Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>=>
[.,[.,.]]=>[2,1]=>1=>0
[[.,.],.]=>[1,2]=>0=>1
[.,[.,[.,.]]]=>[3,2,1]=>11=>00
[.,[[.,.],.]]=>[2,3,1]=>10=>01
[[.,.],[.,.]]=>[1,3,2]=>01=>10
[[.,[.,.]],.]=>[2,1,3]=>10=>01
[[[.,.],.],.]=>[1,2,3]=>00=>11
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>111=>000
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>110=>001
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>101=>010
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>110=>001
[.,[[[.,.],.],.]]=>[2,3,4,1]=>100=>011
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>011=>100
[[.,.],[[.,.],.]]=>[1,3,4,2]=>010=>101
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>101=>010
[[[.,.],.],[.,.]]=>[1,2,4,3]=>001=>110
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>110=>001
[[.,[[.,.],.]],.]=>[2,3,1,4]=>100=>011
[[[.,.],[.,.]],.]=>[1,3,2,4]=>010=>101
[[[.,[.,.]],.],.]=>[2,1,3,4]=>100=>011
[[[[.,.],.],.],.]=>[1,2,3,4]=>000=>111
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>1111=>0000
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>1110=>0001
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>1101=>0010
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>1110=>0001
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>1100=>0011
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>1011=>0100
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>1010=>0101
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>1101=>0010
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>1001=>0110
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>1110=>0001
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>1100=>0011
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>1010=>0101
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>1100=>0011
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>1000=>0111
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>0111=>1000
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>0110=>1001
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>0101=>1010
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>0110=>1001
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>0100=>1011
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>1011=>0100
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>1010=>0101
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>0011=>1100
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>0010=>1101
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>1101=>0010
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>1001=>0110
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>0101=>1010
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>1001=>0110
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>0001=>1110
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1110=>0001
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>1100=>0011
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>1010=>0101
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1100=>0011
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>1000=>0111
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>0110=>1001
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>0100=>1011
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>1010=>0101
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>0010=>1101
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>1100=>0011
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>1000=>0111
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>0100=>1011
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1000=>0111
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0000=>1111
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>11111=>00000
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>11110=>00001
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>11101=>00010
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>11110=>00001
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>11100=>00011
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>11011=>00100
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>11010=>00101
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>11101=>00010
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>11001=>00110
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>11110=>00001
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>11100=>00011
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>11010=>00101
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>11100=>00011
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>11000=>00111
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>10111=>01000
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>10110=>01001
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>10101=>01010
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>10110=>01001
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>10100=>01011
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>11011=>00100
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>11010=>00101
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>10011=>01100
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>10010=>01101
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>11101=>00010
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>11001=>00110
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>10101=>01010
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>11001=>00110
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>10001=>01110
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>11110=>00001
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>11100=>00011
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>11010=>00101
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>11100=>00011
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>11000=>00111
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>10110=>01001
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>10100=>01011
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>11010=>00101
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>10010=>01101
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>11100=>00011
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>11000=>00111
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>10100=>01011
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>11000=>00111
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>10000=>01111
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>01111=>10000
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>01110=>10001
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>01101=>10010
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>01110=>10001
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>01100=>10011
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>01011=>10100
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>01010=>10101
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>01101=>10010
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>01001=>10110
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>01110=>10001
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>01100=>10011
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>01010=>10101
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>01100=>10011
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>01000=>10111
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>10111=>01000
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>10110=>01001
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>10101=>01010
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>10110=>01001
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>10100=>01011
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>00111=>11000
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>00110=>11001
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>00101=>11010
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>00110=>11001
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>00100=>11011
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>11011=>00100
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>11010=>00101
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>10011=>01100
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>10010=>01101
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>01011=>10100
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>01010=>10101
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>10011=>01100
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>10010=>01101
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>00011=>11100
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>00010=>11101
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>11101=>00010
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>11001=>00110
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>10101=>01010
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>11001=>00110
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>10001=>01110
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>01101=>10010
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>01001=>10110
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>10101=>01010
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>00101=>11010
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>11001=>00110
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>10001=>01110
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>01001=>10110
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>10001=>01110
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>00001=>11110
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>11110=>00001
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>11100=>00011
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>11010=>00101
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>11100=>00011
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>11000=>00111
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>10110=>01001
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>10100=>01011
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>11010=>00101
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>10010=>01101
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>11100=>00011
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>11000=>00111
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>10100=>01011
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>11000=>00111
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>10000=>01111
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>01110=>10001
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>01100=>10011
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>01010=>10101
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>01100=>10011
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>01000=>10111
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>10110=>01001
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>10100=>01011
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>00110=>11001
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>00100=>11011
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>11010=>00101
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>10010=>01101
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>01010=>10101
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>10010=>01101
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>00010=>11101
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>11100=>00011
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>11000=>00111
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>10100=>01011
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>11000=>00111
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>10000=>01111
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>01100=>10011
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>01000=>10111
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>10100=>01011
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>00100=>11011
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>11000=>00111
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>10000=>01111
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>01000=>10111
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>10000=>01111
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>00000=>11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>111111=>000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>111110=>000001
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>111101=>000010
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>111110=>000001
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>111100=>000011
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>111011=>000100
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>111010=>000101
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>111101=>000010
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>111001=>000110
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>111110=>000001
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>111100=>000011
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>111010=>000101
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>111100=>000011
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>111000=>000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>110111=>001000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>110110=>001001
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>110101=>001010
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>110110=>001001
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>110100=>001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>111011=>000100
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>111010=>000101
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>110011=>001100
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>110010=>001101
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>111101=>000010
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>111001=>000110
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>110101=>001010
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>111001=>000110
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>110001=>001110
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>111110=>000001
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>111100=>000011
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>111010=>000101
