,1,7]=>0111101=>1011110=>1
[8,6,4,3,7,2,5,1]=>[8,4,3,2,7,1,6,5]=>0110111=>1110110=>3
[7,6,4,3,8,2,1,5]=>[6,5,4,3,8,2,1,7]=>1011101=>1011101=>1
[6,7,4,3,8,1,2,5]=>[2,6,5,4,8,1,3,7]=>0001101=>1011000=>1
[5,7,4,3,1,8,2,6]=>[2,6,5,4,1,8,3,7]=>0011101=>1011100=>1
[4,7,5,1,3,8,2,6]=>[2,6,5,1,4,8,3,7]=>0001101=>1011000=>1
[3,7,1,5,4,8,2,6]=>[2,6,1,5,4,8,3,7]=>0001101=>1011000=>1
[2,1,7,5,4,8,3,6]=>[2,1,6,5,4,8,3,7]=>1001101=>1011001=>1
[3,8,1,5,4,7,6,2]=>[2,8,1,4,3,7,6,5]=>0010111=>1110100=>3
[4,8,5,1,3,7,6,2]=>[2,8,4,1,3,7,6,5]=>0010111=>1110100=>3
[5,8,4,3,1,7,6,2]=>[4,8,3,2,1,7,6,5]=>1100111=>1110011=>3
[6,8,4,3,7,1,5,2]=>[4,8,3,2,7,1,6,5]=>0100111=>1110010=>3
[7,8,4,3,6,5,1,2]=>[4,8,3,2,7,6,1,5]=>0100111=>1110010=>3
[6,8,5,7,3,1,4,2]=>[4,8,3,7,2,1,6,5]=>1000111=>1110001=>3
[5,8,6,7,1,3,4,2]=>[2,8,4,7,1,3,6,5]=>0000111=>1110000=>3
[2,1,8,6,7,4,5,3]=>[2,1,8,4,7,3,6,5]=>1000111=>1110001=>3
[4,7,6,1,8,3,2,5]=>[2,6,5,1,8,4,3,7]=>0011101=>1011100=>1
[5,7,6,8,1,3,2,4]=>[2,6,5,8,1,4,3,7]=>0010101=>1010100=>1
[5,4,7,2,1,8,3,6]=>[4,3,6,2,1,8,5,7]=>1010101=>1010101=>1
[6,4,7,2,8,1,3,5]=>[4,3,6,2,8,1,5,7]=>0010101=>1010100=>1
[7,4,6,2,8,3,1,5]=>[6,2,5,1,8,4,3,7]=>0011101=>1011100=>1
[8,4,6,2,7,3,5,1]=>[8,2,4,1,7,3,6,5]=>0010111=>1110100=>3
[8,3,2,6,7,4,5,1]=>[8,2,1,4,7,3,6,5]=>1000111=>1110001=>3
[7,3,2,6,8,4,1,5]=>[6,2,1,5,8,4,3,7]=>1010101=>1010101=>1
[6,3,2,7,8,1,4,5]=>[4,3,2,6,8,1,5,7]=>0110001=>1000110=>1
[5,3,2,7,1,8,4,6]=>[4,3,2,6,1,8,5,7]=>0110101=>1010110=>1
[4,3,2,1,7,8,5,6]=>[4,3,2,1,6,8,5,7]=>1110001=>1000111=>1
[3,4,1,2,8,7,6,5]=>[2,4,1,3,8,7,6,5]=>0010111=>1110100=>3
[5,3,2,8,1,7,6,4]=>[4,3,2,8,1,7,6,5]=>0110111=>1110110=>3
[6,3,2,8,7,1,5,4]=>[4,3,2,8,7,1,6,5]=>0110111=>1110110=>3
[7,3,2,8,6,5,1,4]=>[4,3,2,8,7,6,1,5]=>0110111=>1110110=>3
[8,4,7,2,6,5,3,1]=>[8,2,7,1,6,5,4,3]=>0011111=>1111100=>5
[7,4,8,2,6,5,1,3]=>[4,3,8,2,7,6,1,5]=>0010111=>1110100=>3
[6,4,8,2,7,1,5,3]=>[4,3,8,2,7,1,6,5]=>0010111=>1110100=>3
[5,4,8,2,1,7,6,3]=>[4,3,8,2,1,7,6,5]=>1010111=>1110101=>3
[4,5,8,1,2,7,6,3]=>[2,4,8,1,3,7,6,5]=>0000111=>1110000=>3
[2,1,5,8,3,7,6,4]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[2,1,6,8,7,3,5,4]=>[2,1,4,8,7,3,6,5]=>1000111=>1110001=>3
[3,6,1,8,7,2,5,4]=>[2,4,1,8,7,3,6,5]=>0010111=>1110100=>3
[4,6,8,1,7,2,5,3]=>[2,4,8,1,7,3,6,5]=>0000111=>1110000=>3
[5,6,8,7,1,2,4,3]=>[2,4,8,7,1,3,6,5]=>0000111=>1110000=>3
[6,5,8,7,2,1,4,3]=>[4,3,8,7,2,1,6,5]=>1010111=>1110101=>3
[7,5,8,6,2,4,1,3]=>[4,3,8,7,2,6,1,5]=>0010111=>1110100=>3
[8,5,7,6,2,4,3,1]=>[8,2,7,6,1,5,4,3]=>0011111=>1111100=>5
[5,7,8,6,1,4,2,3]=>[2,4,8,7,1,6,3,5]=>0000111=>1110000=>3
[3,7,1,8,6,5,2,4]=>[2,4,1,8,7,6,3,5]=>0010111=>1110100=>3
[2,1,7,8,6,5,3,4]=>[2,1,4,8,7,6,3,5]=>1000111=>1110001=>3
[3,8,1,7,6,5,4,2]=>[2,8,1,7,6,5,4,3]=>0011111=>1111100=>5
[4,8,7,1,6,5,3,2]=>[2,8,7,1,6,5,4,3]=>0011111=>1111100=>5
[5,8,7,6,1,4,3,2]=>[2,8,7,6,1,5,4,3]=>0011111=>1111100=>5
[6,8,7,5,4,1,3,2]=>[2,8,7,6,5,1,4,3]=>0011111=>1111100=>5
[6,5,8,1,2,3,4,7]=>[6,5,8,1,2,3,4,7]=>0000101=>1010000=>1
[7,5,8,1,2,3,4,6]=>[6,5,8,1,2,3,4,7]=>0000101=>1010000=>1
[8,5,7,1,2,3,4,6]=>[8,5,7,1,2,3,4,6]=>0000011=>1100000=>2
[3,2,7,8,1,4,5,6]=>[3,2,6,8,1,4,5,7]=>0100001=>1000010=>1
[4,8,2,7,1,3,5,6]=>[4,8,2,7,1,3,5,6]=>0000011=>1100000=>2
[5,8,3,7,1,2,4,6]=>[5,8,3,7,1,2,4,6]=>0000011=>1100000=>2
[6,8,5,7,1,2,3,4]=>[5,8,4,7,1,2,3,6]=>0000011=>1100000=>2
[7,8,2,4,1,3,5,6]=>[6,8,2,4,1,3,5,7]=>0010001=>1000100=>1
[7,8,3,5,1,2,4,6]=>[6,8,3,5,1,2,4,7]=>0001001=>1001000=>1
[5,3,2,6,1,4,7,8]=>[4,3,2,6,1,5,7,8]=>0110100=>0010110=>0
[5,3,2,7,1,4,6,8]=>[5,3,2,7,1,4,6,8]=>0101010=>0101010=>0
[5,3,2,8,1,4,6,7]=>[5,3,2,8,1,4,6,7]=>0101001=>1001010=>1
[7,4,2,8,1,3,5,6]=>[6,4,2,8,1,3,5,7]=>0010101=>1010100=>1
[7,4,3,8,1,2,5,6]=>[6,4,3,8,1,2,5,7]=>0010101=>1010100=>1
[8,4,2,7,1,3,5,6]=>[8,4,2,7,1,3,5,6]=>0010011=>1100100=>2
[5,6,2,4,8,1,3,7]=>[3,6,2,5,8,1,4,7]=>0000101=>1010000=>1
[5,7,2,4,8,1,3,6]=>[3,6,2,5,8,1,4,7]=>0000101=>1010000=>1
[4,7,3,6,8,1,2,5]=>[3,6,2,5,8,1,4,7]=>0000101=>1010000=>1
[7,8,2,4,6,1,3,5]=>[5,8,2,4,7,1,3,6]=>0000011=>1100000=>2
[4,3,2,6,8,1,5,7]=>[4,3,2,6,8,1,5,7]=>0110001=>1000110=>1
[5,4,2,6,8,1,3,7]=>[4,3,2,6,8,1,5,7]=>0110001=>1000110=>1
[6,5,2,4,8,1,3,7]=>[6,5,2,4,8,1,3,7]=>0001101=>1011000=>1
[5,4,2,7,8,1,3,6]=>[4,3,2,6,8,1,5,7]=>0110001=>1000110=>1
[8,7,2,4,6,1,3,5]=>[8,7,2,4,6,1,3,5]=>0000111=>1110000=>3
[6,4,7,2,5,1,3,8]=>[4,3,7,2,6,1,5,8]=>0010110=>0110100=>0
[6,4,8,2,5,1,3,7]=>[6,3,8,2,5,1,4,7]=>0001101=>1011000=>1
[6,4,8,2,7,1,3,5]=>[5,4,8,2,7,1,3,6]=>0001011=>1101000=>2
[7,5,8,2,4,1,3,6]=>[6,5,8,2,4,1,3,7]=>0010101=>1010100=>1
[7,5,8,2,6,1,3,4]=>[5,4,8,2,7,1,3,6]=>0001011=>1101000=>2
[5,4,3,2,8,1,6,7]=>[5,4,3,2,8,1,6,7]=>0111001=>1001110=>1
[4,8,3,7,2,6,1,5]=>[4,8,3,7,2,6,1,5]=>0000111=>1110000=>3
[6,5,3,8,2,7,1,4]=>[5,4,3,8,2,7,1,6]=>0011011=>1101100=>2
[7,5,3,8,2,6,1,4]=>[5,4,3,8,2,7,1,6]=>0011011=>1101100=>2
[8,5,4,7,2,6,1,3]=>[8,4,3,7,2,6,1,5]=>0010111=>1110100=>3
[8,5,4,7,3,6,1,2]=>[8,4,3,7,2,6,1,5]=>0010111=>1110100=>3
[6,5,4,3,2,8,1,7]=>[6,5,4,3,2,8,1,7]=>0111101=>1011110=>1
[8,7,5,4,2,6,1,3]=>[8,7,4,3,2,6,1,5]=>0110111=>1110110=>3
[8,7,6,5,2,4,1,3]=>[8,7,6,5,2,4,1,3]=>0011111=>1111100=>5
[4,1,2,8,7,3,5,6]=>[4,1,2,8,7,3,5,6]=>0010011=>1100100=>2
[3,1,7,2,6,4,8,5]=>[3,1,6,2,5,4,8,7]=>0101101=>1011010=>1
[6,1,5,2,3,8,4,7]=>[6,1,5,2,3,8,4,7]=>0001101=>1011000=>1
[5,1,4,2,7,3,8,6]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[8,1,4,2,6,3,5,7]=>[8,1,4,2,6,3,5,7]=>0010101=>1010100=>1
[7,1,4,2,6,3,8,5]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[8,1,5,2,7,3,4,6]=>[8,1,5,2,7,3,4,6]=>0001011=>1101000=>2
[7,1,5,2,6,3,8,4]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[3,1,8,6,2,4,5,7]=>[3,1,8,6,2,4,5,7]=>0100101=>1010010=>1
[7,1,8,6,2,3,4,5]=>[5,1,8,7,2,3,4,6]=>0001011=>1101000=>2
[8,3,1,2,4,7,5,6]=>[8,3,1,2,4,7,5,6]=>0100011=>1100010=>2
[5,4,1,2,8,3,6,7]=>[5,4,1,2,8,3,6,7]=>0011001=>1001100=>1
[5,8,1,2,7,3,4,6]=>[5,8,1,2,7,3,4,6]=>0000011=>1100000=>2
[8,3,1,5,2,7,4,6]=>[8,3,1,5,2,7,4,6]=>0101011=>1101010=>2
[8,4,1,6,2,3,5,7]=>[8,4,1,6,2,3,5,7]=>0010101=>1010100=>1
[7,4,1,8,2,3,5,6]=>[6,4,1,8,2,3,5,7]=>0010101=>1010100=>1
[8,7,1,6,2,3,4,5]=>[8,7,1,6,2,3,4,5]=>0000111=>1110000=>3
[8,3,1,5,6,2,4,7]=>[8,2,1,4,6,3,5,7]=>1000101=>1010001=>1
[8,3,1,7,6,2,4,5]=>[8,3,1,7,6,2,4,5]=>0100111=>1110010=>3
[6,3,8,1,2,7,4,5]=>[5,3,8,1,2,7,4,6]=>0001011=>1101000=>2
[6,8,5,1,2,3,4,7]=>[6,8,5,1,2,3,4,7]=>0001001=>1001000=>1
[8,5,4,1,2,7,3,6]=>[8,5,4,1,2,7,3,6]=>0011011=>1101100=>2
[2,8,4,6,1,7,3,5]=>[1,8,3,5,2,7,4,6]=>0001011=>1101000=>2
[8,3,4,5,7,1,2,6]=>[8,1,3,5,7,2,4,6]=>0000011=>1100000=>2
[3,5,2,6,1,4,8,7]=>[1,4,3,6,2,5,8,7]=>0010101=>1010100=>1
[3,5,2,6,4,1,8,7]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[3,5,2,7,4,8,1,6]=>[1,3,2,6,5,8,4,7]=>0100101=>1010010=>1
[3,5,2,7,4,8,6,1]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[4,5,7,2,3,8,6,1]=>[1,3,5,2,4,8,7,6]=>0001011=>1101000=>2
[4,5,7,2,3,8,1,6]=>[1,3,6,2,5,8,4,7]=>0000101=>1010000=>1
[4,5,6,2,3,1,8,7]=>[1,3,6,2,5,4,8,7]=>0001101=>1011000=>1
[4,5,6,2,1,3,8,7]=>[1,4,6,3,2,5,8,7]=>0100101=>1010010=>1
[3,5,1,6,4,2,8,7]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[4,5,6,1,3,2,8,7]=>[1,3,6,2,5,4,8,7]=>0001101=>1011000=>1
[4,5,7,3,2,8,1,6]=>[1,2,6,5,4,8,3,7]=>0001101=>1011000=>1
[4,5,7,3,2,8,6,1]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[4,6,7,3,8,2,5,1]=>[1,2,5,4,8,3,7,6]=>0001011=>1101000=>2
[4,6,7,3,8,1,2,5]=>[1,3,6,5,8,2,4,7]=>0000101=>1010000=>1
[4,5,7,3,1,8,2,6]=>[1,3,6,5,2,8,4,7]=>0001101=>1011000=>1
[4,5,7,1,3,8,2,6]=>[1,3,6,2,5,8,4,7]=>0000101=>1010000=>1
[3,5,1,7,4,8,2,6]=>[1,3,2,6,5,8,4,7]=>0100101=>1010010=>1
[2,1,5,7,4,8,3,6]=>[2,1,3,6,5,8,4,7]=>1000101=>1010001=>1
[2,1,5,7,4,8,6,3]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[3,5,1,7,4,8,6,2]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[4,5,7,1,3,8,6,2]=>[1,3,5,2,4,8,7,6]=>0001011=>1101000=>2
[4,5,7,3,1,8,6,2]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[4,6,7,3,8,1,5,2]=>[1,2,5,4,8,3,7,6]=>0001011=>1101000=>2
[4,6,7,3,8,5,1,2]=>[1,2,5,4,8,7,3,6]=>0001011=>1101000=>2
[4,6,7,3,8,5,2,1]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[5,6,7,8,3,1,4,2]=>[1,2,5,8,4,3,7,6]=>0010011=>1100100=>2
[5,6,7,8,1,3,4,2]=>[1,3,5,8,2,4,7,6]=>0000011=>1100000=>2
[4,6,7,1,8,3,5,2]=>[1,3,5,2,8,4,7,6]=>0001011=>1101000=>2
[3,6,1,7,8,4,2,5]=>[1,3,2,6,8,5,4,7]=>0101001=>1001010=>1
[5,6,7,8,1,3,2,4]=>[1,3,6,8,2,5,4,7]=>0001001=>1001000=>1
[4,5,7,2,1,8,3,6]=>[1,4,6,3,2,8,5,7]=>0100101=>1010010=>1
[4,6,7,2,8,3,5,1]=>[1,3,5,2,8,4,7,6]=>0001011=>1101000=>2
