Identifier
Mp00017: to 312-avoiding permutationPermutations
Mp00109: Permutations descent wordBinary words
Mp00104: Binary words reverseBinary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>=> [.,[.,.]]=>[2,1]=>1=>1 [[.,.],.]=>[1,2]=>0=>0 [.,[.,[.,.]]]=>[3,2,1]=>11=>11 [.,[[.,.],.]]=>[2,3,1]=>01=>10 [[.,.],[.,.]]=>[1,3,2]=>01=>10 [[.,[.,.]],.]=>[2,1,3]=>10=>01 [[[.,.],.],.]=>[1,2,3]=>00=>00 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>111=>111 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>011=>110 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>011=>110 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>101=>101 [.,[[[.,.],.],.]]=>[2,3,4,1]=>001=>100 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>011=>110 [[.,.],[[.,.],.]]=>[1,3,4,2]=>001=>100 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>101=>101 [[[.,.],.],[.,.]]=>[1,2,4,3]=>001=>100 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>110=>011 [[.,[[.,.],.]],.]=>[2,3,1,4]=>010=>010 [[[.,.],[.,.]],.]=>[1,3,2,4]=>010=>010 [[[.,[.,.]],.],.]=>[2,1,3,4]=>100=>001 [[[[.,.],.],.],.]=>[1,2,3,4]=>000=>000 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>1111=>1111 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0111=>1110 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>0111=>1110 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>1011=>1101 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0011=>1100 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0111=>1110 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0011=>1100 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>1011=>1101 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0011=>1100 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>1101=>1011 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0101=>1010 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0101=>1010 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>1001=>1001 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0001=>1000 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>0111=>1110 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>0011=>1100 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>0011=>1100 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>0101=>1010 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>0001=>1000 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>1011=>1101 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>1001=>1001 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>0011=>1100 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>0001=>1000 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>1101=>1011 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>0101=>1010 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>0101=>1010 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>1001=>1001 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>0001=>1000 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1110=>0111 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0110=>0110 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>0110=>0110 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1010=>0101 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0010=>0100 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>0110=>0110 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>0010=>0100 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>1010=>0101 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>0010=>0100 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>1100=>0011 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0100=>0010 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>0100=>0010 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1000=>0001 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0000=>0000 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>11111=>11111 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>01111=>11110 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>01111=>11110 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>10111=>11101 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00111=>11100 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>01111=>11110 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>00111=>11100 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>10111=>11101 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>00111=>11100 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>11011=>11011 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>01011=>11010 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>01011=>11010 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>10011=>11001 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00011=>11000 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>01111=>11110 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>00111=>11100 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>00111=>11100 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>01011=>11010 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>00011=>11000 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>10111=>11101 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>10011=>11001 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>00111=>11100 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>00011=>11000 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>11011=>11011 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>01011=>11010 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>01011=>11010 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>10011=>11001 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>00011=>11000 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>11101=>10111 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>01101=>10110 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>01101=>10110 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>10101=>10101 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00101=>10100 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>01101=>10110 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>00101=>10100 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>10101=>10101 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>00101=>10100 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>11001=>10011 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>01001=>10010 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>01001=>10010 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>10001=>10001 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00001=>10000 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>01111=>11110 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>00111=>11100 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>00111=>11100 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>01011=>11010 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>00011=>11000 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>00111=>11100 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>00011=>11000 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>01011=>11010 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>00011=>11000 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>01101=>10110 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>00101=>10100 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>00101=>10100 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>01001=>10010 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>00001=>10000 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>10111=>11101 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>10011=>11001 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>10011=>11001 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>10101=>10101 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>10001=>10001 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>00111=>11100 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>00011=>11000 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>00011=>11000 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>00101=>10100 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>00001=>10000 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>11011=>11011 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>11001=>10011 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>01011=>11010 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>01001=>10010 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>01011=>11010 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>01001=>10010 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>10011=>11001 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>10001=>10001 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>00011=>11000 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>00001=>10000 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>11101=>10111 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>01101=>10110 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>01101=>10110 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>10101=>10101 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>00101=>10100 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>01101=>10110 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>00101=>10100 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>10101=>10101 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>00101=>10100 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>11001=>10011 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>01001=>10010 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>01001=>10010 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>10001=>10001 