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>111100=>000011
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>111000=>000111
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>110110=>001001
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>110100=>001011
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>111010=>000101
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>110010=>001101
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>111100=>000011
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>111000=>000111
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>110100=>001011
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>111000=>000111
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>110000=>001111
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>101111=>010000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>101110=>010001
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>101101=>010010
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>101110=>010001
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>101100=>010011
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>101011=>010100
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>101010=>010101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>101101=>010010
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>101001=>010110
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>101110=>010001
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>101100=>010011
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>101010=>010101
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>101100=>010011
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>101000=>010111
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>110111=>001000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>110110=>001001
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>110101=>001010
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>110110=>001001
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>110100=>001011
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>100111=>011000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>100110=>011001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>100101=>011010
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>100110=>011001
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>100100=>011011
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>111011=>000100
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>111010=>000101
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>110011=>001100
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>110010=>001101
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>101011=>010100
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>101010=>010101
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>110011=>001100
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>110010=>001101
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>100011=>011100
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>100010=>011101
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>111101=>000010
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>111001=>000110
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>110101=>001010
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>111001=>000110
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>110001=>001110
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>101101=>010010
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>101001=>010110
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>110101=>001010
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>100101=>011010
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>111001=>000110
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>110001=>001110
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>101001=>010110
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>110001=>001110
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>100001=>011110
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>111110=>000001
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>111100=>000011
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>111010=>000101
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>111100=>000011
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>111000=>000111
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>110110=>001001
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>110100=>001011
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>111010=>000101
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>110010=>001101
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>111100=>000011
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>111000=>000111
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>110100=>001011
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>111000=>000111
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>110000=>001111
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>101110=>010001
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>101100=>010011
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>101010=>010101
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>101100=>010011
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>101000=>010111
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>110110=>001001
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>110100=>001011
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>100110=>011001
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>100100=>011011
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>111010=>000101
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>110010=>001101
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>101010=>010101
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>110010=>001101
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>100010=>011101
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>111100=>000011
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>111000=>000111
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>110100=>001011
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>111000=>000111
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>110000=>001111
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>101100=>010011
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>101000=>010111
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>110100=>001011
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>100100=>011011
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>111000=>000111
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>110000=>001111
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>101000=>010111
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>110000=>001111
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>100000=>011111
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>011111=>100000
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>011110=>100001
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>011101=>100010
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>011110=>100001
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>011100=>100011
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>011011=>100100
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>011010=>100101
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>011101=>100010
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>011001=>100110
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>011110=>100001
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>011100=>100011
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>011010=>100101
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>011100=>100011
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>011000=>100111
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>010111=>101000
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>010110=>101001
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>010101=>101010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>010110=>101001
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>010100=>101011
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>011011=>100100
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>011010=>100101
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>010011=>101100
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>010010=>101101
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>011101=>100010
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>011001=>100110
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>010101=>101010
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>011001=>100110
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>010001=>101110
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>011110=>100001
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>011100=>100011
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>011010=>100101
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>011100=>100011
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>011000=>100111
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>010110=>101001
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>010100=>101011
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>011010=>100101
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>010010=>101101
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>011100=>100011
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>011000=>100111
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>010100=>101011
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>011000=>100111
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>010000=>101111
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>101111=>010000
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>101110=>010001
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>101101=>010010
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>101110=>010001
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>101100=>010011
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>101011=>010100
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>101010=>010101
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>101101=>010010
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>101001=>010110
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>101110=>010001
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>101100=>010011
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>101010=>010101
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>101100=>010011
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>101000=>010111
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>001111=>110000
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>001110=>110001
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>001101=>110010
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>001110=>110001
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>001100=>110011
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>001011=>110100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>001010=>110101
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>001101=>110010
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>001001=>110110
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>001110=>110001
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>001100=>110011
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>001010=>110101
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>001100=>110011
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>001000=>110111
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>110111=>001000
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>110110=>001001
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>110101=>001010
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>110110=>001001
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>110100=>001011
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>100111=>011000
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>100110=>011001
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>100101=>011010
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>100110=>011001
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>100100=>011011
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>010111=>101000
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>010110=>101001
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>010101=>101010
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>010110=>101001
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>010100=>101011
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>100111=>011000
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>100110=>011001
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>100101=>011010
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>100110=>011001
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>100100=>011011
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>000111=>111000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>000110=>111001
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>000101=>111010
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>000110=>111001
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>000100=>111011
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>111011=>000100
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>111010=>000101
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>110011=>001100
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>110010=>001101
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>101011=>010100
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>101010=>010101
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>110011=>001100
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>110010=>001101
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>100011=>011100
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>100010=>011101
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>011011=>100100
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>011010=>100101
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>010011=>101100
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>010010=>101101
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>101011=>010100
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>101010=>010101