[3,6,2,7,8,4,1,5]=>[1,3,2,6,8,5,4,7]=>0101001=>1001010=>1
[3,6,2,7,8,1,4,5]=>[1,4,3,6,8,2,5,7]=>0010001=>1000100=>1
[3,4,1,2,7,8,6,5]=>[2,4,1,3,5,8,7,6]=>0010011=>1100100=>2
[3,5,2,7,1,8,6,4]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[3,6,2,7,8,5,1,4]=>[1,3,2,5,8,7,4,6]=>0100011=>1100010=>2
[3,6,2,7,8,5,4,1]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010=>3
[4,6,7,2,8,5,3,1]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[4,6,7,2,8,5,1,3]=>[1,2,5,4,8,7,3,6]=>0001011=>1101000=>2
[4,6,7,2,8,1,5,3]=>[1,2,5,4,8,3,7,6]=>0001011=>1101000=>2
[4,5,7,2,1,8,6,3]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[4,5,7,1,2,8,6,3]=>[1,3,5,2,4,8,7,6]=>0001011=>1101000=>2
[3,5,1,7,2,8,6,4]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[2,1,5,7,3,8,6,4]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[4,6,7,1,8,2,5,3]=>[1,3,5,2,8,4,7,6]=>0001011=>1101000=>2
[5,6,7,8,1,2,4,3]=>[1,3,5,8,2,4,7,6]=>0000011=>1100000=>2
[5,6,7,8,2,1,4,3]=>[1,2,5,8,4,3,7,6]=>0010011=>1100100=>2
[5,6,7,8,2,4,1,3]=>[1,2,5,8,4,7,3,6]=>0000011=>1100000=>2
[5,6,7,8,2,4,3,1]=>[1,2,4,8,3,7,6,5]=>0000111=>1110000=>3
[5,6,7,8,1,4,2,3]=>[1,3,5,8,2,7,4,6]=>0000011=>1100000=>2
[4,6,7,1,8,5,2,3]=>[1,3,5,2,8,7,4,6]=>0001011=>1101000=>2
[3,6,1,7,8,5,2,4]=>[1,3,2,5,8,7,4,6]=>0100011=>1100010=>2
[2,1,6,7,8,5,3,4]=>[2,1,3,5,8,7,4,6]=>1000011=>1100001=>2
[3,6,1,7,8,5,4,2]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010=>3
[4,6,7,1,8,5,3,2]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[5,6,7,8,1,4,3,2]=>[1,2,4,8,3,7,6,5]=>0000111=>1110000=>3
[5,6,7,8,4,1,3,2]=>[1,2,4,8,7,3,6,5]=>0000111=>1110000=>3
[6,5,8,7,3,4,1,2]=>[4,3,8,7,2,6,1,5]=>0010111=>1110100=>3
[3,6,7,4,5,8,1,2]=>[1,3,6,2,5,8,4,7]=>0000101=>1010000=>1
[2,6,7,4,5,1,8,3]=>[1,3,6,2,5,4,8,7]=>0001101=>1011000=>1
[1,6,7,4,5,2,3,8]=>[1,4,7,3,6,2,5,8]=>0000110=>0110000=>0
[1,5,4,7,6,2,3,8]=>[1,4,3,7,6,2,5,8]=>0010110=>0110100=>0
[2,5,4,7,6,1,8,3]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[3,5,4,7,6,8,1,2]=>[1,3,2,6,5,8,4,7]=>0100101=>1010010=>1
[4,5,3,7,8,6,1,2]=>[1,3,2,5,8,7,4,6]=>0100011=>1100010=>2
[5,4,3,8,7,6,1,2]=>[4,3,2,8,7,6,1,5]=>0110111=>1110110=>3
[6,4,8,3,7,5,1,2]=>[4,3,8,2,7,6,1,5]=>0010111=>1110100=>3
[5,3,4,8,6,7,1,2]=>[3,1,2,8,5,7,4,6]=>0100011=>1100010=>2
[4,3,5,6,8,7,1,2]=>[2,1,3,5,8,7,4,6]=>1000011=>1100001=>2
[3,2,5,6,1,8,7,4]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[5,2,4,8,6,1,7,3]=>[3,1,2,8,5,4,7,6]=>0101011=>1101010=>2
[7,8,2,4,5,1,6,3]=>[5,8,1,2,4,3,7,6]=>0010011=>1100100=>2
[5,1,4,8,6,2,3,7]=>[4,1,3,8,6,2,5,7]=>0010101=>1010100=>1
[4,1,3,2,8,6,5,7]=>[4,1,3,2,8,6,5,7]=>0110101=>1010110=>1
[5,1,3,8,2,6,4,7]=>[4,1,3,8,2,6,5,7]=>0010101=>1010100=>1
[6,1,8,3,2,5,4,7]=>[6,1,8,3,2,5,4,7]=>0101101=>1011010=>1
[7,8,1,3,2,5,4,6]=>[6,8,1,3,2,5,4,7]=>0101001=>1001010=>1
[7,8,2,3,1,5,6,4]=>[5,8,1,3,2,4,7,6]=>0100011=>1100010=>2
[6,2,8,3,1,5,7,4]=>[5,1,8,3,2,4,7,6]=>0101011=>1101010=>2
[6,3,8,2,1,7,5,4]=>[4,3,8,2,1,7,6,5]=>1010111=>1110101=>3
[7,8,3,2,1,6,5,4]=>[4,8,3,2,1,7,6,5]=>1100111=>1110011=>3
[7,8,4,2,6,1,5,3]=>[4,8,3,2,7,1,6,5]=>0100111=>1110010=>3
[5,4,2,8,7,1,6,3]=>[4,3,2,8,7,1,6,5]=>0110111=>1110110=>3
[2,5,3,7,1,6,8,4]=>[1,4,3,6,2,5,8,7]=>0010101=>1010100=>1
[1,5,3,7,2,6,4,8]=>[1,4,3,7,2,6,5,8]=>0010110=>0110100=>0
[2,6,7,3,1,5,8,4]=>[1,4,6,3,2,5,8,7]=>0100101=>1010010=>1
[3,6,7,2,1,8,5,4]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[7,8,5,6,2,1,4,3]=>[4,8,3,7,2,1,6,5]=>1000111=>1110001=>3
[6,5,8,7,1,2,3,4]=>[5,4,8,7,1,2,3,6]=>0001011=>1101000=>2
[5,4,1,8,7,2,3,6]=>[5,4,1,8,7,2,3,6]=>0011011=>1101100=>2
[5,3,1,8,2,7,4,6]=>[5,3,1,8,2,7,4,6]=>0101011=>1101010=>2
[4,3,1,2,8,7,5,6]=>[4,3,1,2,8,7,5,6]=>0110011=>1100110=>2
[4,2,1,3,8,5,7,6]=>[4,2,1,3,8,5,7,6]=>1010011=>1100101=>2
[5,2,1,8,3,4,7,6]=>[5,2,1,8,3,4,7,6]=>1001011=>1101001=>2
[6,2,8,1,3,4,7,5]=>[5,2,8,1,3,4,7,6]=>0001011=>1101000=>2
[4,3,1,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>0110101=>1010110=>1
[5,3,1,6,2,4,8,7]=>[4,3,1,6,2,5,8,7]=>0110101=>1010110=>1
[6,3,1,5,2,4,8,7]=>[6,3,1,5,2,4,8,7]=>0101101=>1011010=>1
[7,3,1,5,2,8,4,6]=>[6,3,1,5,2,8,4,7]=>0101101=>1011010=>1
[8,4,5,1,2,7,3,6]=>[8,3,5,1,2,7,4,6]=>0001011=>1101000=>2
[7,4,5,1,2,8,3,6]=>[6,3,5,1,2,8,4,7]=>0001101=>1011000=>1
[6,4,5,1,2,3,8,7]=>[6,3,5,1,2,4,8,7]=>0001101=>1011000=>1
[2,1,6,5,3,4,8,7]=>[2,1,6,5,3,4,8,7]=>1001101=>1011001=>1
[3,6,1,5,2,4,8,7]=>[3,6,1,5,2,4,8,7]=>0001101=>1011000=>1
[4,6,5,1,2,3,8,7]=>[3,6,5,1,2,4,8,7]=>0001101=>1011000=>1
[5,6,4,1,2,3,8,7]=>[3,6,5,1,2,4,8,7]=>0001101=>1011000=>1
[6,5,4,1,2,3,8,7]=>[6,5,4,1,2,3,8,7]=>0011101=>1011100=>1
[7,5,4,1,2,8,3,6]=>[6,5,4,1,2,8,3,7]=>0011101=>1011100=>1
[8,6,4,1,7,2,3,5]=>[8,5,4,1,7,2,3,6]=>0011011=>1101100=>2
[6,7,4,1,8,2,3,5]=>[3,6,5,1,8,2,4,7]=>0001101=>1011000=>1
[5,7,4,1,2,8,3,6]=>[3,6,5,1,2,8,4,7]=>0001101=>1011000=>1
[4,7,5,1,2,8,3,6]=>[3,6,5,1,2,8,4,7]=>0001101=>1011000=>1
[2,1,7,5,3,8,4,6]=>[2,1,6,5,3,8,4,7]=>1001101=>1011001=>1
[2,1,8,5,3,7,4,6]=>[2,1,8,5,3,7,4,6]=>1001011=>1101001=>2
[3,8,1,5,2,7,4,6]=>[3,8,1,5,2,7,4,6]=>0001011=>1101000=>2
[5,8,4,1,2,7,3,6]=>[5,8,4,1,2,7,3,6]=>0010011=>1100100=>2
[8,7,4,1,6,2,3,5]=>[8,7,4,1,6,2,3,5]=>0010111=>1110100=>3
[5,8,6,7,1,2,3,4]=>[3,8,5,7,1,2,4,6]=>0000011=>1100000=>2
[4,8,6,1,7,2,3,5]=>[3,8,5,1,7,2,4,6]=>0001011=>1101000=>2
[3,8,1,6,7,2,4,5]=>[3,8,1,5,7,2,4,6]=>0000011=>1100000=>2
[2,1,8,6,7,3,4,5]=>[2,1,8,5,7,3,4,6]=>1000011=>1100001=>2
[3,7,1,6,8,2,4,5]=>[3,6,1,5,8,2,4,7]=>0000101=>1010000=>1
[4,7,6,1,8,2,3,5]=>[3,6,5,1,8,2,4,7]=>0001101=>1011000=>1
[5,7,6,8,1,2,3,4]=>[3,6,5,8,1,2,4,7]=>0000101=>1010000=>1
[5,4,7,1,2,8,3,6]=>[4,3,6,1,2,8,5,7]=>0010101=>1010100=>1
[7,4,6,1,8,2,3,5]=>[6,3,5,1,8,2,4,7]=>0001101=>1011000=>1
[8,4,6,1,7,2,3,5]=>[8,3,5,1,7,2,4,6]=>0001011=>1101000=>2
[8,3,1,6,7,2,4,5]=>[8,3,1,5,7,2,4,6]=>0100011=>1100010=>2
[7,3,1,6,8,2,4,5]=>[6,3,1,5,8,2,4,7]=>0100101=>1010010=>1
[5,3,1,7,2,8,4,6]=>[4,3,1,6,2,8,5,7]=>0110101=>1010110=>1
[4,3,1,2,7,8,5,6]=>[4,3,1,2,6,8,5,7]=>0110001=>1000110=>1
[2,1,4,3,8,7,5,6]=>[2,1,4,3,8,7,5,6]=>1010011=>1100101=>2
[3,4,1,2,8,7,5,6]=>[2,4,1,3,8,7,5,6]=>0010011=>1100100=>2
[6,3,1,8,7,2,4,5]=>[5,3,1,8,7,2,4,6]=>0101011=>1101010=>2
[7,3,1,8,6,2,4,5]=>[5,3,1,8,7,2,4,6]=>0101011=>1101010=>2
[8,4,7,1,6,2,3,5]=>[8,4,7,1,6,2,3,5]=>0000111=>1110000=>3
[5,4,8,1,2,7,3,6]=>[5,4,8,1,2,7,3,6]=>0001011=>1101000=>2
[4,5,8,1,2,7,3,6]=>[3,5,8,1,2,7,4,6]=>0000011=>1100000=>2
[3,5,1,8,2,7,4,6]=>[3,5,1,8,2,7,4,6]=>0001011=>1101000=>2
[2,1,5,8,3,7,4,6]=>[2,1,5,8,3,7,4,6]=>1000011=>1100001=>2
[2,1,6,8,7,3,4,5]=>[2,1,5,8,7,3,4,6]=>1000011=>1100001=>2
[3,6,1,8,7,2,4,5]=>[3,5,1,8,7,2,4,6]=>0001011=>1101000=>2
[4,6,8,1,7,2,3,5]=>[3,5,8,1,7,2,4,6]=>0000011=>1100000=>2
[5,6,8,7,1,2,3,4]=>[3,5,8,7,1,2,4,6]=>0000011=>1100000=>2
[7,5,8,6,1,2,3,4]=>[5,4,8,7,1,2,3,6]=>0001011=>1101000=>2
[8,5,7,6,1,2,3,4]=>[8,4,7,6,1,2,3,5]=>0000111=>1110000=>3
[5,7,8,6,1,2,3,4]=>[3,5,8,7,1,2,4,6]=>0000011=>1100000=>2
[4,7,8,1,6,2,3,5]=>[3,5,8,1,7,2,4,6]=>0000011=>1100000=>2
[3,7,1,8,6,2,4,5]=>[3,5,1,8,7,2,4,6]=>0001011=>1101000=>2
[2,1,7,8,6,3,4,5]=>[2,1,5,8,7,3,4,6]=>1000011=>1100001=>2
[2,1,8,7,6,3,4,5]=>[2,1,8,7,6,3,4,5]=>1000111=>1110001=>3
[3,8,1,7,6,2,4,5]=>[3,8,1,7,6,2,4,5]=>0000111=>1110000=>3
[4,8,7,1,6,2,3,5]=>[4,8,7,1,6,2,3,5]=>0000111=>1110000=>3
[5,8,7,6,1,2,3,4]=>[4,8,7,6,1,2,3,5]=>0000111=>1110000=>3
[6,8,7,5,1,2,3,4]=>[4,8,7,6,1,2,3,5]=>0000111=>1110000=>3
[6,4,7,3,8,5,1,2]=>[2,1,5,4,8,7,3,6]=>1001011=>1101001=>2
[6,4,7,3,5,8,1,2]=>[3,2,6,1,5,8,4,7]=>0100101=>1010010=>1
[6,4,7,2,5,1,8,3]=>[3,2,6,1,5,4,8,7]=>0101101=>1011010=>1
[5,4,2,7,6,1,3,8]=>[4,3,2,7,6,1,5,8]=>0110110=>0110110=>0
[5,4,2,7,6,1,8,3]=>[3,2,1,6,5,4,8,7]=>1101101=>1011011=>1
[5,4,3,7,6,8,1,2]=>[3,2,1,6,5,8,4,7]=>1100101=>1010011=>1
[6,4,8,3,5,7,1,2]=>[5,2,8,1,4,7,3,6]=>0001011=>1101000=>2
[5,4,3,8,6,7,1,2]=>[3,2,1,8,5,7,4,6]=>1100011=>1100011=>2
[5,4,2,6,7,1,3,8]=>[3,2,1,5,7,4,6,8]=>1100010=>0100011=>0
[5,3,2,6,1,7,4,8]=>[3,2,1,5,4,7,6,8]=>1101010=>0101011=>0
[5,4,2,8,6,1,7,3]=>[3,2,1,8,5,4,7,6]=>1101011=>1101011=>2
[6,4,8,2,5,1,7,3]=>[5,2,8,1,4,3,7,6]=>0011011=>1101100=>2
[7,8,4,2,5,1,3,6]=>[6,8,3,2,5,1,4,7]=>0101001=>1001010=>1
[5,4,2,8,6,1,3,7]=>[4,3,2,8,6,1,5,7]=>0110101=>1010110=>1
[5,3,2,6,1,8,4,7]=>[4,3,2,6,1,8,5,7]=>0110101=>1010110=>1
[4,3,2,1,6,8,5,7]=>[4,3,2,1,6,8,5,7]=>1110001=>1000111=>1
[4,3,2,1,8,6,5,7]=>[4,3,2,1,8,6,5,7]=>1110101=>1010111=>1
[5,3,2,8,1,6,4,7]=>[4,3,2,8,1,6,5,7]=>0110101=>1010110=>1
[6,3,8,2,1,5,4,7]=>[6,3,8,2,1,5,4,7]=>1001101=>1011001=>1
[7,8,3,2,1,5,6,4]=>[5,8,3,2,1,4,7,6]=>1100011=>1100011=>2