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>00001=>10000 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>11110=>01111 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>01110=>01110 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>01110=>01110 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>10110=>01101 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00110=>01100 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>01110=>01110 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>00110=>01100 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>10110=>01101 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>00110=>01100 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>11010=>01011 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>01010=>01010 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>01010=>01010 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>10010=>01001 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00010=>01000 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>01110=>01110 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>00110=>01100 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>00110=>01100 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>01010=>01010 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>00010=>01000 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>10110=>01101 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>10010=>01001 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>00110=>01100 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>00010=>01000 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>11010=>01011 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>01010=>01010 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>01010=>01010 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>10010=>01001 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>00010=>01000 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>11100=>00111 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>01100=>00110 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>01100=>00110 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>10100=>00101 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00100=>00100 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>01100=>00110 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>00100=>00100 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>10100=>00101 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>00100=>00100 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>11000=>00011 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>01000=>00010 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>01000=>00010 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>10000=>00001 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>00000=>00000 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>111111=>111111 [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>011111=>111110 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>011111=>111110 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>101111=>111101 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>001111=>111100 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>011111=>111110 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>001111=>111100 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>101111=>111101 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>001111=>111100 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>110111=>111011 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>010111=>111010 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>010111=>111010 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>100111=>111001 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>000111=>111000 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>011111=>111110 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>001111=>111100 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>001111=>111100 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>010111=>111010 [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>000111=>111000 [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>101111=>111101 [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>100111=>111001 [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>001111=>111100 [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>000111=>111000 [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>110111=>111011 [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>010111=>111010 [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>010111=>111010 [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>100111=>111001 [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>000111=>111000 [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>111011=>110111 [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>011011=>110110 [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>011011=>110110 [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>101011=>110101 [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>001011=>110100 [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>011011=>110110 [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>001011=>110100 [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>101011=>110101 [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>001011=>110100 [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>110011=>110011 [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>010011=>110010 [.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>010011=>110010 [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>100011=>110001 [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>000011=>110000 [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>011111=>111110 [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>001111=>111100 [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>001111=>111100 [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>010111=>111010 [.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>000111=>111000 [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>001111=>111100 [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>000111=>111000 [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>010111=>111010 [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>000111=>111000 [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>011011=>110110 [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>001011=>110100 [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>001011=>110100 [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>010011=>110010 [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>000011=>110000 [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>101111=>111101 [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>100111=>111001 [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>100111=>111001 [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>101011=>110101 [.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>100011=>110001 [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>001111=>111100 [.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>000111=>111000 [.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>000111=>111000 [.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>001011=>110100 [.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>000011=>110000 [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>110111=>111011 [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>110011=>110011 [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>010111=>111010 [.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>010011=>110010 [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>010111=>111010 [.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>010011=>110010 [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>100111=>111001 [.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>100011=>110001 [.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>000111=>111000 [.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>000011=>110000 [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>111011=>110111 [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>011011=>110110 [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>011011=>110110 [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>101011=>110101 [.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>001011=>110100 [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>011011=>110110 [.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>001011=>110100 [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>101011=>110101 [.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>001011=>110100 [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>110011=>110011 [.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>010011=>110010 [.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>010011=>110010 [.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>100011=>110001 [.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>000011=>110000 [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>111101=>101111 [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>011101=>101110 [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>011101=>101110 [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>101101=>101101 [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>001101=>101100 [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>011101=>101110 [.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>001101=>101100 [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>101101=>101101 [.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>001101=>101100 [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>110101=>101011 [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>010101=>101010 [.