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>001011=>110100
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>001010=>110101
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>110011=>001100
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>110010=>001101
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>100011=>011100
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>100010=>011101
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>010011=>101100
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>010010=>101101
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>100011=>011100
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>100010=>011101
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>000011=>111100
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>000010=>111101
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>111101=>000010
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>111001=>000110
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>110101=>001010
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>111001=>000110
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>110001=>001110
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>101101=>010010
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>101001=>010110
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>110101=>001010
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>100101=>011010
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>111001=>000110
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>110001=>001110
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>101001=>010110
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>110001=>001110
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>100001=>011110
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>011101=>100010
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>011001=>100110
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>010101=>101010
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>011001=>100110
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>010001=>101110
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>101101=>010010
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>101001=>010110
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>001101=>110010
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>001001=>110110
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>110101=>001010
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>100101=>011010
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>010101=>101010
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>100101=>011010
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>000101=>111010
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>111001=>000110
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>110001=>001110
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>101001=>010110
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>110001=>001110
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>100001=>011110
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>011001=>100110
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>010001=>101110
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>101001=>010110
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>001001=>110110
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>110001=>001110
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>100001=>011110
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>010001=>101110
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>100001=>011110
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>000001=>111110
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>111110=>000001
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>111100=>000011
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>111010=>000101
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>111100=>000011
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>111000=>000111
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>110110=>001001
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>110100=>001011
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>111010=>000101
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>110010=>001101
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>111100=>000011
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>111000=>000111
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>110100=>001011
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>111000=>000111
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>110000=>001111
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>101110=>010001
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>101100=>010011
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>101010=>010101
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>101100=>010011
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>101000=>010111
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>110110=>001001
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>110100=>001011
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>100110=>011001
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>100100=>011011
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>111010=>000101
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>110010=>001101
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>101010=>010101
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>110010=>001101
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>100010=>011101
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>111100=>000011
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>111000=>000111
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>110100=>001011
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>111000=>000111
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>110000=>001111
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>101100=>010011
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>101000=>010111
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>110100=>001011
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>100100=>011011
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>111000=>000111
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>110000=>001111
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>101000=>010111
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>110000=>001111
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>100000=>011111
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>011110=>100001
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>011100=>100011
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>011010=>100101
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>011100=>100011
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>011000=>100111
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>010110=>101001
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>010100=>101011
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>011010=>100101
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>010010=>101101
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>011100=>100011
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>011000=>100111
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>010100=>101011
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>011000=>100111
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>010000=>101111
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>101110=>010001
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>101100=>010011
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>101010=>010101
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>101100=>010011
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>101000=>010111
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>001110=>110001
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>001100=>110011
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>001010=>110101
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>001100=>110011
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>001000=>110111
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>110110=>001001
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>110100=>001011
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>100110=>011001
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>100100=>011011
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>010110=>101001
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>010100=>101011
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>100110=>011001
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>100100=>011011
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>000110=>111001
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>000100=>111011
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>111010=>000101
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>110010=>001101
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>101010=>010101
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>110010=>001101
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>100010=>011101
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>011010=>100101
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>010010=>101101
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>101010=>010101
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>001010=>110101
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>110010=>001101
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>100010=>011101
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>010010=>101101
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>100010=>011101
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>000010=>111101
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>111100=>000011
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>111000=>000111
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>110100=>001011
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>111000=>000111
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>110000=>001111
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>101100=>010011
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>101000=>010111
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>110100=>001011
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>100100=>011011
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>111000=>000111
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>110000=>001111
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>101000=>010111
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>110000=>001111
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>100000=>011111
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>011100=>100011
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>011000=>100111
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>010100=>101011
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>011000=>100111
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>010000=>101111
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>101100=>010011
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>101000=>010111
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>001100=>110011
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>001000=>110111
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>110100=>001011
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>100100=>011011
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>010100=>101011
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>100100=>011011
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>000100=>111011
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>111000=>000111
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>110000=>001111
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>101000=>010111
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>110000=>001111
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>100000=>011111
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>011000=>100111
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>010000=>101111
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>101000=>010111
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>001000=>110111
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>110000=>001111
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>100000=>011111
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>010000=>101111
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>100000=>011111
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>000000=>111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>1111111=>0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>1111110=>0000001
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>1111101=>0000010
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>1111110=>0000001
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>1111100=>0000011
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>1111011=>0000100
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>1111010=>0000101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>1111101=>0000010
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>1111001=>0000110
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>1111110=>0000001
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>1111100=>0000011
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>1111010=>0000101
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>1111100=>0000011
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>1111000=>0000111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>1110111=>0001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>1110110=>0001001
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>1110101=>0001010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>1110110=>0001001
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>1110100=>0001011
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>1111010=>0000101
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>1110011=>0001100
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>1110010=>0001101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>1111101=>0000010
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>1111001=>0000110
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>1110101=>0001010
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>1110001=>0001110