[6,3,8,2,1,5,7,4]=>[5,3,8,2,1,4,7,6]=>1001011=>1101001=>2
[5,3,2,7,1,6,8,4]=>[4,3,2,6,1,5,8,7]=>0110101=>1010110=>1
[6,3,7,2,1,5,4,8]=>[4,3,7,2,1,6,5,8]=>1010110=>0110101=>0
[6,3,7,2,1,8,5,4]=>[2,1,5,4,3,8,7,6]=>1011011=>1101101=>2
[6,4,7,2,8,1,5,3]=>[2,1,5,4,8,3,7,6]=>1001011=>1101001=>2
[6,5,8,7,2,1,3,4]=>[5,4,8,7,2,1,3,6]=>1001011=>1101001=>2
[6,3,7,2,1,8,4,5]=>[4,3,6,2,1,8,5,7]=>1010101=>1010101=>1
[6,3,7,2,1,4,5,8]=>[5,3,7,2,1,4,6,8]=>1001010=>0101001=>0
[5,3,2,7,1,4,8,6]=>[4,3,2,6,1,5,8,7]=>0110101=>1010110=>1
[5,4,2,8,7,1,3,6]=>[5,4,2,8,7,1,3,6]=>0011011=>1101100=>2
[5,3,2,8,1,7,4,6]=>[5,3,2,8,1,7,4,6]=>0101011=>1101010=>2
[4,3,2,1,8,7,5,6]=>[4,3,2,1,8,7,5,6]=>1110011=>1100111=>2
[4,3,2,1,7,5,8,6]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111=>1
[4,3,2,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>1110010=>0100111=>0
[4,3,2,1,8,5,7,6]=>[4,3,2,1,8,5,7,6]=>1110011=>1100111=>2
[5,3,2,8,1,4,7,6]=>[5,3,2,8,1,4,7,6]=>0101011=>1101010=>2
[6,3,8,2,1,4,7,5]=>[5,3,8,2,1,4,7,6]=>1001011=>1101001=>2
[7,8,3,2,1,4,6,5]=>[5,8,3,2,1,4,7,6]=>1100011=>1100011=>2
[6,3,8,2,1,4,5,7]=>[6,3,8,2,1,4,5,7]=>1000101=>1010001=>1
[4,3,2,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>1110001=>1000111=>1
[4,3,2,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>1110001=>1000111=>1
[7,8,5,6,1,2,4,3]=>[4,8,3,7,1,2,6,5]=>0000111=>1110000=>3
[7,8,4,1,6,2,5,3]=>[4,8,3,1,7,2,6,5]=>0100111=>1110010=>3
[7,8,1,4,6,2,5,3]=>[4,8,1,3,7,2,6,5]=>0000111=>1110000=>3
[6,1,8,4,7,2,5,3]=>[4,1,8,3,7,2,6,5]=>0010111=>1110100=>3
[1,6,8,4,7,2,5,3]=>[1,4,8,3,7,2,6,5]=>0000111=>1110000=>3
[1,6,8,3,2,7,5,4]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[6,1,8,3,2,7,5,4]=>[4,1,8,3,2,7,6,5]=>0110111=>1110110=>3
[7,8,1,3,2,6,5,4]=>[4,8,1,3,2,7,6,5]=>0100111=>1110010=>3
[7,8,3,1,2,6,5,4]=>[4,8,3,1,2,7,6,5]=>0100111=>1110010=>3
[7,8,3,4,6,5,1,2]=>[4,8,1,3,7,6,2,5]=>0000111=>1110000=>3
[7,8,2,4,6,1,5,3]=>[4,8,1,3,7,2,6,5]=>0000111=>1110000=>3
[7,8,2,3,1,6,5,4]=>[4,8,1,3,2,7,6,5]=>0100111=>1110010=>3
[7,8,2,1,3,6,5,4]=>[4,8,2,1,3,7,6,5]=>1000111=>1110001=>3
[7,8,1,2,3,6,5,4]=>[4,8,1,2,3,7,6,5]=>0000111=>1110000=>3
[6,1,8,2,3,7,5,4]=>[4,1,8,2,3,7,6,5]=>0010111=>1110100=>3
[1,6,8,2,3,7,5,4]=>[1,4,8,2,3,7,6,5]=>0000111=>1110000=>3
[1,5,2,8,3,7,6,4]=>[1,4,2,8,3,7,6,5]=>0010111=>1110100=>3
[5,1,2,8,3,7,6,4]=>[4,1,2,8,3,7,6,5]=>0010111=>1110100=>3
[5,2,1,8,3,7,6,4]=>[4,2,1,8,3,7,6,5]=>1010111=>1110101=>3
[6,2,8,1,3,7,5,4]=>[4,2,8,1,3,7,6,5]=>0010111=>1110100=>3
[6,2,8,3,1,7,5,4]=>[4,1,8,3,2,7,6,5]=>0110111=>1110110=>3
[6,2,8,4,7,1,5,3]=>[4,1,8,3,7,2,6,5]=>0010111=>1110100=>3
[3,6,8,4,7,5,1,2]=>[1,4,8,3,7,6,2,5]=>0000111=>1110000=>3
[2,6,8,4,7,1,5,3]=>[1,4,8,3,7,2,6,5]=>0000111=>1110000=>3
[2,6,8,3,1,7,5,4]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[2,6,8,1,3,7,5,4]=>[2,4,8,1,3,7,6,5]=>0000111=>1110000=>3
[1,2,5,8,3,7,6,4]=>[1,2,4,8,3,7,6,5]=>0000111=>1110000=>3
[2,4,1,3,8,7,6,5]=>[2,4,1,3,8,7,6,5]=>0010111=>1110100=>3
[2,5,4,8,7,1,6,3]=>[1,4,3,8,7,2,6,5]=>0010111=>1110100=>3
[5,2,4,8,7,1,6,3]=>[4,1,3,8,7,2,6,5]=>0010111=>1110100=>3
[4,2,1,3,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>1010111=>1110101=>3
[4,1,2,3,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>0010111=>1110100=>3
[1,4,2,3,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>0010111=>1110100=>3
[4,1,3,2,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>0110111=>1110110=>3
[4,3,1,2,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>0110111=>1110110=>3
[6,3,8,1,2,7,5,4]=>[4,3,8,1,2,7,6,5]=>0010111=>1110100=>3
[1,5,4,8,7,2,6,3]=>[1,4,3,8,7,2,6,5]=>0010111=>1110100=>3
[5,1,4,8,7,2,6,3]=>[4,1,3,8,7,2,6,5]=>0010111=>1110100=>3
[6,4,8,1,7,2,5,3]=>[4,3,8,1,7,2,6,5]=>0010111=>1110100=>3
[6,5,8,7,1,2,4,3]=>[4,3,8,7,1,2,6,5]=>0010111=>1110100=>3
[5,6,8,7,3,4,1,2]=>[1,4,8,7,3,6,2,5]=>0000111=>1110000=>3
[4,5,1,8,7,2,6,3]=>[2,4,1,8,7,3,6,5]=>0010111=>1110100=>3
[4,1,5,8,7,2,6,3]=>[2,1,4,8,7,3,6,5]=>1000111=>1110001=>3
[1,4,5,8,7,2,6,3]=>[1,2,4,8,7,3,6,5]=>0000111=>1110000=>3
[1,3,5,8,2,7,6,4]=>[1,2,4,8,3,7,6,5]=>0000111=>1110000=>3
[3,1,5,8,2,7,6,4]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[3,6,8,1,2,7,5,4]=>[2,4,8,1,3,7,6,5]=>0000111=>1110000=>3
[3,6,8,2,1,7,5,4]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[4,6,8,2,7,1,5,3]=>[1,4,8,3,7,2,6,5]=>0000111=>1110000=>3
[4,6,8,3,7,5,1,2]=>[1,4,8,3,7,6,2,5]=>0000111=>1110000=>3
[4,5,2,8,7,1,6,3]=>[1,4,3,8,7,2,6,5]=>0010111=>1110100=>3
[3,1,4,2,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[3,1,2,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>0100111=>1110010=>3
[3,2,5,8,1,7,6,4]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[4,2,5,8,7,1,6,3]=>[2,1,4,8,7,3,6,5]=>1000111=>1110001=>3
[4,3,5,8,7,6,1,2]=>[2,1,4,8,7,6,3,5]=>1000111=>1110001=>3
[3,4,5,8,7,6,1,2]=>[1,2,4,8,7,6,3,5]=>0000111=>1110000=>3
[2,4,5,8,7,1,6,3]=>[1,2,4,8,7,3,6,5]=>0000111=>1110000=>3
[2,3,5,8,1,7,6,4]=>[1,2,4,8,3,7,6,5]=>0000111=>1110000=>3
[4,1,3,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[5,1,3,2,6,4,8,7]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[6,1,3,2,5,4,8,7]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[7,1,3,2,5,4,8,6]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[8,1,3,2,5,4,7,6]=>[8,1,3,2,5,4,7,6]=>0101011=>1101010=>2
[8,1,4,2,5,3,7,6]=>[8,1,3,2,5,4,7,6]=>0101011=>1101010=>2
[7,1,4,2,5,3,8,6]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[6,1,4,2,5,3,8,7]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[5,1,4,2,6,3,8,7]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[2,1,6,3,5,4,8,7]=>[2,1,6,3,5,4,8,7]=>1001101=>1011001=>1
[3,1,6,2,5,4,8,7]=>[3,1,6,2,5,4,8,7]=>0101101=>1011010=>1
[4,1,6,2,5,3,8,7]=>[3,1,6,2,5,4,8,7]=>0101101=>1011010=>1
[6,2,5,1,4,3,8,7]=>[6,2,5,1,4,3,8,7]=>0011101=>1011100=>1
[5,2,6,1,4,3,8,7]=>[3,2,6,1,5,4,8,7]=>0101101=>1011010=>1
[5,2,7,1,4,3,8,6]=>[3,2,6,1,5,4,8,7]=>0101101=>1011010=>1
[5,2,8,1,4,3,7,6]=>[5,2,8,1,4,3,7,6]=>0011011=>1101100=>2
[6,2,8,1,4,3,7,5]=>[5,2,8,1,4,3,7,6]=>0011011=>1101100=>2
[6,2,7,1,4,3,8,5]=>[3,2,6,1,5,4,8,7]=>0101101=>1011010=>1
[7,2,6,1,4,3,8,5]=>[6,2,5,1,4,3,8,7]=>0011101=>1011100=>1
[7,2,5,1,4,3,8,6]=>[6,2,5,1,4,3,8,7]=>0011101=>1011100=>1
[4,1,7,2,5,3,8,6]=>[3,1,6,2,5,4,8,7]=>0101101=>1011010=>1
[3,1,7,2,5,4,8,6]=>[3,1,6,2,5,4,8,7]=>0101101=>1011010=>1
[2,1,7,3,5,4,8,6]=>[2,1,6,3,5,4,8,7]=>1001101=>1011001=>1
[2,1,8,3,5,4,7,6]=>[2,1,8,3,5,4,7,6]=>1001011=>1101001=>2
[3,1,8,2,5,4,7,6]=>[3,1,8,2,5,4,7,6]=>0101011=>1101010=>2
[4,1,8,2,5,3,7,6]=>[3,1,8,2,5,4,7,6]=>0101011=>1101010=>2
[8,2,5,1,4,3,7,6]=>[8,2,5,1,4,3,7,6]=>0011011=>1101100=>2
[8,2,6,1,4,3,7,5]=>[8,2,5,1,4,3,7,6]=>0011011=>1101100=>2
[7,1,4,3,8,2,6,5]=>[5,1,4,3,8,2,7,6]=>0011011=>1101100=>2
[8,1,4,3,7,2,6,5]=>[8,1,4,3,7,2,6,5]=>0010111=>1110100=>3
[8,1,5,3,7,2,6,4]=>[8,1,4,3,7,2,6,5]=>0010111=>1110100=>3
[7,1,5,3,8,2,6,4]=>[5,1,4,3,8,2,7,6]=>0011011=>1101100=>2
[8,2,6,1,5,3,7,4]=>[8,2,5,1,4,3,7,6]=>0011011=>1101100=>2
[5,1,8,2,6,3,7,4]=>[3,1,8,2,5,4,7,6]=>0101011=>1101010=>2
[4,1,8,2,6,3,7,5]=>[3,1,8,2,5,4,7,6]=>0101011=>1101010=>2
[3,1,8,2,6,4,7,5]=>[3,1,8,2,5,4,7,6]=>0101011=>1101010=>2
[2,1,8,3,6,4,7,5]=>[2,1,8,3,5,4,7,6]=>1001011=>1101001=>2
[2,1,7,3,6,4,8,5]=>[2,1,6,3,5,4,8,7]=>1001101=>1011001=>1
[4,1,7,2,6,3,8,5]=>[3,1,6,2,5,4,8,7]=>0101101=>1011010=>1
[5,1,7,2,6,3,8,4]=>[3,1,6,2,5,4,8,7]=>0101101=>1011010=>1
[7,2,6,1,5,3,8,4]=>[6,2,5,1,4,3,8,7]=>0011101=>1011100=>1
[6,2,7,1,5,3,8,4]=>[3,2,6,1,5,4,8,7]=>0101101=>1011010=>1
[6,2,8,1,5,3,7,4]=>[5,2,8,1,4,3,7,6]=>0011011=>1101100=>2
[8,1,5,2,6,3,7,4]=>[8,1,3,2,5,4,7,6]=>0101011=>1101010=>2
[6,1,5,2,7,3,8,4]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[6,1,4,2,7,3,8,5]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[8,1,4,2,6,3,7,5]=>[8,1,3,2,5,4,7,6]=>0101011=>1101010=>2
[8,1,3,2,6,4,7,5]=>[8,1,3,2,5,4,7,6]=>0101011=>1101010=>2
[7,1,3,2,6,4,8,5]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[6,1,3,2,7,4,8,5]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[5,1,3,2,7,4,8,6]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[4,1,3,2,7,5,8,6]=>[4,1,3,2,6,5,8,7]=>0110101=>1010110=>1
[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,5,7,6]=>1010011=>1100101=>2
[3,1,4,2,8,5,7,6]=>[2,1,4,3,8,5,7,6]=>1010011=>1100101=>2
[4,1,3,2,8,5,7,6]=>[4,1,3,2,8,5,7,6]=>0110011=>1100110=>2
[5,1,3,2,8,4,7,6]=>[5,1,3,2,8,4,7,6]=>0101011=>1101010=>2
[6,1,3,2,8,4,7,5]=>[5,1,3,2,8,4,7,6]=>0101011=>1101010=>2
[8,4,7,1,3,2,6,5]=>[8,4,7,1,3,2,6,5]=>0100111=>1110010=>3
[7,4,8,1,3,2,6,5]=>[5,4,8,1,3,2,7,6]=>0101011=>1101010=>2