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>010101=>101010 [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>100101=>101001 [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>000101=>101000 [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>011101=>101110 [.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>001101=>101100 [.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>001101=>101100 [.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>010101=>101010 [.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>000101=>101000 [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>101101=>101101 [.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>100101=>101001 [.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>001101=>101100 [.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>000101=>101000 [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>110101=>101011 [.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>010101=>101010 [.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>010101=>101010 [.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>100101=>101001 [.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>000101=>101000 [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>111001=>100111 [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>011001=>100110 [.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>011001=>100110 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>101001=>100101 [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>001001=>100100 [.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>011001=>100110 [.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>001001=>100100 [.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>101001=>100101 [.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>001001=>100100 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>110001=>100011 [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>010001=>100010 [.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>010001=>100010 [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>100001=>100001 [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>000001=>100000 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>011111=>111110 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>001111=>111100 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>001111=>111100 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>010111=>111010 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>000111=>111000 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>001111=>111100 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>000111=>111000 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>010111=>111010 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>000111=>111000 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>011011=>110110 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>001011=>110100 [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>001011=>110100 [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>010011=>110010 [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>000011=>110000 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>001111=>111100 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>000111=>111000 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>000111=>111000 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>001011=>110100 [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>000011=>110000 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>010111=>111010 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>010011=>110010 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>000111=>111000 [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>000011=>110000 [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>011011=>110110 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>001011=>110100 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>001011=>110100 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>010011=>110010 [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>000011=>110000 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>011101=>101110 [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>001101=>101100 [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>001101=>101100 [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>010101=>101010 [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>000101=>101000 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>001101=>101100 [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>000101=>101000 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>010101=>101010 [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>000101=>101000 [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>011001=>100110 [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>001001=>100100 [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>001001=>100100 [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>010001=>100010 [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>000001=>100000 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>101111=>111101 [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>100111=>111001 [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>100111=>111001 [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>101011=>110101 [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>100011=>110001 [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>100111=>111001 [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>100011=>110001 [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>101011=>110101 [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>100011=>110001 [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>101101=>101101 [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>100101=>101001 [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>100101=>101001 [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>101001=>100101 [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>100001=>100001 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>001111=>111100 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>000111=>111000 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>000111=>111000 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>001011=>110100 [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>000011=>110000 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>000111=>111000 [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>000011=>110000 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>001011=>110100 [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>000011=>110000 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>001101=>101100 [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>000101=>101000 [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>000101=>101000 [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>001001=>100100 [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>000001=>100000 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>110111=>111011 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>110011=>110011 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>110011=>110011 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>110101=>101011 [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>110001=>100011 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>010111=>111010 [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>010011=>110010 [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>010011=>110010 [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>010101=>101010 [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>010001=>100010 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>010111=>111010 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>010011=>110010 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>010011=>110010 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>010101=>101010 [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>010001=>100010 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>100111=>111001 [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>100011=>110001 [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>100011=>110001 [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>100101=>101001 [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>100001=>100001 [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>000111=>111000 [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>000011=>110000 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[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>001011=>110100 [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>001001=>100100 [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>101011=>110101 [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>101001=>100101 [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>001011=>110100 [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>001001=>100100 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>110011=>110011 [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>110001=>100011 [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>010011=>110010 [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>010001=>100010 [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>010011=>110010 [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>010001=>100010 [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>100011=>110001 [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>100001=>100001 [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>000011=>110000 