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>1111110=>0000001
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>1111100=>0000011
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>1111010=>0000101
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>1111100=>0000011
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>1111000=>0000111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>1110110=>0001001
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>1110100=>0001011
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>1111010=>0000101
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>1110010=>0001101
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>1111100=>0000011
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>1111000=>0000111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>1110100=>0001011
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>1111000=>0000111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>1110000=>0001111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>1101111=>0010000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>1101110=>0010001
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>1101101=>0010010
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>1101110=>0010001
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>1101011=>0010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>1101010=>0010101
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>1101001=>0010110
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>1101110=>0010001
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>1101100=>0010011
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[3,5,7,6,8,4,2,1]=>1101010=>0010101
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>1101000=>0010111
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>1110111=>0001000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>1110110=>0001001
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>1110100=>0001011
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>1100111=>0011000
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>1100100=>0011011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>1111011=>0000100
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>1111010=>0000101
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>1110010=>0001101
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[3,5,4,7,8,6,2,1]=>1101010=>0010101
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>1110010=>0001101
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>1100011=>0011100
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>1100010=>0011101
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>1111101=>0000010
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>1111001=>0000110
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>1110001=>0001110
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[3,6,5,4,8,7,2,1]=>1101101=>0010010
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>1110101=>0001010
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>1111001=>0000110
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>1110001=>0001110
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>1110001=>0001110
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[3,4,5,6,8,7,2,1]=>1100001=>0011110
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>1111110=>0000001
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>1111100=>0000011
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>1111010=>0000101
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>1111100=>0000011
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>1111000=>0000111
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>1110110=>0001001
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>1111010=>0000101
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>1111100=>0000011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>1111000=>0000111
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>1110000=>0001111
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>1101110=>0010001
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>1101010=>0010101
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>1101000=>0010111
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1]=>1110110=>0001001
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>1100110=>0011001
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[3,4,6,7,5,8,2,1]=>1100100=>0011011
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>1110010=>0001101
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>1101010=>0010101
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>1110010=>0001101
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>1100010=>0011101
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>1111100=>0000011
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>1110000=>0001111
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[3,6,5,4,7,8,2,1]=>1101100=>0010011
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>1101000=>0010111
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>1110100=>0001011
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>1100100=>0011011
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>1111000=>0000111
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[3,5,4,6,7,8,2,1]=>1101000=>0010111
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>1110000=>0001111
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>1100000=>0011111
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>1011111=>0100000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>1011110=>0100001
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>1011101=>0100010
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>1011110=>0100001
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>1011100=>0100011
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[2,5,8,7,6,4,3,1]=>1011011=>0100100
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>1011100=>0100011
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[2,6,5,7,8,4,3,1]=>1011100=>0100011
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>1011000=>0100111
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>1010111=>0101000
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>1010110=>0101001
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>1010101=>0101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>1010100=>0101011
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>1011011=>0100100
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[2,5,4,7,8,6,3,1]=>1011010=>0100101
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>1010010=>0101101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>1011101=>0100010
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>1011001=>0100110
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>1010101=>0101010
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[2,4,5,6,8,7,3,1]=>1010001=>0101110
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>1011110=>0100001
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>1011100=>0100011
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[2,5,6,7,4,8,3,1]=>1011000=>0100111
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>1010110=>0101001
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>1010100=>0101011
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[2,5,4,7,6,8,3,1]=>1011010=>0100101
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>1011100=>0100011
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>1011000=>0100111
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>1010100=>0101011
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[2,5,4,6,7,8,3,1]=>1011000=>0100111
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>1010000=>0101111
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>1101111=>0010000
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>1101101=>0010010
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[3,2,5,7,8,6,4,1]=>1101010=>0010101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>1101101=>0010010
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>1101010=>0010101
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>1101000=>0010111
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>1001111=>0110000
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>1001100=>0110011
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>1001011=>0110100
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>1001010=>0110101
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>1001101=>0110010
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>1001001=>0110110
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>1001110=>0110001
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>1001010=>0110101
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>1001000=>0110111
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>1110111=>0001000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>1110110=>0001001
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>1110101=>0001010
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>1100111=>0011000
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>1100110=>0011001
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>1010111=>0101000
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>1010101=>0101010
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>1010100=>0101011
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>1100111=>0011000
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[3,2,4,7,8,6,5,1]=>1100110=>0011001
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>1000111=>0111000
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>1000110=>0111001
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[2,3,4,6,8,7,5,1]=>1000101=>0111010
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[2,3,4,7,6,8,5,1]=>1000110=>0111001
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>1000100=>0111011
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>1111011=>0000100
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>1111010=>0000101
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>1110011=>0001100
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[3,5,4,2,7,8,6,1]=>1101010=>0010101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>1110011=>0001100
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[3,4,5,2,7,8,6,1]=>1100010=>0011101
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>1011011=>0100100
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>1011010=>0100101
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>1010011=>0101100
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>1010010=>0101101
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[3,2,5,4,7,8,6,1]=>1101010=>0010101
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>1001011=>0110100
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>1001010=>0110101
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>1110011=>0001100
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[4,3,2,5,7,8,6,1]=>1110010=>0001101
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[3,4,2,5,8,7,6,1]=>1100011=>0011100
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>1100010=>0011101
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>1010011=>0101100
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[3,2,4,5,7,8,6,1]=>1100010=>0011101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>1000011=>0111100
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>1000010=>0111101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>1111101=>0000010
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>1110101=>0001010
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>1111001=>0000110
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>1110001=>0001110
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>1101101=>0010010
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>1101001=>0010110
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>1110101=>0001010
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>1111001=>0000110
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>1110001=>0001110
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[3,5,4,6,2,8,7,1]=>1101001=>0010110
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[3,4,5,6,2,8,7,1]=>1100001=>0011110
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>1011101=>0100010
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>1010101=>0101010
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>1010001=>0101110
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>1101101=>0010010
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[2,3,5,6,4,8,7,1]=>1001001=>0110110
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>1110101=>0001010
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>1100101=>0011010
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>1010101=>0101010
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>1100101=>0011010
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>1000101=>0111010
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>1111001=>0000110
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>1110001=>0001110
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>1011001=>0100110
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[2,4,5,3,6,8,7,1]=>1010001=>0101110
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[3,2,5,4,6,8,7,1]=>1101001=>0010110
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>1110001=>0001110
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>1100001=>0011110
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>1010001=>0101110
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>1100001=>0011110
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>1000001=>0111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>1111110=>0000001
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>1111100=>0000011
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>1111010=>0000101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>1111100=>0000011
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>1111000=>0000111
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>1110110=>0001001
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[4,6,7,5,3,2,8,1]=>1110100=>0001011
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>1111100=>0000011
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>1110100=>0001011
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>1110000=>0001111