[7,3,8,1,4,2,6,5]=>[5,2,8,1,4,3,7,6]=>0011011=>1101100=>2
[8,3,7,1,4,2,6,5]=>[8,2,7,1,4,3,6,5]=>0010111=>1110100=>3
[6,1,4,2,8,3,7,5]=>[5,1,4,2,8,3,7,6]=>0011011=>1101100=>2
[5,1,4,2,8,3,7,6]=>[5,1,4,2,8,3,7,6]=>0011011=>1101100=>2
[4,1,5,2,8,3,7,6]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[3,1,5,2,8,4,7,6]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[2,1,5,3,8,4,7,6]=>[2,1,5,3,8,4,7,6]=>1001011=>1101001=>2
[2,1,6,3,8,4,7,5]=>[2,1,5,3,8,4,7,6]=>1001011=>1101001=>2
[3,1,6,2,8,4,7,5]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[4,1,6,2,8,3,7,5]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[5,1,6,2,8,3,7,4]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[6,1,5,2,8,3,7,4]=>[5,1,4,2,8,3,7,6]=>0011011=>1101100=>2
[8,3,7,1,5,2,6,4]=>[8,2,7,1,4,3,6,5]=>0010111=>1110100=>3
[7,3,8,1,5,2,6,4]=>[5,2,8,1,4,3,7,6]=>0011011=>1101100=>2
[6,2,7,3,8,1,5,4]=>[2,1,5,4,8,3,7,6]=>1001011=>1101001=>2
[6,2,8,3,7,1,5,4]=>[4,1,8,3,7,2,6,5]=>0010111=>1110100=>3
[8,3,7,2,6,1,5,4]=>[8,3,7,2,6,1,5,4]=>0001111=>1111000=>4
[5,1,8,3,7,2,6,4]=>[4,1,8,3,7,2,6,5]=>0010111=>1110100=>3
[4,1,8,3,7,2,6,5]=>[4,1,8,3,7,2,6,5]=>0010111=>1110100=>3
[3,1,8,4,7,2,6,5]=>[2,1,8,4,7,3,6,5]=>1000111=>1110001=>3
[2,1,8,4,7,3,6,5]=>[2,1,8,4,7,3,6,5]=>1000111=>1110001=>3
[2,1,7,4,8,3,6,5]=>[2,1,5,4,8,3,7,6]=>1001011=>1101001=>2
[3,1,7,4,8,2,6,5]=>[2,1,5,4,8,3,7,6]=>1001011=>1101001=>2
[4,1,7,3,8,2,6,5]=>[2,1,5,4,8,3,7,6]=>1001011=>1101001=>2
[5,1,7,3,8,2,6,4]=>[2,1,5,4,8,3,7,6]=>1001011=>1101001=>2
[7,3,8,2,6,1,5,4]=>[4,3,8,2,7,1,6,5]=>0010111=>1110100=>3
[8,2,6,3,7,1,5,4]=>[8,1,4,3,7,2,6,5]=>0010111=>1110100=>3
[7,2,6,3,8,1,5,4]=>[5,1,4,3,8,2,7,6]=>0011011=>1101100=>2
[3,4,2,6,8,1,5,7]=>[1,4,3,6,8,2,5,7]=>0010001=>1000100=>1
[5,3,6,2,8,1,4,7]=>[4,3,6,2,8,1,5,7]=>0010101=>1010100=>1
[5,3,6,2,4,8,1,7]=>[3,2,6,1,5,8,4,7]=>0100101=>1010010=>1
[5,7,3,8,2,4,1,6]=>[3,6,2,8,1,5,4,7]=>0001101=>1011000=>1
[7,4,2,5,8,3,1,6]=>[6,2,1,5,8,4,3,7]=>1010101=>1010101=>1
[4,5,2,6,3,8,1,7]=>[1,3,2,6,5,8,4,7]=>0100101=>1010010=>1
[5,6,2,8,1,3,4,7]=>[4,6,2,8,1,3,5,7]=>0000101=>1010000=>1
[3,5,6,1,4,8,2,7]=>[1,3,6,2,5,8,4,7]=>0000101=>1010000=>1
[4,1,5,6,3,8,2,7]=>[2,1,3,6,5,8,4,7]=>1000101=>1010001=>1
[4,5,1,6,3,8,2,7]=>[1,3,2,6,5,8,4,7]=>0100101=>1010010=>1
[4,5,6,3,2,8,1,7]=>[1,2,6,5,4,8,3,7]=>0001101=>1011000=>1
[7,4,5,3,8,2,1,6]=>[6,1,5,4,8,3,2,7]=>0101101=>1011010=>1
[7,4,5,3,8,2,6,1]=>[5,1,4,3,8,2,7,6]=>0011011=>1101100=>2
[6,7,4,8,3,2,5,1]=>[1,5,4,8,3,2,7,6]=>0101011=>1101010=>2
[6,7,4,8,3,2,1,5]=>[1,6,5,8,4,3,2,7]=>0110101=>1010110=>1
[6,7,4,1,8,3,2,5]=>[2,6,5,1,8,4,3,7]=>0011101=>1011100=>1
[7,4,5,3,1,8,2,6]=>[6,2,5,4,1,8,3,7]=>0011101=>1011100=>1
[5,3,7,8,1,4,2,6]=>[3,2,6,8,1,5,4,7]=>0101001=>1001010=>1
[7,5,8,2,4,6,1,3]=>[5,4,8,1,3,7,2,6]=>0001011=>1101000=>2
[7,3,5,8,1,4,6,2]=>[5,2,4,8,1,3,7,6]=>0001011=>1101000=>2
[6,7,4,8,3,1,5,2]=>[1,5,4,8,3,2,7,6]=>0101011=>1101010=>2
[5,6,7,3,8,4,2,1]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[5,6,7,3,1,8,4,2]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[5,6,1,7,3,8,4,2]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[5,1,6,7,3,8,4,2]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[6,4,7,1,8,3,5,2]=>[3,2,5,1,8,4,7,6]=>0101011=>1101010=>2
[6,7,8,3,1,4,5,2]=>[3,5,8,2,1,4,7,6]=>1000011=>1100001=>2
[6,7,2,8,4,5,1,3]=>[2,5,1,8,4,7,3,6]=>0001011=>1101000=>2
[6,7,2,8,4,1,3,5]=>[3,6,2,8,5,1,4,7]=>0001101=>1011000=>1
[5,1,6,7,3,2,8,4]=>[2,1,3,6,5,4,8,7]=>1001101=>1011001=>1
[5,6,1,7,3,2,8,4]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[5,6,7,3,2,8,4,1]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[5,6,2,7,3,8,4,1]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[5,6,2,7,3,1,8,4]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[6,1,7,4,2,8,3,5]=>[3,1,6,5,2,8,4,7]=>0101101=>1011010=>1
[6,7,2,1,8,3,4,5]=>[4,6,2,1,8,3,5,7]=>1000101=>1010001=>1
[7,4,2,5,1,8,3,6]=>[6,3,2,5,1,8,4,7]=>0101101=>1011010=>1
[6,7,4,2,1,8,3,5]=>[3,6,5,2,1,8,4,7]=>1001101=>1011001=>1
[6,7,4,2,8,3,1,5]=>[2,6,5,1,8,4,3,7]=>0011101=>1011100=>1
[6,7,4,2,8,3,5,1]=>[2,5,4,1,8,3,7,6]=>0011011=>1101100=>2
[3,6,7,2,8,4,5,1]=>[1,3,5,2,8,4,7,6]=>0001011=>1101000=>2
[3,6,7,2,1,8,4,5]=>[1,4,6,3,2,8,5,7]=>0100101=>1010010=>1
[5,7,3,8,2,1,4,6]=>[4,6,3,8,2,1,5,7]=>1000101=>1010001=>1
[3,4,7,8,2,1,5,6]=>[1,4,6,8,3,2,5,7]=>0100001=>1000010=>1
[3,4,7,8,2,6,1,5]=>[1,2,5,8,4,7,3,6]=>0000011=>1100000=>2
[5,7,3,8,2,6,1,4]=>[1,5,4,8,3,7,2,6]=>0001011=>1101000=>2
[3,6,7,2,8,5,1,4]=>[1,2,5,4,8,7,3,6]=>0001011=>1101000=>2
[3,6,7,8,5,2,1,4]=>[1,2,5,8,7,4,3,6]=>0010011=>1100100=>2
[3,6,7,8,5,2,4,1]=>[1,2,4,8,7,3,6,5]=>0000111=>1110000=>3
[6,4,7,8,2,5,3,1]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[6,7,2,8,5,1,3,4]=>[3,5,2,8,7,1,4,6]=>0001011=>1101000=>2
[5,1,6,2,7,8,4,3]=>[2,1,4,3,5,8,7,6]=>1010011=>1100101=>2
[5,6,2,1,7,8,4,3]=>[1,4,3,2,5,8,7,6]=>0110011=>1100110=>2
[5,6,2,7,1,8,4,3]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[5,6,2,7,8,4,3,1]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010=>3
[5,6,7,2,8,4,3,1]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[5,6,7,2,1,8,4,3]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[5,6,1,7,2,8,4,3]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[5,1,6,7,2,8,4,3]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[6,4,7,1,8,2,5,3]=>[3,2,5,1,8,4,7,6]=>0101011=>1101010=>2
[3,6,7,1,8,5,2,4]=>[1,3,5,2,8,7,4,6]=>0001011=>1101000=>2
[6,7,8,5,2,4,1,3]=>[1,4,8,7,3,6,2,5]=>0000111=>1110000=>3
[6,7,8,3,5,1,4,2]=>[1,4,8,3,7,2,6,5]=>0000111=>1110000=>3
[4,6,7,8,1,5,3,2]=>[1,2,4,8,3,7,6,5]=>0000111=>1110000=>3
[5,1,6,7,8,4,3,2]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001=>3
[5,6,1,7,8,4,3,2]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010=>3
[5,6,7,1,8,4,3,2]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[8,6,1,3,4,2,5,7]=>[8,6,1,2,4,3,5,7]=>0010101=>1010100=>1
[8,3,2,5,1,6,4,7]=>[8,2,1,4,3,6,5,7]=>1010101=>1010101=>1
[8,5,3,6,2,4,1,7]=>[8,3,2,6,1,5,4,7]=>0101101=>1011010=>1
[5,3,2,7,4,1,8,6]=>[3,2,1,6,5,4,8,7]=>1101101=>1011011=>1
[7,5,3,8,2,4,6,1]=>[5,4,2,8,1,3,7,6]=>0011011=>1101100=>2
[7,2,4,5,8,3,6,1]=>[5,1,2,4,8,3,7,6]=>0001011=>1101000=>2
[2,4,5,3,7,1,8,6]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100=>1
[8,2,4,5,6,3,1,7]=>[8,1,2,3,6,5,4,7]=>0001101=>1011000=>1
[8,2,4,5,6,1,3,7]=>[8,1,2,4,6,3,5,7]=>0000101=>1010000=>1
[8,1,2,4,5,6,3,7]=>[8,1,2,3,4,6,5,7]=>0000101=>1010000=>1
[8,2,5,1,3,6,4,7]=>[8,2,4,1,3,6,5,7]=>0010101=>1010100=>1
[8,5,6,2,1,4,3,7]=>[8,3,6,2,1,5,4,7]=>1001101=>1011001=>1
[8,5,3,6,4,1,2,7]=>[8,3,2,6,5,1,4,7]=>0101101=>1011010=>1
[8,4,1,5,6,3,2,7]=>[8,2,1,3,6,5,4,7]=>1001101=>1011001=>1
[8,1,4,5,6,3,2,7]=>[8,1,2,3,6,5,4,7]=>0001101=>1011000=>1
[4,5,3,7,2,1,8,6]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[7,4,5,8,3,2,6,1]=>[5,1,4,8,3,2,7,6]=>0101011=>1101010=>2
[4,3,6,7,2,8,5,1]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[4,3,6,7,2,8,1,5]=>[2,1,3,6,5,8,4,7]=>1000101=>1010001=>1
[1,4,3,6,7,2,8,5]=>[1,3,2,4,6,5,8,7]=>0100101=>1010010=>1
[4,1,5,3,7,2,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,3,4,7,1,2,8,6]=>[4,1,3,6,2,5,8,7]=>0010101=>1010100=>1
[7,5,8,2,1,4,6,3]=>[5,4,8,2,1,3,7,6]=>1001011=>1101001=>2
[7,4,5,8,3,6,1,2]=>[5,1,4,8,3,7,2,6]=>0001011=>1101000=>2
[6,4,7,8,3,5,2,1]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[3,5,6,7,8,4,1,2]=>[1,2,3,5,8,7,4,6]=>0000011=>1100000=>2
[3,1,5,6,7,8,4,2]=>[2,1,3,4,5,8,7,6]=>1000011=>1100001=>2
[3,6,7,1,4,8,5,2]=>[1,3,5,2,4,8,7,6]=>0001011=>1101000=>2
[2,6,7,1,4,8,3,5]=>[1,3,6,2,5,8,4,7]=>0000101=>1010000=>1
[4,3,6,7,8,1,2,5]=>[2,1,4,6,8,3,5,7]=>1000001=>1000001=>1
[1,5,3,6,7,8,2,4]=>[1,3,2,4,6,8,5,7]=>0100001=>1000010=>1
[3,5,6,7,8,2,1,4]=>[1,2,3,6,8,5,4,7]=>0001001=>1001000=>1
[3,5,6,7,8,2,4,1]=>[1,2,3,5,8,4,7,6]=>0000011=>1100000=>2
[5,2,7,1,3,8,4,6]=>[4,2,6,1,3,8,5,7]=>0010101=>1010100=>1
[4,5,2,7,8,1,3,6]=>[1,4,3,6,8,2,5,7]=>0010001=>1000100=>1
[3,6,2,7,4,8,5,1]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[3,6,2,7,4,8,1,5]=>[1,3,2,6,5,8,4,7]=>0100101=>1010010=>1
[1,7,3,4,2,5,8,6]=>[1,6,2,4,3,5,8,7]=>0010101=>1010100=>1
[4,7,2,1,3,5,8,6]=>[4,6,2,1,3,5,8,7]=>1000101=>1010001=>1
[7,8,4,2,1,3,6,5]=>[5,8,4,2,1,3,7,6]=>1010011=>1100101=>2
[7,8,1,3,4,2,6,5]=>[5,8,1,2,4,3,7,6]=>0010011=>1100100=>2
[7,8,3,4,2,1,6,5]=>[5,8,1,4,3,2,7,6]=>0110011=>1100110=>2
[3,6,2,7,1,8,5,4]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[6,4,7,8,5,2,3,1]=>[2,1,4,8,7,3,6,5]=>1000111=>1110001=>3
[7,4,5,8,6,2,1,3]=>[5,1,4,8,7,3,2,6]=>0101011=>1101010=>2