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[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>001000=>000100 [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>011000=>000110 [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>001000=>000100 [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>101000=>000101 [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>001000=>000100 [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>110000=>000011 [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>010000=>000010 [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>010000=>000010 [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>100000=>000001 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>000000=>000000 [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>1111111=>1111111 [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>0111111=>1111110 [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>0111111=>1111110 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>1011111=>1111101 [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>0011111=>1111100 [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>0111111=>1111110 [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>0011111=>1111100 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>1011111=>1111101 [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>0011111=>1111100 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>1101111=>1111011 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>0101111=>1111010 [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>0101111=>1111010 [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>1001111=>1111001 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>0001111=>1111000 [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>0111111=>1111110 [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>0011111=>1111100 [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>0011111=>1111100 [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>0101111=>1111010 [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>0001111=>1111000 [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>0011111=>1111100 [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>0001111=>1111000 [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>0101111=>1111010 [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>0001111=>1111000 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>1110111=>1110111 [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>0110111=>1110110 [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>0110111=>1110110 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>1010111=>1110101 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>0010111=>1110100 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>0110111=>1110110 [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>0010111=>1110100 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>1010111=>1110101 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>0010111=>1110100 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>1100111=>1110011 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>0100111=>1110010 [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>0100111=>1110010 [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>1000111=>1110001 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>0000111=>1110000 [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>0111111=>1111110 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>0011111=>1111100 [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>0001111=>1111000 [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>0001111=>1111000 [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>0110111=>1110110 [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>0010111=>1110100 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>0000111=>1110000 [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>0011111=>1111100 [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>0000111=>1110000 [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>1100111=>1110011 [.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>0000111=>1110000 [.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>0010111=>1110100 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>1010111=>1110101 [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>1100111=>1110011 [.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>0100111=>1110010 [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>1111011=>1101111 [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>0111011=>1101110 [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>0111011=>1101110 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>1001011=>1101001 [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>0001011=>1101000 [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>0011011=>1101100 [.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>0101011=>1101010 [.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>1001011=>1101001 [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>1110011=>1100111 [.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>0010011=>1100100 [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>0111111=>1111110 [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>0101111=>1111010 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>0000111=>1110000 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>0011111=>1111100 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>0001111=>1111000 [.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>0000111=>1110000 [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>0101111=>1111010 [.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>0000111=>1110000 [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>0010111=>1110100 [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>0010111=>1110100 [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>0111011=>1101110 [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>0011011=>1101100 [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>0011011=>1101100 [.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>0110011=>1100110 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>1011111=>1111101 [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>1001111=>1111001 [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>1001011=>1101001 [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>1000011=>1100001 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>0011111=>1111100 [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>0000111=>1110000 [.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>0000111=>1110000 [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>0011011=>1101100 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>0000011=>1100000 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>1101111=>1111011 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>0101111=>1111010 [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>0100111=>1110010 [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>0101111=>1111010 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>0100111=>1110010 [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>1001111=>1111001 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>0001111=>1111000 [.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>0000011=>1100000 [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>1110111=>1110111 [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>1110011=>1100111 [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>0110111=>1110110 [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>0110011=>1100110 [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>0010111=>1110100 [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>0010111=>1110100 [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>1100111=>1110011 [.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>0100111=>1110010 [.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>0000111=>1110000 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>1111011=>1101111 [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>0111011=>1101110 [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>1011011=>1101101 [.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>0011011=>1101100 [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>0111011=>1101110 [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>0011011=>1101100 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>1011011=>1101101 [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>1101011=>1101011 [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>0111011=>1101110 [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>0011011=>1101100 [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>1101011=>1101011 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>0101011=>1101010 [.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>0001011=>1101000 [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>1110011=>1100111 [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>0110011=>1100110 [.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>1100011=>1100011 [.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>0100011=>1100010 [.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>0100011=>1100010 [.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>0000011=>1100000 [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>0111101=>1011110 [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>0101101=>1011010 [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>0001101=>1011000 [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>0011101=>1011100 [.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>0001101=>1011000 [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>1011101=>1011101 [.