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>1101010=>0010101
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>1101000=>0010111
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>1110110=>0001001
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>1110100=>0001011
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>1100110=>0011001
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>1100100=>0011011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>1111010=>0000101
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[4,5,3,7,6,2,8,1]=>1110010=>0001101
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[3,5,4,7,6,2,8,1]=>1101010=>0010101
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[3,4,5,7,6,2,8,1]=>1100010=>0011101
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>1111100=>0000011
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>1110100=>0001011
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>1111000=>0000111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>1110000=>0001111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>1101100=>0010011
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>1101000=>0010111
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>1110100=>0001011
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>1100100=>0011011
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>1111000=>0000111
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>1110000=>0001111
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>1101000=>0010111
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>1110000=>0001111
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>1100000=>0011111
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>1011110=>0100001
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[2,6,5,7,4,3,8,1]=>1011100=>0100011
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>1011000=>0100111
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>1010100=>0101011
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>1011010=>0100101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>1010100=>0101011
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>1011000=>0100111
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>1010000=>0101111
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[3,2,7,6,5,4,8,1]=>1101110=>0010001
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>1101100=>0010011
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[3,2,5,7,6,4,8,1]=>1101010=>0010101
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>1101100=>0010011
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>1101000=>0010111
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>1001110=>0110001
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[2,3,5,7,6,4,8,1]=>1001010=>0110101
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>1001000=>0110111
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>1110110=>0001001
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>1110100=>0001011
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>1100110=>0011001
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>1100100=>0011011
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>1010110=>0101001
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[2,4,3,6,7,5,8,1]=>1010100=>0101011
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>1100110=>0011001
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>1000110=>0111001
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[2,3,4,6,7,5,8,1]=>1000100=>0111011
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>1111010=>0000101
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[3,5,4,2,7,6,8,1]=>1101010=>0010101
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>1110010=>0001101
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>1100010=>0011101
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>1011010=>0100101
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>1101010=>0010101
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>1001010=>0110101
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>1110010=>0001101
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[3,4,2,5,7,6,8,1]=>1100010=>0011101
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>1010010=>0101101
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>1100010=>0011101
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>1000010=>0111101
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>1111100=>0000011
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>1111000=>0000111
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>1110000=>0001111
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>1101100=>0010011
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>1101000=>0010111
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[3,4,6,5,2,7,8,1]=>1100100=>0011011
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>1111000=>0000111
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>1101000=>0010111
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>1110000=>0001111
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>1100000=>0011111
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>1011100=>0100011
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[2,5,6,4,3,7,8,1]=>1011000=>0100111
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[2,4,6,5,3,7,8,1]=>1010100=>0101011
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>1011000=>0100111
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[2,4,5,6,3,7,8,1]=>1010000=>0101111
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[3,2,5,6,4,7,8,1]=>1101000=>0010111
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>1001100=>0110011
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>1001000=>0110111
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>1110100=>0001011
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>1100100=>0011011
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>1010100=>0101011
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>1000100=>0111011
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>1111000=>0000111
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>1110000=>0001111
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>1101000=>0010111
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>1110000=>0001111
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>1100000=>0011111
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>1011000=>0100111
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>1010000=>0101111
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>1101000=>0010111
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>1001000=>0110111
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>1110000=>0001111
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>1100000=>0011111
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>1010000=>0101111
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>1100000=>0011111
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>1000000=>0111111
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>0111111=>1000000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>0111110=>1000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>0111101=>1000010
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>0111110=>1000001
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>0111100=>1000011
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>0111011=>1000100
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>0111101=>1000010
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>0111110=>1000001
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>0111100=>1000011
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>0111010=>1000101
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>0111100=>1000011
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>0111000=>1000111
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>0110111=>1001000
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>0110110=>1001001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>0110101=>1001010
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>0110100=>1001011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>0111010=>1000101
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>0110011=>1001100
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>0110010=>1001101
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,6,5,4,8,7,3,2]=>0111101=>1000010
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>0110101=>1001010
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>0111001=>1000110
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>0111110=>1000001
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>0110110=>1001001
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>0110100=>1001011
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>0111100=>1000011
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,5,6,4,7,8,3,2]=>0111000=>1000111
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>0111000=>1000111
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>0110000=>1001111
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>0101111=>1010000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>0101110=>1010001
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>0101101=>1010010
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>0101100=>1010011
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>0101011=>1010100
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>0101010=>1010101
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>0101001=>1010110
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>0101010=>1010101
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>0101100=>1010011
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>0101000=>1010111
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>0110111=>1001000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>0110110=>1001001
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>0110101=>1001010
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>0110110=>1001001
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>0110100=>1001011
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>0100111=>1011000
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>0100110=>1011001
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>0100100=>1011011
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>0111011=>1000100
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>0110011=>1001100
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>0101011=>1010100
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>0101010=>1010101
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>0110011=>1001100
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>0110010=>1001101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>0100011=>1011100
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>0100010=>1011101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>0111101=>1000010
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>0111001=>1000110
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>0110101=>1001010
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,4,5,6,3,8,7,2]=>0110001=>1001110
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>0101101=>1010010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>0110101=>1001010
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>0111001=>1000110
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>0110001=>1001110
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>0100001=>1011110
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>0111110=>1000001
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>0111100=>1000011
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>0111100=>1000011
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,5,6,7,4,3,8,2]=>0111000=>1000111
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>0110100=>1001011
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,5,6,4,7,3,8,2]=>0111000=>1000111
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,4,6,5,7,3,8,2]=>0110100=>1001011
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>0111000=>1000111
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>0110000=>1001111
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>0101010=>1010101
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,3,6,5,7,4,8,2]=>0101100=>1010011
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>0101000=>1010111
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>0110100=>1001011
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>0100110=>1011001
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,3,4,6,7,5,8,2]=>0100100=>1011011
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>0101010=>1010101
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,3,4,5,7,6,8,2]=>0100010=>1011101
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>0111100=>1000011
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>0111000=>1000111
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>0101000=>1010111
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>0110100=>1001011
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>0100100=>1011011
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>0111000=>1000111
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>0110000=>1001111
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>0101000=>1010111
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>0110000=>1001111
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>0100000=>1011111
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>1011111=>0100000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>1011110=>0100001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>1011101=>0100010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>1011110=>0100001
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>1011100=>0100011
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>1011011=>0100100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>1011010=>0100101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>1011101=>0100010
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[2,1,5,6,8,7,4,3]=>1011001=>0100110
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>1011110=>0100001
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>1011100=>0100011
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>1011010=>0100101
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>1011100=>0100011
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>1011000=>0100111