[7,5,8,2,1,6,3,4]=>[5,4,8,2,1,7,3,6]=>1001011=>1101001=>2
[6,2,7,1,3,8,5,4]=>[3,2,5,1,4,8,7,6]=>0101011=>1101010=>2
[4,6,1,7,8,5,2,3]=>[1,3,2,5,8,7,4,6]=>0100011=>1100010=>2
[5,2,6,7,8,4,1,3]=>[2,1,3,5,8,7,4,6]=>1000011=>1100001=>2
[5,2,6,7,8,4,3,1]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001=>3
[2,5,6,7,8,4,1,3]=>[1,2,3,5,8,7,4,6]=>0000011=>1100000=>2
[1,5,2,6,7,8,4,3]=>[1,3,2,4,5,8,7,6]=>0100011=>1100010=>2
[1,6,4,7,8,5,2,3]=>[1,3,2,5,8,7,4,6]=>0100011=>1100010=>2
[2,6,7,1,3,8,5,4]=>[1,3,5,2,4,8,7,6]=>0001011=>1101000=>2
[6,7,8,2,1,5,4,3]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[6,7,3,8,5,1,4,2]=>[1,4,3,8,7,2,6,5]=>0010111=>1110100=>3
[6,4,7,8,5,3,1,2]=>[2,1,4,8,7,6,3,5]=>1000111=>1110001=>3
[8,4,3,6,5,1,2,7]=>[8,3,2,6,5,1,4,7]=>0101101=>1011010=>1
[1,5,6,3,4,8,7,2]=>[1,3,5,2,4,8,7,6]=>0001011=>1101000=>2
[5,7,6,2,4,3,1,8]=>[2,7,6,1,5,4,3,8]=>0011110=>0111100=>0
[8,7,5,4,1,3,2,6]=>[8,7,5,4,1,3,2,6]=>0111011=>1101110=>2
[6,8,5,4,2,1,3,7]=>[6,8,5,4,2,1,3,7]=>1011001=>1001101=>1
[4,8,2,6,5,1,3,7]=>[3,8,2,6,5,1,4,7]=>0001101=>1011000=>1
[3,2,8,6,5,1,4,7]=>[3,2,8,6,5,1,4,7]=>0101101=>1011010=>1
[5,1,6,2,4,8,7,3]=>[3,1,5,2,4,8,7,6]=>0101011=>1101010=>2
[6,1,5,4,2,8,7,3]=>[5,1,4,3,2,8,7,6]=>0111011=>1101110=>2
[7,1,5,4,8,2,6,3]=>[5,1,4,3,8,2,7,6]=>0011011=>1101100=>2
[1,8,6,7,4,5,3,2]=>[1,8,3,7,2,6,5,4]=>0001111=>1111000=>4
[8,1,6,7,4,5,2,3]=>[8,1,4,7,3,6,2,5]=>0000111=>1110000=>3
[7,1,6,8,4,2,5,3]=>[5,1,4,8,3,2,7,6]=>0101011=>1101010=>2
[5,1,7,2,8,4,6,3]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[3,2,8,7,1,5,4,6]=>[3,2,8,7,1,5,4,6]=>0101011=>1101010=>2
[4,8,2,7,1,5,3,6]=>[3,8,2,7,1,5,4,6]=>0001011=>1101000=>2
[5,8,7,2,1,4,3,6]=>[5,8,7,2,1,4,3,6]=>1010011=>1100101=>2
[6,8,7,1,2,4,3,5]=>[5,8,7,1,2,4,3,6]=>0010011=>1100100=>2
[7,8,6,1,4,2,3,5]=>[5,8,7,1,4,2,3,6]=>0010011=>1100100=>2
[8,7,6,1,4,3,2,5]=>[8,7,6,1,4,3,2,5]=>0110111=>1110110=>3
[1,7,6,8,4,3,5,2]=>[1,5,4,8,3,2,7,6]=>0101011=>1101010=>2
[1,6,7,8,3,4,5,2]=>[1,3,5,8,2,4,7,6]=>0000011=>1100000=>2
[7,6,8,1,3,2,4,5]=>[6,5,8,1,3,2,4,7]=>0100101=>1010010=>1
[5,7,8,2,1,3,4,6]=>[4,6,8,2,1,3,5,7]=>1000001=>1000001=>1
[4,7,2,8,1,3,5,6]=>[4,6,2,8,1,3,5,7]=>0000101=>1010000=>1
[3,2,6,8,4,1,5,7]=>[2,1,6,8,4,3,5,7]=>1010001=>1000101=>1
[4,6,2,8,3,1,5,7]=>[4,6,1,8,3,2,5,7]=>0100101=>1010010=>1
[6,5,8,3,2,1,4,7]=>[6,5,8,3,2,1,4,7]=>1100101=>1010011=>1
[8,5,7,3,1,4,2,6]=>[8,5,7,2,1,4,3,6]=>1010011=>1100101=>2
[1,5,7,3,8,4,6,2]=>[1,3,5,2,8,4,7,6]=>0001011=>1101000=>2
[8,4,3,7,1,5,2,6]=>[8,3,2,7,1,5,4,6]=>0101011=>1101010=>2
[6,4,3,8,2,1,5,7]=>[6,4,3,8,2,1,5,7]=>1010101=>1010101=>1
[4,5,2,3,1,8,7,6]=>[2,5,1,4,3,8,7,6]=>0011011=>1101100=>2
[6,4,3,1,2,8,7,5]=>[5,4,3,1,2,8,7,6]=>0111011=>1101110=>2
[7,4,3,1,8,2,6,5]=>[5,4,3,1,8,2,7,6]=>0111011=>1101110=>2
[8,4,3,1,7,6,2,5]=>[8,4,3,1,7,6,2,5]=>0110111=>1110110=>3
[1,5,8,3,7,6,4,2]=>[1,3,8,2,7,6,5,4]=>0001111=>1111000=>4
[8,5,1,3,7,6,2,4]=>[8,4,1,3,7,6,2,5]=>0010111=>1110100=>3
[6,5,1,3,2,8,7,4]=>[5,4,1,3,2,8,7,6]=>0111011=>1101110=>2
[5,6,1,2,3,8,7,4]=>[3,5,1,2,4,8,7,6]=>0001011=>1101000=>2
[3,2,6,1,4,8,7,5]=>[3,2,5,1,4,8,7,6]=>0101011=>1101010=>2
[3,2,7,1,8,4,6,5]=>[3,2,5,1,8,4,7,6]=>0101011=>1101010=>2
[5,7,1,2,8,3,6,4]=>[3,5,1,2,8,4,7,6]=>0001011=>1101000=>2
[6,7,1,8,2,3,5,4]=>[3,5,1,8,2,4,7,6]=>0001011=>1101000=>2
[8,6,1,7,3,5,2,4]=>[8,4,1,7,3,6,2,5]=>0010111=>1110100=>3
[1,7,8,6,5,3,4,2]=>[1,3,8,7,6,2,5,4]=>0001111=>1111000=>4
[8,7,1,6,5,3,2,4]=>[8,7,1,6,5,3,2,4]=>0101111=>1111010=>4
[7,8,1,6,5,2,3,4]=>[4,8,1,7,6,2,3,5]=>0000111=>1110000=>3
[6,8,1,7,2,5,3,4]=>[4,8,1,7,2,6,3,5]=>0000111=>1110000=>3
[5,8,1,2,7,6,3,4]=>[4,8,1,2,7,6,3,5]=>0000111=>1110000=>3
[4,8,2,1,7,6,3,5]=>[4,8,2,1,7,6,3,5]=>1000111=>1110001=>3
[3,2,8,1,7,6,4,5]=>[3,2,8,1,7,6,4,5]=>0100111=>1110010=>3
[4,1,2,8,7,6,5,3]=>[3,1,2,8,7,6,5,4]=>0101111=>1111010=>4
[5,1,8,2,7,6,4,3]=>[3,1,8,2,7,6,5,4]=>0101111=>1111010=>4
[7,1,8,6,5,2,4,3]=>[3,1,8,7,6,2,5,4]=>0101111=>1111010=>4
[8,1,7,6,5,4,2,3]=>[8,1,7,6,5,4,2,3]=>0011111=>1111100=>5
[3,1,6,2,4,8,7,5]=>[3,1,5,2,4,8,7,6]=>0101011=>1101010=>2
[3,1,5,2,4,8,7,6]=>[3,1,5,2,4,8,7,6]=>0101011=>1101010=>2
[4,5,1,2,3,8,7,6]=>[3,5,1,2,4,8,7,6]=>0001011=>1101000=>2
[4,6,1,2,3,8,7,5]=>[3,5,1,2,4,8,7,6]=>0001011=>1101000=>2
[1,6,5,3,4,8,7,2]=>[1,5,4,2,3,8,7,6]=>0011011=>1101100=>2
[6,1,5,2,4,8,7,3]=>[5,1,4,2,3,8,7,6]=>0011011=>1101100=>2
[6,5,1,2,3,8,7,4]=>[5,4,1,2,3,8,7,6]=>0011011=>1101100=>2
[6,4,1,2,3,8,7,5]=>[5,4,1,2,3,8,7,6]=>0011011=>1101100=>2
[5,4,1,2,3,8,7,6]=>[5,4,1,2,3,8,7,6]=>0011011=>1101100=>2
[5,4,1,2,7,3,6,8]=>[5,4,1,2,7,3,6,8]=>0011010=>0101100=>0
[6,4,1,8,2,3,5,7]=>[6,4,1,8,2,3,5,7]=>0010101=>1010100=>1
[7,4,1,2,8,3,6,5]=>[5,4,1,2,8,3,7,6]=>0011011=>1101100=>2
[7,5,1,2,8,3,6,4]=>[5,4,1,2,8,3,7,6]=>0011011=>1101100=>2
[7,1,5,2,8,4,6,3]=>[5,1,4,2,8,3,7,6]=>0011011=>1101100=>2
[1,7,5,3,8,4,6,2]=>[1,5,4,2,8,3,7,6]=>0011011=>1101100=>2
[1,8,5,3,7,4,6,2]=>[1,8,4,2,7,3,6,5]=>0010111=>1110100=>3
[8,1,5,2,7,4,6,3]=>[8,1,4,2,7,3,6,5]=>0010111=>1110100=>3
[8,5,1,2,7,3,6,4]=>[8,4,1,2,7,3,6,5]=>0010111=>1110100=>3
[8,4,1,2,7,3,6,5]=>[8,4,1,2,7,3,6,5]=>0010111=>1110100=>3
[8,4,1,7,2,3,5,6]=>[8,4,1,7,2,3,5,6]=>0010011=>1100100=>2
[7,4,1,6,2,3,5,8]=>[7,4,1,6,2,3,5,8]=>0010110=>0110100=>0
[8,6,1,7,2,3,5,4]=>[8,4,1,7,2,3,6,5]=>0010111=>1110100=>3
[8,1,6,7,2,4,5,3]=>[8,1,4,7,2,3,6,5]=>0000111=>1110000=>3
[1,8,6,7,3,4,5,2]=>[1,8,4,7,2,3,6,5]=>0000111=>1110000=>3
[1,7,6,8,3,4,5,2]=>[1,5,4,8,2,3,7,6]=>0001011=>1101000=>2
[7,1,6,8,2,4,5,3]=>[5,1,4,8,2,3,7,6]=>0001011=>1101000=>2
[7,6,1,8,2,3,5,4]=>[5,4,1,8,2,3,7,6]=>0011011=>1101100=>2
[4,7,1,2,8,3,6,5]=>[3,5,1,2,8,4,7,6]=>0001011=>1101000=>2
[3,1,7,2,8,4,6,5]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[1,4,3,8,7,5,6,2]=>[1,3,2,8,7,4,6,5]=>0100111=>1110010=>3
[4,1,2,8,7,5,6,3]=>[3,1,2,8,7,4,6,5]=>0100111=>1110010=>3
[3,1,2,8,7,5,6,4]=>[3,1,2,8,7,4,6,5]=>0100111=>1110010=>3
[3,1,8,2,7,4,6,5]=>[3,1,8,2,7,4,6,5]=>0100111=>1110010=>3
[3,1,8,7,2,4,5,6]=>[3,1,8,7,2,4,5,6]=>0100011=>1100010=>2
[3,1,7,6,2,4,5,8]=>[3,1,7,6,2,4,5,8]=>0100110=>0110010=>0
[4,7,1,6,2,3,5,8]=>[4,7,1,6,2,3,5,8]=>0000110=>0110000=>0
[4,8,1,6,2,3,5,7]=>[4,8,1,6,2,3,5,7]=>0000101=>1010000=>1
[4,8,1,7,2,3,5,6]=>[4,8,1,7,2,3,5,6]=>0000011=>1100000=>2
[4,8,1,2,7,3,6,5]=>[4,8,1,2,7,3,6,5]=>0000111=>1110000=>3
[5,8,1,2,7,3,6,4]=>[4,8,1,2,7,3,6,5]=>0000111=>1110000=>3
[1,6,8,7,3,4,5,2]=>[1,4,8,7,2,3,6,5]=>0000111=>1110000=>3
[6,1,8,7,2,4,5,3]=>[4,1,8,7,2,3,6,5]=>0010111=>1110100=>3
[6,8,7,1,2,3,4,5]=>[5,8,7,1,2,3,4,6]=>0000011=>1100000=>2
[5,8,7,1,2,3,4,6]=>[5,8,7,1,2,3,4,6]=>0000011=>1100000=>2
[5,7,6,1,2,3,4,8]=>[4,7,6,1,2,3,5,8]=>0000110=>0110000=>0
[7,1,8,6,2,4,5,3]=>[4,1,8,7,2,3,6,5]=>0010111=>1110100=>3
[1,7,8,6,3,4,5,2]=>[1,4,8,7,2,3,6,5]=>0000111=>1110000=>3
[8,7,1,6,2,3,5,4]=>[8,7,1,6,2,3,5,4]=>0001111=>1111000=>4
[3,2,5,1,6,4,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,5,4,7,1,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,5,3,7,6,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,5,3,7,1,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,5,3,6,1,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,5,1,6,3,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,5,4,6,2,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,5,3,6,2,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,5,1,6,2,8,7]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,5,2,7,1,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,6,2,7,5,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,6,2,7,1,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,6,1,7,2,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,5,1,7,2,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,5,4,7,2,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,5,4,7,3,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,5,4,7,6,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,5,3,7,6,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,5,1,7,6,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,6,1,7,5,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,3,6,5,7,1,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,3,6,4,7,2,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,3,6,4,7,1,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,3,6,1,7,4,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,1,6,3,7,4,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,6,3,7,5,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,6,4,7,5,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,6,4,7,5,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,6,4