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>1001101=>1011001 [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>0011101=>1011100 [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>1101101=>1011011 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>1110101=>1010111 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>0110101=>1010110 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>1010101=>1010101 [.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>0010101=>1010100 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>0110101=>1010110 [.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>0010101=>1010100 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>1010101=>1010101 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>1100101=>1010011 [.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>0100101=>1010010 [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>0101101=>1011010 [.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>0010101=>1010100 [.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>0000101=>1010000 [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>1001101=>1011001 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>1010101=>1010101 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>0011101=>1011100 [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>1101101=>1011011 [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>1100101=>1010011 [.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>0101101=>1011010 [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>0101101=>1011010 [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>1001101=>1011001 [.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>0001101=>1011000 [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>1110101=>1010111 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>1010101=>1010101 [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>0110101=>1010110 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>1010101=>1010101 [.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>0010101=>1010100 [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>1100101=>1010011 [.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>0100101=>1010010 [.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>1000101=>1010001 [.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>0000101=>1010000 [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>1111001=>1001111 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>1011001=>1001101 [.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>0111001=>1001110 [.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>0011001=>1001100 [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>1101001=>1001011 [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>0001001=>1001000 [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>0111001=>1001110 [.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>0101001=>1001010 [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>0011001=>1001100 [.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>0001001=>1001000 [.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>1101001=>1001011 [.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>0101001=>1001010 [.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>0101001=>1001010 [.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>0001001=>1001000 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>1110001=>1000111 [.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>0110001=>1000110 [.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>1010001=>1000101 [.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>0110001=>1000110 [.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>0010001=>1000100 [.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>1010001=>1000101 [.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>0010001=>1000100 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>1100001=>1000011 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>0100001=>1000010 [.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>0100001=>1000010 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>1000001=>1000001 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>0000001=>1000000 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>0111111=>1111110 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>0011111=>1111100 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>0011111=>1111100 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>0101111=>1111010 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>0001111=>1111000 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>0110111=>1110110 [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>0010111=>1110100 [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>0010111=>1110100 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>0100111=>1110010 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>0000111=>1110000 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>0011111=>1111100 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>0001111=>1111000 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>0001111=>1111000 [[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>0000111=>1110000 [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>0000111=>1110000 [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>0010111=>1110100 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>0011011=>1101100 [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>0110011=>1100110 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>0011111=>1111100 [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>0001111=>1111000 [[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>0000111=>1110000 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>0001111=>1111000 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>0000111=>1110000 [[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>0001011=>1101000 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>0010011=>1100100 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>0000011=>1100000 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>0101111=>1111010 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>0100111=>1110010 [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>0100111=>1110010 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>0101011=>1101010 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>0001111=>1111000 [[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>0001011=>1101000 [[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>0000011=>1100000 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>0110111=>1110110 [[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>0010011=>1100100 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>0100111=>1110010 [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>0100011=>1100010 [[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>0000111=>1110000 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>0111011=>1101110 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>0011011=>1101100 [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>0011011=>1101100 [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>0011011=>1101100 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>0101011=>1101010 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>0110011=>1100110 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>0011101=>1011100 [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>0001101=>1011000 [[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>0001101=>1011000 [[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>0010101=>1010100 [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>0101001=>1001010 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>0110001=>1000110 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>1001111=>1111001 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>1001111=>1111001 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>1010111=>1110101 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>1000111=>1110001 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>1000111=>1110001 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>1010111=>1110101 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>1011011=>1101101 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>1001011=>1101001 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>1010011=>1100101 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>1000011=>1100001 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>1001111=>1111001 [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>1000111=>1110001 [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>1000111=>1110001 [[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>1000011=>1100001 [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>1000111=>1110001 [[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>1000011=>1100001 [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>1001011=>1101001 [[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>1000011=>1100001 [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>1001101=>1011001 [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>1010101=>1010101 [[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>1000101=>1010001 [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>1001101=>1011001 [[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>1000101=>1010001 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>1010101=>1010101 [[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>1001001=>1001001 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>1000001=>1000001 [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>0011111=>1111100 