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>1010111=>0101000
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>1010110=>0101001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>1010101=>0101010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[2,1,4,7,6,8,5,3]=>1010110=>0101001
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>1010100=>0101011
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>1011011=>0100100
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>1011010=>0100101
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>1010011=>0101100
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>1010010=>0101101
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[2,1,6,5,4,8,7,3]=>1011101=>0100010
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[2,1,5,6,4,8,7,3]=>1011001=>0100110
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>1010101=>0101010
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>1011001=>0100110
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>1010001=>0101110
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[2,1,7,6,5,4,8,3]=>1011110=>0100001
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[2,1,6,7,5,4,8,3]=>1011100=>0100011
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>1011010=>0100101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>1011100=>0100011
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>1011000=>0100111
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>1010110=>0101001
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>1010100=>0101011
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>1011010=>0100101
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>1011000=>0100111
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>1011000=>0100111
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>1010000=>0101111
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>0011111=>1100000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>0011110=>1100001
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>0011110=>1100001
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>0011100=>1100011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>0011011=>1100100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>0011101=>1100010
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>0011001=>1100110
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>0011110=>1100001
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>0011010=>1100101
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>0011100=>1100011
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>0011000=>1100111
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>0010111=>1101000
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>0010110=>1101001
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>0010101=>1101010
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,2,4,7,6,8,5,3]=>0010110=>1101001
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>0010100=>1101011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>0011011=>1100100
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>0011010=>1100101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>0010011=>1101100
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>0010010=>1101101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>0011101=>1100010
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>0010101=>1101010
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>0011001=>1100110
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>0010001=>1101110
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>0011110=>1100001
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>0011010=>1100101
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>0011000=>1100111
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>0010110=>1101001
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,2,5,4,7,6,8,3]=>0011010=>1100101
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>0011100=>1100011
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>0011000=>1100111
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,2,4,6,5,7,8,3]=>0010100=>1101011
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>0011000=>1100111
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>0010000=>1101111
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>1101111=>0010000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>1101110=>0010001
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>1101101=>0010010
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>1101110=>0010001
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>1101100=>0010011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>1101011=>0010100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>1101010=>0010101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>1101101=>0010010
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>1101001=>0010110
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>1101110=>0010001
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>1101100=>0010011
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>1101010=>0010101
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>1101100=>0010011
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>1101000=>0010111
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>1001111=>0110000
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>1001110=>0110001
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>1001101=>0110010
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>1001110=>0110001
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>1001100=>0110011
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>1001101=>0110010
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>1001110=>0110001
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>1001100=>0110011
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>1001010=>0110101
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>1001000=>0110111
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>0101111=>1010000
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>0101101=>1010010
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>0101110=>1010001
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,3,2,6,7,8,5,4]=>0101100=>1010011
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>0101011=>1010100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>0101010=>1010101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>0101101=>1010010
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,3,2,5,6,8,7,4]=>0101001=>1010110
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>0101110=>1010001
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>0101100=>1010011
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>0101010=>1010101
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>0101100=>1010011
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>0101000=>1010111
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>1001111=>0110000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>1001110=>0110001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>1001101=>0110010
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>1001100=>0110011
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[2,1,3,6,5,8,7,4]=>1001101=>0110010
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>1001010=>0110101
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>1001000=>0110111
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>0001111=>1110000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>0001110=>1110001
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>0001101=>1110010
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>0001110=>1110001
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>0001100=>1110011
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>0001011=>1110100
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>0001010=>1110101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>0001101=>1110010
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>0001001=>1110110
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>0001110=>1110001
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>0001100=>1110011
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>0001010=>1110101
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>0001100=>1110011
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>0001000=>1110111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>1110111=>0001000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>1110110=>0001001
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>1110101=>0001010
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>1110110=>0001001
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>1110100=>0001011
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>1100111=>0011000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>1100110=>0011001
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>1100101=>0011010
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>1100110=>0011001
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>1100100=>0011011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>1010111=>0101000
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>1010110=>0101001
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>1010101=>0101010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>1010110=>0101001
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>1010100=>0101011
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>1100111=>0011000
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>1100110=>0011001
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>1100101=>0011010
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>1100110=>0011001
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>1100100=>0011011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>1000111=>0111000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>1000110=>0111001
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>1000101=>0111010
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>1000110=>0111001
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>1000100=>0111011
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>0110111=>1001000
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>0110101=>1001010
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>0110110=>1001001
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>0110100=>1001011
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>0100111=>1011000
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>0100110=>1011001
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>0100101=>1011010
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>0100110=>1011001
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>0100100=>1011011
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>1010111=>0101000
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>1010110=>0101001
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>1010101=>0101010
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>1010110=>0101001
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>1010100=>0101011
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>0010111=>1101000
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>0010110=>1101001
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>0010101=>1101010
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>0010110=>1101001
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>0010100=>1101011
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>1100111=>0011000
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>1100110=>0011001
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>1100101=>0011010
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>1100110=>0011001
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>1100100=>0011011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>1000111=>0111000
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>1000110=>0111001
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>1000110=>0111001
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>1000100=>0111011
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>0100111=>1011000
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>0100101=>1011010
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>0100110=>1011001
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>0100100=>1011011
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>1000111=>0111000
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>1000110=>0111001
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>1000110=>0111001
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>1000100=>0111011
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>0000111=>1111000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>0000110=>1111001
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>0000101=>1111010
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>0000110=>1111001
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>0000100=>1111011
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>1111011=>0000100
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>1111010=>0000101
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>1110011=>0001100
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>1101011=>0010100
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>1101010=>0010101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>1110011=>0001100
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>1100011=>0011100
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>1100010=>0011101
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>1011011=>0100100
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>1011010=>0100101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>1010011=>0101100
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>1010010=>0101101
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>1101011=>0010100
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>1101010=>0010101
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>1001011=>0110100
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>1110011=>0001100
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>1110010=>0001101
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>1100011=>0011100
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>1100010=>0011101
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>1010011=>0101100
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>1010010=>0101101