,7,3,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,6,4,7,2,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,6,3,7,2,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,1,6,3,7,2,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,3,6,1,7,2,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,3,6,2,7,1,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,3,6,2,7,4,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,2,6,3,7,4,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,2,6,3,7,1,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,2,6,1,7,3,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,5,1,7,3,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,6,1,7,3,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,6,3,7,1,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,6,3,7,5,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,6,4,7,5,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,6,4,7,1,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,6,1,7,4,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,5,1,7,4,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,4,1,7,5,8,6]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,4,2,7,6,8,5]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,5,1,7,6,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,6,1,7,5,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,2,6,5,7,1,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,6,5,7,3,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,6,5,7,1,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,6,1,7,5,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,2,5,1,7,6,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,5,2,7,6,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,5,2,7,6,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,5,3,7,6,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,6,3,7,5,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,6,2,7,5,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,6,2,7,5,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,1,6,2,7,4,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,2,6,1,7,4,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,2,6,4,7,1,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,2,6,4,7,3,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,4,6,2,7,3,8,1]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,4,6,2,7,1,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,4,6,1,7,2,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,1,6,4,7,2,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,6,5,7,2,8,3]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,6,5,7,2,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[2,1,6,5,7,3,8,4]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,6,5,7,4,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[4,1,6,5,7,3,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,1,6,4,7,3,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,4,6,1,7,3,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[5,4,6,3,7,1,8,2]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101=>1
[8,3,5,2,1,6,4,7]=>[8,1,4,3,2,6,5,7]=>0110101=>1010110=>1
[3,7,5,2,4,1,8,6]=>[2,6,5,1,4,3,8,7]=>0011101=>1011100=>1
[8,3,7,5,2,4,6,1]=>[8,2,7,4,1,3,6,5]=>0010111=>1110100=>3
[2,4,5,7,3,1,8,6]=>[1,2,3,6,5,4,8,7]=>0001101=>1011000=>1
[8,2,4,6,5,3,1,7]=>[8,1,2,6,5,4,3,7]=>0011101=>1011100=>1
[8,2,5,4,6,1,3,7]=>[8,1,4,3,6,2,5,7]=>0010101=>1010100=>1
[8,6,1,4,5,3,2,7]=>[8,6,1,2,5,4,3,7]=>0011101=>1011100=>1
[8,1,5,6,4,3,2,7]=>[8,1,2,6,5,4,3,7]=>0011101=>1011100=>1
[5,7,4,3,2,1,8,6]=>[1,6,5,4,3,2,8,7]=>0111101=>1011110=>1
[4,6,8,3,2,7,5,1]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[4,7,6,3,2,8,1,5]=>[1,6,5,4,3,8,2,7]=>0011101=>1011100=>1
[1,4,6,7,3,2,8,5]=>[1,2,3,6,5,4,8,7]=>0001101=>1011000=>1
[5,4,7,3,1,8,2,6]=>[3,2,6,5,1,8,4,7]=>0101101=>1011010=>1
[3,7,5,1,4,2,8,6]=>[2,6,5,1,4,3,8,7]=>0011101=>1011100=>1
[5,7,4,2,1,3,8,6]=>[3,6,5,2,1,4,8,7]=>1001101=>1011001=>1
[8,3,7,5,1,4,6,2]=>[8,2,7,4,1,3,6,5]=>0010111=>1110100=>3
[8,4,1,7,5,3,6,2]=>[8,2,1,7,4,3,6,5]=>1010111=>1110101=>3
[4,6,3,8,7,1,5,2]=>[1,4,3,8,7,2,6,5]=>0010111=>1110100=>3
[1,7,4,8,6,3,5,2]=>[1,4,3,8,7,2,6,5]=>0010111=>1110100=>3
[8,4,7,6,3,5,2,1]=>[8,2,7,6,1,5,4,3]=>0011111=>1111100=>5
[3,1,5,8,6,7,4,2]=>[2,1,3,8,4,7,6,5]=>1000111=>1110001=>3
[3,6,4,1,8,7,5,2]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110=>3
[8,2,6,1,4,7,5,3]=>[8,2,4,1,3,7,6,5]=>0010111=>1110100=>3
[2,7,6,8,1,4,3,5]=>[2,6,5,8,1,4,3,7]=>0010101=>1010100=>1
[3,7,1,6,4,8,2,5]=>[2,6,1,5,4,8,3,7]=>0001101=>1011000=>1
[1,7,3,5,6,8,2,4]=>[1,6,2,3,5,8,4,7]=>0000101=>1010000=>1
[1,3,6,7,5,8,2,4]=>[1,2,3,6,5,8,4,7]=>0000101=>1010000=>1
[3,7,6,5,8,2,1,4]=>[1,6,5,4,8,3,2,7]=>0101101=>1011010=>1
[3,6,8,5,7,2,4,1]=>[1,4,8,3,7,2,6,5]=>0000111=>1110000=>3
[2,3,5,7,6,8,1,4]=>[1,2,3,6,5,8,4,7]=>0000101=>1010000=>1
[2,1,6,5,7,8,3,4]=>[2,1,4,3,6,8,5,7]=>1010001=>1000101=>1
[4,2,6,8,7,3,5,1]=>[2,1,4,8,7,3,6,5]=>1000111=>1110001=>3
[3,7,2,6,4,8,1,5]=>[2,6,1,5,4,8,3,7]=>0001101=>1011000=>1
[3,2,6,1,4,7,8,5]=>[3,2,5,1,4,6,8,7]=>0101001=>1001010=>1
[5,3,7,2,1,8,4,6]=>[4,3,6,2,1,8,5,7]=>1010101=>1010101=>1
[4,7,3,2,1,5,8,6]=>[4,6,3,2,1,5,8,7]=>1100101=>1010011=>1
[8,7,6,1,3,4,2,5]=>[8,7,6,1,2,4,3,5]=>0010111=>1110100=>3
[8,7,6,3,5,2,4,1]=>[8,7,6,2,5,1,4,3]=>0011111=>1111100=>5
[4,6,8,2,1,7,5,3]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[8,4,1,5,7,2,6,3]=>[8,2,1,4,7,3,6,5]=>1000111=>1110001=>3
[8,5,7,2,1,3,6,4]=>[8,4,7,2,1,3,6,5]=>1000111=>1110001=>3
[8,2,6,7,1,3,5,4]=>[8,2,4,7,1,3,6,5]=>0000111=>1110000=>3
[8,3,6,1,7,5,2,4]=>[8,2,4,1,7,6,3,5]=>0010111=>1110100=>3
[4,6,1,8,7,2,5,3]=>[2,4,1,8,7,3,6,5]=>0010111=>1110100=>3
[8,1,2,5,6,7,4,3]=>[8,1,2,3,4,7,6,5]=>0000111=>1110000=>3
[2,1,7,8,5,6,4,3]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[8,2,5,7,6,4,3,1]=>[8,1,2,7,6,5,4,3]=>0011111=>1111100=>5
[1,7,2,5,8,6,4,3]=>[1,4,2,3,8,7,6,5]=>0010111=>1110100=>3
[2,7,8,6,1,3,5,4]=>[2,4,8,7,1,3,6,5]=>0000111=>1110000=>3
[8,7,6,3,5,1,4,2]=>[8,7,6,2,5,1,4,3]=>0011111=>1111100=>5
[8,4,7,6,5,1,3,2]=>[8,2,7,6,5,1,4,3]=>0011111=>1111100=>5
[8,7,1,5,6,4,3,2]=>[8,7,1,2,6,5,4,3]=>0011111=>1111100=>5
[8,1,6,7,5,4,3,2]=>[8,1,2,7,6,5,4,3]=>0011111=>1111100=>5
[6,5,3,1,2,4,8,7]=>[6,5,3,1,2,4,8,7]=>0101101=>1011010=>1
[4,6,3,5,1,2,8,7]=>[3,6,2,5,1,4,8,7]=>0001101=>1011000=>1
[8,5,3,7,2,1,4,6]=>[8,5,3,7,2,1,4,6]=>1001011=>1101001=>2
[6,8,1,4,5,7,3,2]=>[4,8,1,2,3,7,6,5]=>0000111=>1110000=>3
[3,6,2,4,5,1,8,7]=>[2,6,1,3,5,4,8,7]=>0001101=>1011000=>1
[2,6,1,4,5,3,8,7]=>[2,6,1,3,5,4,8,7]=>0001101=>1011000=>1
[5,6,3,2,1,4,8,7]=>[4,6,3,2,1,5,8,7]=>1100101=>1010011=>1
[5,4,3,6,1,2,8,7]=>[4,3,2,6,1,5,8,7]=>0110101=>1010110=>1
[3,1,6,4,5,2,8,7]=>[2,1,6,3,5,4,8,7]=>1001101=>1011001=>1
[8,3,7,4,5,1,2,6]=>[8,1,7,3,5,2,4,6]=>0001011=>1101000=>2
[5,8,7,4,2,6,3,1]=>[3,8,7,2,1,6,5,4]=>1001111=>1111001=>4
[2,8,7,4,1,6,3,5]=>[2,8,7,4,1,6,3,5]=>0010111=>1110100=>3
[8,1,7,4,2,6,3,5]=>[8,1,7,4,2,6,3,5]=>0010111=>1110100=>3
[3,7,8,4,5,1,2,6]=>[1,6,8,3,5,2,4,7]=>0001001=>1001000=>1
[2,1,8,7,5,3,4,6]=>[2,1,8,7,5,3,4,6]=>1001011=>1101001=>2
[2,1,6,8,5,7,3,4]=>[2,1,5,8,4,7,3,6]=>1000011=>1100001=>2
[5,6,3,8,1,7,2,4]=>[2,5,4,8,1,7,3,6]=>0001011=>1101000=>2
[7,6,1,4,5,8,3,2]=>[5,4,1,2,3,8,7,6]=>0011011=>1101100=>2
[3,7,6,4,5,8,2,1]=>[1,5,4,2,3,8,7,6]=>0011011=>1101100=>2
[8,5,7,4,1,6,3,2]=>[8,3,7,2,1,6,5,4]=>1001111=>1111001=>4
[2,5,8,4,7,6,1,3]=>[1,4,8,3,7,6,2,5]=>0000111=>1110000=>3
[2,4,8,3,5,6,7,1]=>[1,3,8,2,4,5,7,6]=>0000011=>1100000=>2
[4,1,8,3,5,6,7,2]=>[3,1,8,2,4,5,7,6]=>0100011=>1100010=>2
[3,8,4,2,5,6,7,1]=>[1,8,3,2,4,5,7,6]=>0100011=>1100010=>2
[8,4,1,3,5,6,7,2]=>[8,3,1,2,4,5,7,6]=>0100011=>1100010=>2
[7,5,8,4,3,6,1,2]=>[5,4,8,3,2,7,1,6]=>0101011=>1101010=>2
[2,1,5,8,4,6,7,3]=>[2,1,4,8,3,5,7,6]=>1000011=>1100001=>2
[2,1,4,8,3,6,7,5]=>[2,1,4,8,3,5,7,6]=>1000011=>1100001=>2
[6,4,3,8,2,1,7,5]=>[5,4,3,8,2,1,7,6]=>1011011=>1101101=>2
[7,3,8,4,2,6,1,5]=>[5,1,8,4,3,7,2,6]=>0011011=>1101100=>2
[8,3,1,2,5,6,7,4]=>[8,3,1,2,4,5,7,6]=>0100011=>1100010=>2
[3,1,8,2,5,6,7,4]=>[3,1,8,2,4,5,7,6]=>0100011=>1100010=>2
[2,3,8,1,5,6,7,4]=>[1,3,8,2,4,5,7,6]=>0000011=>1100000=>2
[4,3,8,2,5,6,7,1]=>[3,2,8,1,4,5,7,6]=>0100011=>1100010=>2
[4,8,2,3,5,6,7,1]=>[3,8,1,2,4,5,7,6]=>0000011=>1100000=>2
[3,8,2,1,5,6,7,4]=>[3,8,2,1,4,5,7,6]=>1000011=>1100001=>2
[2,8,1,3,5,6,7,4]=>[2,8,1,3,4,5,7,6]=>0000011=>1100000=>2
[8,1,2,3,5,6,7,4]=>[8,1,2,3,4,5,7,6]=>0000011=>1100000=>2
[7,8,2,4,3,6,1,5]=>[5,8,1,4,3,7,2,6]=>0010011=>1100100=>2