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>0000111=>1110000 [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>0010111=>1110100 [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>0011011=>1101100 [[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>0001011=>1101000 [[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>0010011=>1100100 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>0000011=>1100000 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>0001111=>1111000 [[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>0000111=>1110000 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>0000111=>1110000 [[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>0000011=>1100000 [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>0010111=>1110100 [[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>0000011=>1100000 [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>0011011=>1101100 [[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>0001101=>1011000 [[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>0000101=>1010000 [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>0001101=>1011000 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>0011001=>1001100 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>1101111=>1111011 [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>1100111=>1110011 [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>1100111=>1110011 [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>1101011=>1101011 [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>1100011=>1100011 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>1100111=>1110011 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>1100011=>1100011 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>1101011=>1101011 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>1100011=>1100011 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>1101101=>1011011 [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>1100101=>1010011 [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>1100101=>1010011 [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>1101001=>1001011 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>1100001=>1000011 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>0101111=>1111010 [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>0100111=>1110010 [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>0101011=>1101010 [[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>0100011=>1100010 [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>0101011=>1101010 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>0100001=>1000010 [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>0101111=>1111010 [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>0100111=>1110010 [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>0100011=>1100010 [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>0101011=>1101010 [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>0101101=>1011010 [[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>0100101=>1010010 [[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>0101001=>1001010 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>1001111=>1111001 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>1000111=>1110001 [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>1000111=>1110001 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>0001111=>1111000 [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>0000111=>1110000 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>0000111=>1110000 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>0001011=>1101000 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>0000011=>1100000 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>0000111=>1110000 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>0000011=>1100000 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>0001011=>1101000 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>0000011=>1100000 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>0001101=>1011000 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>0000101=>1010000 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>0000101=>1010000 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>0001001=>1001000 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>0000001=>1000000 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111 [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>1110011=>1100111 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>1110011=>1100111 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>1110101=>1010111 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>1110001=>1000111 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>0110111=>1110110 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>0110011=>1100110 [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>0110011=>1100110 [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>0110101=>1010110 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>0110001=>1000110 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>0110111=>1110110 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>0110011=>1100110 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>0110101=>1010110 [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>0110001=>1000110 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>1010111=>1110101 [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>1010011=>1100101 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>1010011=>1100101 [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>1010101=>1010101 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>1010001=>1000101 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>0010111=>1110100 [[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>0010011=>1100100 [[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>0010011=>1100100 [[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>0010101=>1010100 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>0010001=>1000100 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110 [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>0110101=>1010110 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>0110001=>1000110 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>0010111=>1110100 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>0010011=>1100100 [[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>0010011=>1100100 [[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>0010101=>1010100 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>0010001=>1000100 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101 [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>1010011=>1100101 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>1010011=>1100101 [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>1010101=>1010101 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>1010001=>1000101 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100 [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>0010011=>1100100 [[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>0010011=>1100100 [[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>0010101=>1010100 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>0010001=>1000100 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>1100111=>1110011 [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>1100011=>1100011 [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>1100011=>1100011 [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>1100101=>1010011 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>1100001=>1000011 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>0100111=>1110010 [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>0100011=>1100010 [[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>0100101=>1010010 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>0100001=>1000010 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010 [[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>0100011=>1100010 [[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>0100101=>1010010 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>0100001=>1000010 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001 [[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>1000101=>1010001 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>1000001=>1000001 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000 [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>0000011=>1100000 [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>0000011=>1100000 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>0000101=>1010000 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>0000001=>1000000 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>1111011=>1101111 [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>1111001=>1001111 [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>0111011=>1101110 [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>0111011=>1101110 [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>0111001=>1001110 [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>1011011=>1101101 [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>0011011=>1101100 [[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>0011001=>1001100 [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>0111011=>1101110 [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>0111001=>1001110 [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>0011011=>1101100 [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>1011011=>1101101 [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>1011001=>1001101 [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>0011011=>1101100 [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>1101011=>1101011 [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>0101011=>1101010 [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>0101001=>1001010 [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>0101011=>1101010 [[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>0101001=>1001010 [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>1001011=>1101001 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>0001011=>1101000 [[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>0011001=>1001100 [[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>0101001=>1001010 [[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>0001011=>1101000 [[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>0001001=>1001000 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>0011001=>1001100 [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>0001011=>1101000 [[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>0001001=>1001000 [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>0101001=>1001010 [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>0001011=>1101000 [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>0001001=>1001000 [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>1110011=>1100111 [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>1110001=>1000111 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>1010011=>1100101 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>1010001=>1000101 [[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>0010011=>1100100 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>0010001=>1000100 [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>0110011=>1100110 [[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>0110001=>1000110 [[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>0010011=>1100100 [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>0010001=>1000100 [[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>0010001=>1000100 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>1100011=>1100011 [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>1100001=>1000011 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>0100001=>1000010 [[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>0100001=>1000010 [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>0000011=>1100000 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>0000001=>1000000 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>1111101=>1011111 [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>0111101=>1011110 [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>0111101=>1011110 [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>1011101=>1011101 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>0011101=>1011100 [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>0111101=>1011110 [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>0011101=>1011100 [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>1011101=>1011101 [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>1101101=>1011011 [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>0101101=>1011010 [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>0001101=>1011000 [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>0111101=>1011110 [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>0011101=>1011100 [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>0011101=>1011100 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>0011101=>1011100 [[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>0001101=>1011000 [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>0101101=>1011010 [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>1110101=>1010111 [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>0110101=>1010110 [[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>0110101=>1010110 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>1010101=>1010101 [[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>0010101=>1010100 [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>0110101=>1010110 [[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>0010101=>1010100 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>1010101=>1010101 [[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>0100101=>1010010 [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>0000101=>1010000 [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>0101101=>1011010 [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>0011101=>1011100 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101 [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>1001101=>1011001 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>1001101=>1011001 [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>1010101=>1010101 [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>1000101=>1010001 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>0101101=>1011010 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>0001101=>1011000 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>0000101=>1010000 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>0110101=>1010110 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>0110101=>1010110 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>1010101=>1010101 [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>0010101=>1010100 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101 [[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100 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[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>1110001=>1000111 [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>1010001=>1000101 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>0010001=>1000100 [[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>0110001=>1000110 [[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>0010001=>1000100 [[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>1010001=>1000101 [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>0010001=>1000100 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>1000001=>1000001 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>0000001=>1000000 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>1111110=>0111111 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0111110=>0111110 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>0111110=>0111110 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>1011110=>0111101 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0011110=>0111100 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>0111110=>0111110 [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>0011110=>0111100 [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>0011110=>0111100 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>1101110=>0111011 [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>0101110=>0111010 [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>0101110=>0111010 [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>0001110=>0111000 [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>0011110=>0111100 [[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>0001110=>0111000 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>0011110=>0111100 [[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>0101110=>0111010 [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>0101110=>0111010 [[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>1001110=>0111001 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>1110110=>0110111 [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>1010110=>0110101 [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>1100110=>0110011 [[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>0001110=>0111000 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>0001110=>0111000 [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>1011110=>0111101 [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>1001110=>0111001 [[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>1001110=>0111001 [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>0011110=>0111100 [[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>0001110=>0111000 [[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>0001110=>0111000 [[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>0010110=>0110100 [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>0000110=>0110000 [[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>1000110=>0110001 [[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>0001110=>0111000 [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>1110110=>0110111 [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>0110110=>0110110 [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>0110110=>0110110 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>1010110=>0110101 [[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>1100110=>0110011 [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>1011010=>0101101 [[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>0111010=>0101110 [[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>0011010=>0101100 [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>1101010=>0101011 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>0101010=>0101010 [[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>0101010=>0101010 [[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>0001010=>0101000 [[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>0101010=>0101010 [[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>1011010=>0101101 [[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>0101010=>0101010 [[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>0101010=>0101010 [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>1110010=>0100111 [[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>0110010=>0100110 [[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>0110010=>0100110 [[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>0001110=>0111000 [[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>0010110=>0110100 [[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>0001110=>0111000 [[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>0000110=>0110000 [[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>0010110=>0110100 [[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>0100110=>0110010 [[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>0101010=>0101010 [[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>0011010=>0101100 [[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>0101010=>0101010 [[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>0110010=>0100110 [[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>0000010=>0100000 [[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>1000110=>0110001 [[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>0001110=>0111000 [[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>0000110=>0110000 [[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>0001010=>0101000 [[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>0010010=>0100100 [[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>1100110=>0110011 [[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>1100010=>0100011 [[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>0100110=>0110010 [[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>0101010=>0101010 [[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>0100010=>0100010 [[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>0100110=>0110010 [[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>0101010=>0101010 [[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>0100010=>0100010 [[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>1000110=>0110001 [[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>0001110=>0111000 [[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>0000110=>0110000 [[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>0000110=>0110000 [[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>0001010=>0101000 [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>0000010=>0100000 [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>1110110=>0110111 [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>1110010=>0100111 [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>1010110=>0110101 [[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>1010010=>0100101 [[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>0010110=>0110100 [[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>0010010=>0100100 [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>0110110=>0110110 [[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>0110010=>0100110 [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>0010010=>0100100 [[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>0010010=>0100100 [[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>0100010=>0100010 [[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>0100110=>0110010 [[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>0000110=>0110000 [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>0000010=>0100000 [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>1111010=>0101111 [[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>0111010=>0101110 [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>0111010=>0101110 [[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>0111010=>0101110 [[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>0011010=>0101100 [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>1011010=>0101101 [[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>0101010=>0101010 [[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>0101010=>0101010 [[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>0011010=>0101100 [[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>0101010=>0101010 [[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>0001010=>0101000 [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>0101010=>0101010 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>0101010=>0101010 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>0001010=>0101000 [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>1110010=>0100111 [[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>1010010=>0100101 [[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>0010010=>0100100 [[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>0110010=>0100110 [[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>0010010=>0100100 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>0100010=>0100010 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>0000010=>0100000 [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>0111100=>0011110 [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>1011100=>0011101 [[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>0011100=>0011100 [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>0111100=>0011110 [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>1011100=>0011101 [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>1101100=>0011011 [[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>0001100=>0011000 [[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>0011100=>0011100 [[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>0001100=>0011000 [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>1101100=>0011011 [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>1110100=>0010111 [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>0110100=>0010110 [[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>0110100=>0010110 [[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>0011100=>0011100 [[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>0011100=>0011100 [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>0101100=>0011010 [[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>0001100=>0011000 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>0001100=>0011000 [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>0101100=>0011010 [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>0110100=>0010110 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>1001100=>0011001 [[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>1001100=>0011001 [[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>0011100=>0011100 [[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>0001100=>0011000 [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>0000100=>0010000 [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>1100100=>0010011 [[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>0100100=>0010010 [[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>0000100=>0010000 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>1110100=>0010111 [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>1010100=>0010101 [[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>0010100=>0010100 [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>1010100=>0010101 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>0010100=>0010100 [[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>0100100=>0010010 [[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>1000100=>0010001 [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>0000100=>0010000 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>1111000=>0001111 [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>0111000=>0001110 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>0111000=>0001110 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>1011000=>0001101 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>0011000=>0001100 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>0111000=>0001110 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>0011000=>0001100 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>1011000=>0001101 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>0011000=>0001100 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>1101000=>0001011 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>0101000=>0001010 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>0101000=>0001010 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>1001000=>0001001 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0001000=>0001000 [[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>0011000=>0001100 [[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>0001000=>0001000 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>0101000=>0001010 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>0001000=>0001000 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>1110000=>0000111 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>0110000=>0000110 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>0110000=>0000110 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>1010000=>0000101 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>0010000=>0000100 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>0110000=>0000110 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>0010000=>0000100 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>1010000=>0000101 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>0010000=>0000100 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>1100000=>0000011 [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>0100000=>0000010 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>0100000=>0000010 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>1000000=>0000001 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>0000000=>0000000
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
Map
reverse
Description
Return the reversal of a binary word.