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>1100011=>0011100
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>1000011=>0111100
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>1000010=>0111101
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>0111011=>1000100
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>0111010=>1000101
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>0110011=>1001100
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,4,5,3,2,7,8,6]=>0110010=>1001101
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>0101010=>1010101
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>0110011=>1001100
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>0110010=>1001101
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>0100011=>1011100
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>0100010=>1011101
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]=>1011011=>0100100
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[2,1,4,5,3,8,7,6]=>1010011=>0101100
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>0011011=>1100100
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>0011010=>1100101
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>0010011=>1101100
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>0010010=>1101101
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>0101011=>1010100
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>0101010=>1010101
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>1001011=>0110100
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[2,1,3,5,4,7,8,6]=>1001010=>0110101
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>0001011=>1110100
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>0001010=>1110101
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>1110011=>0001100
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>1110010=>0001101
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>1100011=>0011100
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[2,4,3,1,5,8,7,6]=>1010011=>0101100
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>1100011=>0011100
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>1100010=>0011101
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>1000011=>0111100
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>1000010=>0111101
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>0110011=>1001100
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>0110010=>1001101
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>0100011=>1011100
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>0100010=>1011101
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]=>1010011=>0101100
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[2,1,4,3,5,7,8,6]=>1010010=>0101101
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]=>0010011=>1101100
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>0010010=>1101101
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>1100011=>0011100
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>1100010=>0011101
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>1000010=>0111101
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]=>0100011=>1011100
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>0100010=>1011101
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>1000011=>0111100
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>1000010=>0111101
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>0000011=>1111100
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>0000010=>1111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>1111101=>0000010
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>1111001=>0000110
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>1110101=>0001010
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>1111001=>0000110
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>1110001=>0001110
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>1101101=>0010010
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>1101001=>0010110
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>1110101=>0001010
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[3,4,6,5,2,1,8,7]=>1100101=>0011010
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>1111001=>0000110
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>1110001=>0001110
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>1110001=>0001110
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>1100001=>0011110
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>1011101=>0100010
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>1011001=>0100110
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>1010101=>0101010
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[3,2,6,5,4,1,8,7]=>1101101=>0010010
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>1101001=>0010110
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>1001101=>0110010
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>1001001=>0110110
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[4,3,2,6,5,1,8,7]=>1110101=>0001010
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>1100101=>0011010
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>1010101=>0101010
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>1111001=>0000110
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>1110001=>0001110
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>1101001=>0010110
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>1110001=>0001110
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>1100001=>0011110
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>1011001=>0100110
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>1010001=>0101110
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>1101001=>0010110
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>1110001=>0001110
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>1100001=>0011110
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[2,4,3,5,6,1,8,7]=>1010001=>0101110
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>1000001=>0111110
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>0111101=>1000010
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,5,6,4,3,2,8,7]=>0111001=>1000110
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>0111001=>1000110
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>0101101=>1010010
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,3,4,5,6,2,8,7]=>0100001=>1011110
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>1011101=>0100010
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>1011001=>0100110
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>1010101=>0101010
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>1011001=>0100110
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>1010001=>0101110
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>0010001=>1101110
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>1101101=>0010010
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>1001101=>0110010
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]=>0101101=>1010010
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,3,2,5,6,4,8,7]=>0101001=>1010110
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>1001101=>0110010
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[2,1,3,5,6,4,8,7]=>1001001=>0110110
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>0001101=>1110010
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>0001001=>1110110
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>1110101=>0001010
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>1100101=>0011010
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>1010101=>0101010
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>1100101=>0011010
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>1000101=>0111010
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>0100101=>1011010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>1010101=>0101010
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>0010101=>1101010
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[2,3,1,4,6,5,8,7]=>1000101=>0111010
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>0100101=>1011010
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>1000101=>0111010
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>0000101=>1111010
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>1111001=>0000110
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>1110001=>0001110
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>1101001=>0010110
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[4,3,5,2,1,6,8,7]=>1110001=>0001110
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>1100001=>0011110
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>1011001=>0100110
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>1010001=>0101110
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>1101001=>0010110
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>1001001=>0110110
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[2,4,3,5,1,6,8,7]=>1010001=>0101110
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>1000001=>0111110
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,4,5,3,2,6,8,7]=>0110001=>1001110
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>0101001=>1010110
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,3,4,5,2,6,8,7]=>0100001=>1011110
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>1011001=>0100110
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>1010001=>0101110
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>0011001=>1100110
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>1001001=>0110110
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>0001001=>1110110
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>1110001=>0001110
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[3,4,2,1,5,6,8,7]=>1100001=>0011110
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>1100001=>0011110
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>1000001=>0111110
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>0110001=>1001110
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>0100001=>1011110
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>1010001=>0101110
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>0010001=>1101110
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>1100001=>0011110
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>1000001=>0111110
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]=>0100001=>1011110
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>1000001=>0111110
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>0000001=>1111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>1111110=>0000001
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>1111100=>0000011
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>1111010=>0000101
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>1111100=>0000011
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>1111000=>0000111
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>1110110=>0001001
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>1110100=>0001011
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>1111010=>0000101
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>1110010=>0001101
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>1111100=>0000011
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>1111000=>0000111
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>1110100=>0001011
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>1111000=>0000111
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>1110000=>0001111
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>1101010=>0010101
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>1101000=>0010111
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>1110110=>0001001
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>1100110=>0011001
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[5,4,3,7,6,2,1,8]=>1111010=>0000101
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>1110010=>0001101
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>1101010=>0010101
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>1110010=>0001101
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>1111100=>0000011
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>1111000=>0000111
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>1111000=>0000111
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>1101100=>0010011
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>1101000=>0010111
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[4,3,6,5,7,2,1,8]=>1110100=>0001011
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>1111000=>0000111
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>1100000=>0011111
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>1011110=>0100001
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[2,6,7,5,4,3,1,8]=>1011100=>0100011
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[2,5,7,6,4,3,1,8]=>1011010=>0100101
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>1011000=>0100111
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>1010100=>0101011
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[2,5,4,7,6,3,1,8]=>1011010=>0100101
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>1011000=>0100111
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>1011000=>0100111
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[2,4,5,6,7,3,1,8]=>1010000=>0101111
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>1101110=>0010001
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>1101100=>0010011
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>1101010=>0010101
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[3,2,6,5,7,4,1,8]=>1101100=>0010011
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>1101000=>0010111
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>1001110=>0110001
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>1001100=>0110011
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>1001010=>0110101
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>1001100=>0110011
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>1001000=>0110111
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[4,3,2,6,7,5,1,8]=>1110100=>0001011
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>1100110=>0011001
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>1100100=>0011011
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>1000110=>0111001