[2,1,7,8,5,4,3,6]=>[2,1,6,8,5,4,3,7]=>1011001=>1001101=>1
[5,7,3,8,1,4,2,6]=>[3,6,2,8,1,5,4,7]=>0001101=>1011000=>1
[8,7,1,4,3,6,2,5]=>[8,7,1,4,3,6,2,5]=>0010111=>1110100=>3
[3,8,7,4,2,6,1,5]=>[1,8,7,4,3,6,2,5]=>0010111=>1110100=>3
[5,7,8,4,3,6,2,1]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[5,6,3,8,4,2,7,1]=>[2,5,1,8,4,3,7,6]=>0011011=>1101100=>2
[8,6,3,1,4,2,7,5]=>[8,5,2,1,4,3,7,6]=>1011011=>1101101=>2
[7,5,3,8,2,4,1,6]=>[6,5,2,8,1,4,3,7]=>0011101=>1011100=>1
[8,6,3,5,1,2,7,4]=>[8,5,2,4,1,3,7,6]=>0011011=>1101100=>2
[5,8,3,2,6,1,7,4]=>[3,8,2,1,5,4,7,6]=>1001011=>1101001=>2
[4,5,3,8,6,2,7,1]=>[1,3,2,8,5,4,7,6]=>0101011=>1101010=>2
[3,5,8,4,7,6,2,1]=>[1,3,8,2,7,6,5,4]=>0001111=>1111000=>4
[5,8,2,4,7,6,1,3]=>[4,8,1,3,7,6,2,5]=>0000111=>1110000=>3
[8,7,5,4,1,6,2,3]=>[8,7,4,3,1,6,2,5]=>0110111=>1110110=>3
[2,7,6,4,5,8,1,3]=>[1,6,5,2,4,8,3,7]=>0001101=>1011000=>1
[7,1,6,4,5,8,2,3]=>[6,1,5,2,4,8,3,7]=>0001101=>1011000=>1
[2,1,7,6,5,8,3,4]=>[2,1,6,5,4,8,3,7]=>1001101=>1011001=>1
[2,1,8,5,3,6,7,4]=>[2,1,8,4,3,5,7,6]=>1010011=>1100101=>2
[6,8,3,5,2,1,7,4]=>[5,8,1,4,3,2,7,6]=>0110011=>1100110=>2
[7,8,5,4,2,6,1,3]=>[5,8,4,3,2,7,1,6]=>0110011=>1100110=>2
[8,1,4,2,5,6,7,3]=>[8,1,3,2,4,5,7,6]=>0100011=>1100010=>2
[2,8,4,1,5,6,7,3]=>[1,8,3,2,4,5,7,6]=>0100011=>1100010=>2
[4,8,1,2,5,6,7,3]=>[3,8,1,2,4,5,7,6]=>0000011=>1100000=>2
[3,4,8,1,5,6,7,2]=>[1,3,8,2,4,5,7,6]=>0000011=>1100000=>2
[3,4,2,8,5,6,7,1]=>[1,3,2,8,4,5,7,6]=>0100011=>1100010=>2
[2,4,1,8,5,6,7,3]=>[1,3,2,8,4,5,7,6]=>0100011=>1100010=>2
[4,1,2,8,5,6,7,3]=>[3,1,2,8,4,5,7,6]=>0100011=>1100010=>2
[8,4,2,1,5,6,7,3]=>[8,3,2,1,4,5,7,6]=>1100011=>1100011=>2
[6,5,3,2,8,1,7,4]=>[5,4,3,2,8,1,7,6]=>0111011=>1101110=>2
[2,1,5,3,8,6,7,4]=>[2,1,4,3,8,5,7,6]=>1010011=>1100101=>2
[8,3,4,1,5,6,7,2]=>[8,1,3,2,4,5,7,6]=>0100011=>1100010=>2
[4,3,1,8,5,6,7,2]=>[3,2,1,8,4,5,7,6]=>1100011=>1100011=>2
[3,1,4,8,5,6,7,2]=>[2,1,3,8,4,5,7,6]=>1000011=>1100001=>2
[6,3,7,4,5,8,2,1]=>[3,1,5,2,4,8,7,6]=>0101011=>1101010=>2
[6,7,2,4,5,8,3,1]=>[3,5,1,2,4,8,7,6]=>0001011=>1101000=>2
[5,1,7,4,8,6,3,2]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[2,5,7,4,8,6,3,1]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[5,6,3,7,1,8,4,2]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010=>2
[3,8,7,4,5,2,1,6]=>[1,8,7,2,5,4,3,6]=>0011011=>1101100=>2
[3,7,5,4,8,6,2,1]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110=>3
[5,7,1,4,8,6,2,3]=>[2,5,1,4,8,7,3,6]=>0001011=>1101000=>2
[5,6,3,1,8,2,7,4]=>[2,5,4,1,8,3,7,6]=>0011011=>1101100=>2
[4,6,3,5,8,2,7,1]=>[2,5,1,4,8,3,7,6]=>0001011=>1101000=>2
[4,6,3,8,1,2,7,5]=>[2,5,4,8,1,3,7,6]=>0001011=>1101000=>2
[3,7,8,4,1,6,2,5]=>[2,5,8,4,1,7,3,6]=>0010011=>1100100=>2
[3,2,5,1,6,8,4,7]=>[2,1,4,3,6,8,5,7]=>1010001=>1000101=>1
[3,6,2,5,4,8,1,7]=>[2,6,1,5,4,8,3,7]=>0001101=>1011000=>1
[3,5,2,4,7,1,8,6]=>[2,4,1,3,6,5,8,7]=>0010101=>1010100=>1
[3,5,8,2,4,7,6,1]=>[2,4,8,1,3,7,6,5]=>0000111=>1110000=>3
[4,2,5,8,3,7,6,1]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[4,2,6,5,3,8,1,7]=>[2,1,6,5,4,8,3,7]=>1001101=>1011001=>1
[5,4,2,1,6,8,3,7]=>[4,3,2,1,6,8,5,7]=>1110001=>1000111=>1
[6,3,5,1,4,8,2,7]=>[6,2,5,1,4,8,3,7]=>0001101=>1011000=>1
[4,6,1,5,3,8,2,7]=>[2,6,1,5,4,8,3,7]=>0001101=>1011000=>1
[5,1,6,4,3,8,2,7]=>[2,1,6,5,4,8,3,7]=>1001101=>1011001=>1
[5,4,3,2,7,1,8,6]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111=>1
[5,4,3,8,2,7,6,1]=>[4,3,2,8,1,7,6,5]=>0110111=>1110110=>3
[4,3,6,2,8,7,5,1]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[4,3,7,6,2,1,8,5]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101=>1
[6,4,3,1,7,2,8,5]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111=>1
[7,5,4,3,1,8,2,6]=>[6,5,4,3,1,8,2,7]=>0111101=>1011110=>1
[7,2,5,8,4,1,3,6]=>[6,2,5,8,4,1,3,7]=>0010101=>1010100=>1
[2,8,5,7,4,6,1,3]=>[1,8,4,7,3,6,2,5]=>0000111=>1110000=>3
[3,5,8,7,1,4,6,2]=>[2,4,8,7,1,3,6,5]=>0000111=>1110000=>3
[1,4,5,8,7,3,6,2]=>[1,2,4,8,7,3,6,5]=>0000111=>1110000=>3
[1,5,4,8,7,3,6,2]=>[1,4,3,8,7,2,6,5]=>0010111=>1110100=>3
[6,4,3,8,1,7,5,2]=>[4,3,2,8,1,7,6,5]=>0110111=>1110110=>3
[4,3,7,1,8,6,5,2]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[4,8,3,7,6,5,2,1]=>[2,8,1,7,6,5,4,3]=>0011111=>1111100=>5
[5,3,8,7,6,4,2,1]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101=>5
[7,5,3,1,8,6,4,2]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111=>3
[1,8,6,5,3,7,4,2]=>[1,8,4,3,2,7,6,5]=>0110111=>1110110=>3
[1,5,8,6,3,7,4,2]=>[1,2,8,4,3,7,6,5]=>0010111=>1110100=>3
[4,6,1,8,7,3,5,2]=>[2,4,1,8,7,3,6,5]=>0010111=>1110100=>3
[7,6,2,8,4,1,3,5]=>[6,5,2,8,4,1,3,7]=>0011101=>1011100=>1
[7,3,1,6,8,4,2,5]=>[6,2,1,5,8,4,3,7]=>1010101=>1010101=>1
[1,7,6,4,8,3,2,5]=>[1,6,5,4,8,3,2,7]=>0101101=>1011010=>1
[5,7,1,6,3,2,8,4]=>[2,6,1,5,4,3,8,7]=>0011101=>1011100=>1
[6,1,7,5,3,2,8,4]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101=>1
[7,6,5,3,2,1,8,4]=>[6,5,4,3,2,1,8,7]=>1111101=>1011111=>1
[6,5,3,2,8,7,4,1]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111=>3
[5,2,6,3,8,7,4,1]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[5,2,7,6,3,1,8,4]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101=>1
[6,5,2,1,7,3,8,4]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111=>1
[5,2,7,4,1,8,3,6]=>[3,2,6,5,1,8,4,7]=>0101101=>1011010=>1
[4,7,2,6,3,1,8,5]=>[2,6,1,5,4,3,8,7]=>0011101=>1011100=>1
[2,4,8,6,3,7,5,1]=>[1,2,8,4,3,7,6,5]=>0010111=>1110100=>3
[3,8,6,2,4,7,5,1]=>[2,8,4,1,3,7,6,5]=>0010111=>1110100=>3
[7,3,6,2,4,1,8,5]=>[6,2,5,1,4,3,8,7]=>0011101=>1011100=>1
[3,6,7,2,1,4,8,5]=>[1,4,6,3,2,5,8,7]=>0100101=>1010010=>1
[4,3,7,8,2,1,5,6]=>[4,3,6,8,2,1,5,7]=>1010001=>1000101=>1
[8,3,7,1,4,6,2,5]=>[8,2,7,1,4,6,3,5]=>0000111=>1110000=>3
[8,3,6,2,7,1,5,4]=>[8,1,4,3,7,2,6,5]=>0010111=>1110100=>3
[7,8,3,6,2,1,5,4]=>[4,8,3,7,2,1,6,5]=>1000111=>1110001=>3
[8,7,3,6,2,5,4,1]=>[8,7,2,6,1,5,4,3]=>0011111=>1111100=>5
[4,7,8,2,1,6,5,3]=>[1,4,8,3,2,7,6,5]=>0100111=>1110010=>3
[4,2,6,8,1,7,5,3]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[5,4,8,2,7,1,6,3]=>[4,3,8,2,7,1,6,5]=>0010111=>1110100=>3
[5,8,3,7,1,6,2,4]=>[4,8,3,7,1,6,2,5]=>0000111=>1110000=>3
[5,8,7,2,6,1,3,4]=>[4,8,7,2,6,1,3,5]=>0000111=>1110000=>3
[8,6,2,7,5,1,3,4]=>[8,4,2,7,6,1,3,5]=>0010111=>1110100=>3
[5,1,6,8,2,7,4,3]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[6,5,2,8,1,7,4,3]=>[4,3,2,8,1,7,6,5]=>0110111=>1110110=>3
[5,2,7,1,8,6,4,3]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[5,8,2,7,6,4,3,1]=>[2,8,1,7,6,5,4,3]=>0011111=>1111100=>5
[6,2,8,7,5,4,3,1]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101=>5
[7,6,2,1,8,5,4,3]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111=>3
[6,1,7,2,8,5,4,3]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[4,7,1,8,6,2,5,3]=>[2,4,1,8,7,3,6,5]=>0010111=>1110100=>3
[8,7,4,6,1,5,3,2]=>[8,7,2,6,1,5,4,3]=>0011111=>1111100=>5
[8,5,7,1,6,4,3,2]=>[8,2,7,1,6,5,4,3]=>0011111=>1111100=>5
[6,8,1,7,5,4,3,2]=>[2,8,1,7,6,5,4,3]=>0011111=>1111100=>5
[7,1,8,6,5,4,3,2]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101=>5
[7,4,2,6,3,5,1,8]=>[7,3,1,6,2,5,4,8]=>0101110=>0111010=>0
[8,4,2,6,3,1,5,7]=>[8,4,1,6,3,2,5,7]=>0110101=>1010110=>1
[4,7,2,6,3,5,1,8]=>[3,7,1,6,2,5,4,8]=>0001110=>0111000=>0
[1,6,5,2,3,8,4,7]=>[1,6,5,2,3,8,4,7]=>0001101=>1011000=>1
[1,7,5,2,8,3,4,6]=>[1,6,5,2,8,3,4,7]=>0001101=>1011000=>1
[5,8,6,2,3,1,4,7]=>[4,8,6,1,3,2,5,7]=>0100101=>1010010=>1
[4,8,2,6,3,1,5,7]=>[4,8,1,6,3,2,5,7]=>0100101=>1010010=>1
[3,2,8,6,4,1,5,7]=>[2,1,8,6,4,3,5,7]=>1010101=>1010101=>1
[3,2,1,6,4,8,5,7]=>[3,2,1,6,4,8,5,7]=>1100101=>1010011=>1
[7,1,5,2,8,3,4,6]=>[6,1,5,2,8,3,4,7]=>0001101=>1011000=>1
[1,8,5,2,7,3,4,6]=>[1,8,5,2,7,3,4,6]=>0001011=>1101000=>2
[1,8,6,7,2,3,4,5]=>[1,8,5,7,2,3,4,6]=>0000011=>1100000=>2
[7,1,6,8,2,3,4,5]=>[6,1,5,8,2,3,4,7]=>0000101=>1010000=>1
[3,2,1,7,8,4,5,6]=>[3,2,1,6,8,4,5,7]=>1100001=>1000011=>1
[3,2,8,7,1,4,5,6]=>[3,2,8,7,1,4,5,6]=>0100011=>1100010=>2
[5,8,7,2,1,3,4,6]=>[5,8,7,2,1,3,4,6]=>1000011=>1100001=>2
[1,7,6,8,2,3,4,5]=>[1,6,5,8,2,3,4,7]=>0000101=>1010000=>1
[6,5,8,2,3,1,4,7]=>[6,5,8,1,3,2,4,7]=>0100101=>1010010=>1
[8,5,7,2,1,3,4,6]=>[8,5,7,2,1,3,4,6]=>1000011=>1100001=>2
[6,4,2,8,3,1,5,7]=>[6,4,1,8,3,2,5,7]=>0110101=>1010110=>1
[5,4,2,3,8,1,6,7]=>[5,4,1,3,8,2,6,7]=>0011001=>1001100=>1
[4,5,2,3,1,8,6,7]=>[2,5,1,4,3,8,6,7]=>0011001=>1001100=>1
[5,4,2,3,1,8,6,7]=>[5,4,1,3,2,8,6,7]=>0111001=>1001110=>1
[6,4,2,1,3,8,5,7]=>[6,4,2,1,3,8,5,7]=>1010101=>1010101=>1
[7,4,2,1,8,3,5,6]=>[6,4,2,1,8,3,5,7]=>1010101=>1010101=>1
[8,4,2,1,7,3,5,6]=>[8,4,2,1,7,3,5,6]=>1010011=>1100101=>2
[1,4,2,8,7,3,5,6]=>[1,4,2,8,7,3,5,6]=>0010011=>1100100=>2
[1,5,8,2,7,3,4,6]=>[1,5,8,2,7,3,4,6]=>0000011=>1100000=>2
[8,5,1,2,7,3,4,6]=>[8,5,1,2,7,3,4,6]=>0001011=>1101000=>2
[7,5,1,2,8,3,4,6]=>[6,5,1,2,8,3,4,7]=>0001101=>1011000=>1
[6,5,1,2,3,8,4,7]=>[6,5,1,2,3,8,4,7]=>0001101=>1011000=>1
[4,6,2,1,3,8,5,7]=>[4,6,2,1,3,8,5,7]=>1000101=>1010001=>1
[3,2,6,1,4,8,5,7]=>[3,2,6,1,4,8,5,7]=>0100101=>1010010=>1
[4,7,2,1,8,3,5,6]=>[4,6,2,1,8,3,5,7]=>1000101=>1010001=>1
[7,6,1,8,2,3,4,5]=>[6,5,1,8,2,3,4,7]=>0001101=>1011000=>1
[8,6,1,7,2,3,4,5]=>[8,5,1,7,2,3,4,6]=>0001011=>1101000=>2
[1,6,8,7,2,3,4,5]=>[1,5,8,7,2,3,4,6]=>0000011=>1100000=>2
[1,7,8,6,2,3,4,5]=>[1,5,8,7,2,3,4,6]=>0000011=>1100000=>2
[4,8,2,1,7,3,5,6]=>[4,8,2,1,7,3,5,6]=>1000011=>1100001=>2
[3,2,8,1,7,4,5,6]=>[3,2,8,1,7,4,5,6]=>0100011=>1100010=>2
[3,2,1,8,7,4,5,6]=>[3,2,1,8,7,4,5,6]=>1100011=>1100011=>2
[5,1,8,2,7,3,4,6]=>[5,1,8,2,7,3,4,6]=>0001011=>1101000=>2
[6,1,8,7,2,3,4,5]=>[5,1,8,7,2,3,4,6]=>0001011=>1101000=>2
[8,1,7,6,2,3,4,5]=>[8,1,7,6,2,3,4,5]=>0000111=>1110000=>3
[1,8,7,6,2,3,4,5]=>[1,8,7,6,2,3,4,5]=>0000111=>1110000=>3
[6,3,5,1,2,4,8,7]=>[6,3,5,1,2,4,8,7]=>0001101=>1011000=>1
[4,3,5,6,1,2,8,7]=>[2,1,4,6,3,5,8,7]=>1000101=>1010001=>1
[8,3,7,5,2,1,4,6]=>[8,3,7,5,2,1,4,6]=>1001011=>1101001=>2
[6,3,7,5,1,8,4,2]=>[2,1,5,4,3,8,7,6]=>1011011=>1101101=>2
[6,5,2,7,1,8,3,4]=>[4,3,2,6,1,8,5,7]=>0110101=>1010110=>1
[8,5,2,7,4,1,3,6]=>[8,5,2,7,4,1,3,6]=>0011011=>1101100=>2
[2,6,1,5,4,3,8,7]=>[2,6,1,5,4,3,8,7]=>0011101=>1011100=>1
[6,4,3,5,1,2,8,7]=>[6,3,2,5,1,4,8,7]=>0101101=>1011010=>1
[5,3,1,4,6,2,8,7]=>[4,2,1,3,6,5,8,7]=>1010101=>1010101=>1
[3,1,4,6,5,2,8,7]=>[2,1,3,6,5,4,8,7]=>1001101=>1011001=>1
[5,7,4,6,2,8,3,1]=>[2,5,1,4,3,8,7,6]=>0011011=>1101100=>2
[8,1,4,7,2,6,3,5]=>[8,1,4,7,2,6,3,5]=>0000111=>1110000=>3
[3,4,7,8,5,2,1,6]=>[1,2,6,8,5,4,3,7]=>0011001=>1001100=>1
[2,1,8,5,7,3,4,6]=>[2,1,8,5,7,3,4,6]=>1000011=>1100001=>2
[8,6,3,5,1,7,4,2]=>[8,4,1,3,2,7,6,5]=>0110111=>1110110=>3
[5,8,2,4,6,7,3,1]=>[3,8,1,2,4,7,6,5]=>0000111=>1110000=>3
[3,4,8,6,5,7,1,2]=>[1,2,8,5,4,7,3,6]=>0001011=>1101000=>2
[7,5,4,8,1,6,3,2]=>[4,3,2,8,1,7,6,5]=>0110111=>1110110=>3
[2,5,4,6,7,1,8,3]=>[1,3,2,4,6,5,8,7]=>0100101=>1010010=>1
[2,4,6,3,7,5,8,1]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100=>1
[4,1,6,3,8,5,7,2]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[3,7,4,2,8,6,5,1]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110=>3
[7,4,1,3,5,8,6,2]=>[5,3,1,2,4,8,7,6]=>0101011=>1101010=>2
[6,5,8,4,1,7,3,2]=>[4,3,8,2,1,7,6,5]=>1010111=>1110101=>3
[8,5,3,7,4,1,6,2]=>[8,4,1,7,3,2,6,5]=>0110111=>1110110=>3
[2,1,4,8,3,7,6,5]=>[2,1,4,8,3,7,6,5]=>1000111=>1110001=>3
[7,4,3,8,2,1,6,5]=>[5,4,3,8,2,1,7,6]=>1011011=>1101101=>2
[6,3,7,4,1,8,2,5]=>[3,2,6,5,1,8,4,7]=>0101101=>1011010=>1
[8,3,1,2,5,7,6,4]=>[8,3,1,2,4,7,6,5]=>0100111=>1110010=>3
[3,1,8,2,7,6,5,4]=>[3,1,8,2,7,6,5,4]=>0101111=>1111010=>4
[2,3,8,1,6,7,5,4]=>[1,3,8,2,4,7,6,5]=>0000111=>1110000=>3
[4,3,7,2,6,8,5,1]=>[3,2,5,1,4,8,7,6]=>0101011=>1101010=>2
[4,7,2,3,8,5,6,1]=>[3,5,1,2,8,4,7,6]=>0001011=>1101000=>2
[2,8,1,3,6,5,7,4]=>[2,8,1,3,5,4,7,6]=>0001011=>1101000=>2
[2,7,8,5,4,3,1,6]=>[1,6,8,5,4,3,2,7]=>0111001=>1001110=>1
[3,8,6,7,2,4,1,5]=>[2,8,5,7,1,4,3,6]=>0010011=>1100100=>2
[5,3,8,7,4,2,6,1]=>[4,1,8,7,3,2,6,5]=>0110111=>1110110=>3
[4,3,8,7,2,1,6,5]=>[4,3,8,7,2,1,6,5]=>1010111=>1110101=>3
[8,3,6,1,4,2,7,5]=>[8,2,5,1,4,3,7,6]=>0011011=>1101100=>2
[7,3,5,8,2,4,1,6]=>[6,2,5,8,1,4,3,7]=>0010101=>1010100=>1
[2,3,4,1,8,5,7,6]=>[1,2,4,3,8,5,7,6]=>0010011=>1100100=>2
[5,3,6,1,8,7,2,4]=>[3,2,5,1,8,7,4,6]=>0101011=>1101010=>2
[7,8,5,6,1,4,2,3]=>[4,8,3,7,1,6,2,5]=>0000111=>1110000=>3
[2,8,6,5,4,7,1,3]=>[1,8,5,4,3,7,2,6]=>0011011=>1101100=>2
[8,1,6,4,5,7,2,3]=>[8,1,5,2,4,7,3,6]=>0001011=>1101000=>2
[5,8,3,6,1,7,2,4]=>[3,8,2,5,1,7,4,6]=>0001011=>1101000=>2
[2,1,8,6,5,7,3,4]=>[2,1,8,5,4,7,3,6]=>1001011=>1101001=>2
[2,1,7,5,3,6,8,4]=>[2,1,6,4,3,5,8,7]=>1010101=>1010101=>1
[6,7,3,5,2,1,8,4]=>[2,6,1,5,4,3,8,7]=>0011101=>1011100=>1
[7,1,4,2,5,6,8,3]=>[6,1,3,2,4,5,8,7]=>0100101=>1010010=>1
[4,6,1,2,8,7,3,5]=>[3,5,1,2,8,7,4,6]=>0001011=>1101000=>2
[2,4,1,5,8,7,6,3]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010=>3
[4,1,2,5,8,6,7,3]=>[3,1,2,4,8,5,7,6]=>0100011=>1100010=>2
[6,4,2,1,5,8,7,3]=>[5,3,2,1,4,8,7,6]=>1101011=>1101011=>2
[8,5,2,4,6,1,7,3]=>[8,3,1,2,5,4,7,6]=>0101011=>1101010=>2
[7,5,3,2,6,8,1,4]=>[6,3,2,1,5,8,4,7]=>1100101=>1010011=>1
[2,1,5,3,6,8,7,4]=>[2,1,4,3,5,8,7,6]=>1010011=>1100101=>2
[7,3,5,4,6,1,8,2]=>[6,1,3,2,5,4,8,7]=>0101101=>1011010=>1
[6,3,4,1,5,7,8,2]=>[5,1,3,2,4,6,8,7]=>0101001=>1001010=>1
[3,1,4,5,6,8,7,2]=>[2,1,3,4,5,8,7,6]=>1000011=>1100001=>2
[4,5,2,6,3,1,8,7]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010=>1
[6,5,2,1,4,3,8,7]=>[6,5,2,1,4,3,8,7]=>1011101=>1011101=>1
[8,5,2,7,4,1,6,3]=>[8,4,1,7,3,2,6,5]=>0110111=>1110110=>3
[8,3,7,5,2,1,6,4]=>[8,1,7,4,3,2,6,5]=>0110111=>1110110=>3
[6,3,7,5,2,8,4,1]=>[2,1,5,4,3,8,7,6]=>1011011=>1101101=>2
[3,1,6,5,4,2,8,7]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101=>1
[3,6,2,4,1,5,8,7]=>[2,6,1,4,3,5,8,7]=>0010101=>1010100=>1
[2,6,1,3,5,4,8,7]=>[2,6,1,3,5,4,8,7]=>0001101=>1011000=>1
[6,7,2,3,4,8,5,1]=>[3,5,1,2,4,8,7,6]=>0001011=>1101000=>2
[8,7,2,3,4,1,6,5]=>[8,7,1,2,4,3,6,5]=>0010111=>1110100=>3
[5,1,7,3,8,4,6,2]=>[3,1,5,2,8,4,7,6]=>0101011=>1101010=>2
[2,5,7,3,8,6,4,1]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100=>3
[7,6,1,3,5,8,4,2]=>[5,4,1,2,3,8,7,6]=>0011011=>1101100=>2
[3,6,7,4,1,8,5,2]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100=>2
[5,6,3,7,4,8,1,2]=>[1,3,2,6,5,8,4,7]=>0100101=>1010010=>1
[2,1,6,7,4,8,5,3]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001=>2
[2,1,8,7,4,3,6,5]=>[2,1,8,7,4,3,6,5]=>1010111=>1110101=>3
[3,8,7,4,1,2,6,5]=>[2,8,7,4,1,3,6,5]=>0010111=>1110100=>3
[7,8,1,3,5,2,6,4]=>[5,8,1,2,4,3,7,6]=>0010011=>1100100=>2
[5,8,7,3,2,6,1,4]=>[4,8,7,3,2,6,1,5]=>0100111=>1110010=>3
[2,8,6,3,1,5,7,4]=>[1,8,5,3,2,4,7,6]=>0101011=>1101010=>2
[8,1,6,3,2,5,4,7]=>[8,1,6,3,2,5,4,7]=>0101101=>1011010=>1
[2,8,4,1,6,3,7,5]=>[1,8,3,2,5,4,7,6]=>0101011=>1101010=>2
[4,8,1,2,7,6,3,5]=>[4,8,1,2,7,6,3,5]=>0000111=>1110000=>3
[3,8,4,2,5,7,1,6]=>[1,8,3,2,5,7,4,6]=>0100011=>1100010=>2
[6,8,3,5,2,7,4,1]=>[4,8,1,3,2,7,6,5]=>0100111=>1110010=>3
[2,1,5,3,8,7,6,4]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101=>3
[6,5,3,2,8,7,1,4]=>[5,4,3,2,8,7,1,6]=>0111011=>1101110=>2
[2,4,1,8,7,6,5,3]=>[1,3,2,8,7,6,5,4]=>0101111=>1111010=>4
[4,3,1,8,6,7,5,2]=>[3,2,1,8,4,7,6,5]=>1100111=>1110011=>3
[3,1,4,8,6,5,7,2]=>[2,1,3,8,5,4,7,6]=>1001011=>1101001=>2
[7,1,6,5,4,8,2,3]=>[6,1,5,4,3,8,2,7]=>0011101=>1011100=>1
[3,7,5,6,8,4,2,1]=>[1,4,2,3,8,7,6,5]=>0010111=>1110100=>3
[5,7,1,6,8,2,4,3]=>[2,5,1,4,8,3,7,6]=>0001011=>1101000=>2
[8,6,2,5,1,7,4,3]=>[8,4,1,3,2,7,6,5]=>0110111=>1110110=>3
[4,6,2,5,8,3,7,1]=>[2,5,1,4,8,3,7,6]=>0001011=>1101000=>2
[4,1,2,3,6,8,7,5]=>[4,1,2,3,5,8,7,6]=>0010011=>1100100=>2
[2,4,3,1,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>0110001=>1000110=>1
[7,5,2,8,3,4,6,1]=>[5,4,1,8,2,3,7,6]=>0011011=>1101100=>2
[5,6,2,8,4,3,1,7]=>[2,6,1,8,5,4,3,7]=>0011101=>1011100=>1
[4,7,2,8,1,5,3,6]=>[3,6,2,8,1,5,4,7]=>0001101=>1011000=>1
[8,7,2,1,4,5,6,3]=>[8,7,2,1,3,4,6,5]=>1000111=>1110001=>3
[5,7,8,6,3,4,1,2]=>[1,4,8,7,3,6,2,5]=>0000111=>1110000=>3
[2,7,8,4,5,3,6,1]=>[1,5,8,2,4,3,7,6]=>0010011=>1100100=>2
[2,1,5,8,4,6,3,7]=>[2,1,4,8,3,6,5,7]=>1000101=>1010001=>1
[6,5,3,8,4,1,2,7]=>[6,5,2,8,4,1,3,7]=>0011101=>1011100=>1
[7,5,8,4,3,6,2,1]=>[4,3,8,2,1,7,6,5]=>1010111=>1110101=>3
[2,4,8,3,5,6,1,7]=>[1,3,8,2,4,6,5,7]=>0000101=>1010000=>1
[4,1,8,3,6,5,2,7]=>[3,1,8,2,6,5,4,7]=>0101101=>1011010=>1
[3,4,8,1,7,2,5,6]=>[2,4,8,1,7,3,5,6]=>0000011=>1100000=>2
[8,4,1,3,7,2,6,5]=>[8,4,1,3,7,2,6,5]=>0010111=>1110100=>3
[3,1,8,2,4,7,6,5]=>[3,1,8,2,4,7,6,5]=>0100111=>1110010=>3
[2,3,8,1,4,6,7,5]=>[1,3,8,2,4,5,7,6]=>0000011=>1100000=>2
[4,3,8,2,5,1,7,6]=>[3,2,8,1,5,4,7,6]=>0101011=>1101010=>2
[6,3,8,4,2,5,7,1]=>[5,1,8,3,2,4,7,6]=>0101011=>1101010=>2
[2,1,4,8,3,5,7,6]=>[2,1,4,8,3,5,7,6]=>1000011=>1100001=>2
[6,8,2,4,3,5,1,7]=>[6,8,1,3,2,5,4,7]=>0101001=>1001010=>1
[3,8,2,1,4,6,5,7]=>[3,8,2,1,4,6,5,7]=>1000101=>1010001=>1
[2,8,1,3,4,5,7,6]=>[2,8,1,3,4,5,7,6]=>0000011=>1100000=>2
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Description
The number of leading ones in a binary word.
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
Map
reverse
Description
Return the reversal of a binary word.
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.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
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