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[2,3,4,6,7,5,1,8]=>1000100=>0111011
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>1111010=>0000101
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>1110010=>0001101
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>1101010=>0010101
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>1110010=>0001101
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[3,4,5,2,7,6,1,8]=>1100010=>0011101
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>1101010=>0010101
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>1110010=>0001101
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[3,4,2,5,7,6,1,8]=>1100010=>0011101
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>1000010=>0111101
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>1111100=>0000011
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>1111000=>0000111
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>1111000=>0000111
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>1101100=>0010011
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>1100100=>0011011
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>1111000=>0000111
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>1110000=>0001111
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>1101000=>0010111
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>1110000=>0001111
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>1100000=>0011111
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>1011000=>0100111
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>1101100=>0010011
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>1001000=>0110111
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[4,3,2,6,5,7,1,8]=>1110100=>0001011
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>1100100=>0011011
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>1010100=>0101011
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>1000100=>0111011
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>1111000=>0000111
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>1101000=>0010111
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>1100000=>0011111
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>1011000=>0100111
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[2,4,5,3,6,7,1,8]=>1010000=>0101111
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>1001000=>0110111
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>1110000=>0001111
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>1100000=>0011111
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>1100000=>0011111
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>1000000=>0111111
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>0111110=>1000001
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,6,7,5,4,3,2,8]=>0111100=>1000011
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,6,5,7,4,3,2,8]=>0111100=>1000011
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>0111000=>1000111
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,4,7,6,5,3,2,8]=>0110110=>1001001
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,4,6,7,5,3,2,8]=>0110100=>1001011
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,5,4,7,6,3,2,8]=>0111010=>1000101
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,5,6,4,7,3,2,8]=>0111000=>1000111
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>0110100=>1001011
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,5,4,6,7,3,2,8]=>0111000=>1000111
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>0110000=>1001111
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>0101110=>1010001
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>0101100=>1010011
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>0101010=>1010101
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,3,6,5,7,4,2,8]=>0101100=>1010011
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>0101000=>1010111
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>0100100=>1011011
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>0101010=>1010101
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>0110010=>1001101
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>0100010=>1011101
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>0111000=>1000111
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>0110000=>1001111
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>0101100=>1010011
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>0101000=>1010111
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>0110100=>1001011
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,3,4,6,5,7,2,8]=>0100100=>1011011
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>0111000=>1000111
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,4,5,3,6,7,2,8]=>0110000=>1001111
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,3,5,4,6,7,2,8]=>0101000=>1010111
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>0100000=>1011111
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>1011110=>0100001
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[2,1,6,7,5,4,3,8]=>1011100=>0100011
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>1011000=>0100111
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>1010100=>0101011
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>1011000=>0100111
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[2,1,4,5,6,7,3,8]=>1010000=>0101111
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>0011110=>1100001
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,2,6,7,5,4,3,8]=>0011100=>1100011
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>0011010=>1100101
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>0011000=>1100111
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,2,4,6,7,5,3,8]=>0010100=>1101011
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>0011000=>1100111
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>0011000=>1100111
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>0010000=>1101111
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>1101110=>0010001
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[3,2,1,6,7,5,4,8]=>1101100=>0010011
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>1101010=>0010101
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>1101100=>0010011
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>1101000=>0010111
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>1001100=>0110011
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>1001100=>0110011
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>1001000=>0110111
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>0101110=>1010001
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>0101100=>1010011
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>0101010=>1010101
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>0101100=>1010011
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>0101000=>1010111
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>1001100=>0110011
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>0001110=>1110001
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>0001100=>1110011
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>0001010=>1110101
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>0001100=>1110011
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>0001000=>1110111
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>1110110=>0001001
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>1110100=>0001011
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>1100110=>0011001
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>1100100=>0011011
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>1000110=>0111001
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>1000100=>0111011
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>0110110=>1001001
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>0110100=>1001011
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>0100100=>1011011
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>1010100=>0101011
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>0010100=>1101011
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>1100110=>0011001
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>1000100=>0111011
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>0100110=>1011001
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[2,1,3,4,6,7,5,8]=>1000100=>0111011
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>0000110=>1111001
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>0000100=>1111011
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>1111010=>0000101
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>1110010=>0001101
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>1101010=>0010101
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8]=>1100010=>0011101
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>1011010=>0100101
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>1010010=>0101101
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>1101010=>0010101
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>1001010=>0110101
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>1100010=>0011101
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>1010010=>0101101
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>1000010=>0111101
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>0111010=>1000101
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>0110010=>1001101
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>0101010=>1010101
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>0110010=>1001101
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>0100010=>1011101
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]=>1011010=>0100101
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,2,4,5,3,7,6,8]=>0010010=>1101101
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>1101010=>0010101
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>1001010=>0110101
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>0101010=>1010101
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>0001010=>1110101
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>1110010=>0001101
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>1100010=>0011101
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>1000010=>0111101
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>0110010=>1001101
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>0100010=>1011101
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]=>0010010=>1101101
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>1100010=>0011101
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>1000010=>0111101
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>0100010=>1011101
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>1000010=>0111101
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>0000010=>1111101
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>1111100=>0000011
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>1111000=>0000111
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>1111000=>0000111
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>1110000=>0001111
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>1101100=>0010011
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>1110100=>0001011
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>1111000=>0000111
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>1100000=>0011111
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>1010100=>0101011
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>1010000=>0101111
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[2,3,6,5,4,1,7,8]=>1001100=>0110011
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[2,3,5,6,4,1,7,8]=>1001000=>0110111
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>1110100=>0001011
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[2,4,3,6,5,1,7,8]=>1010100=>0101011
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>1000100=>0111011
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>1111000=>0000111
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>1110000=>0001111
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>1101000=>0010111
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>1110000=>0001111
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>1100000=>0011111
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>1001000=>0110111
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>1110000=>0001111
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>1100000=>0011111
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>1100000=>0011111
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>1000000=>0111111
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>0111100=>1000011
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>0111000=>1000111
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>0110100=>1001011
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>0111000=>1000111
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>0110000=>1001111
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>0101000=>1010111
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>0110100=>1001011
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>0111000=>1000111
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,4,5,3,6,2,7,8]=>0110000=>1001111
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>0101000=>1010111
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,4,3,5,6,2,7,8]=>0110000=>1001111
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,3,4,5,6,2,7,8]=>0100000=>1011111
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>1011000=>0100111
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>1010100=>0101011
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>0011100=>1100011
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>0011000=>1100111
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>0010100=>1101011
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>0010000=>1101111
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>1101100=>0010011
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>1101000=>0010111
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>1001100=>0110011
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[2,3,1,5,6,4,7,8]=>1001000=>0110111
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>0101100=>1010011
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>0101000=>1010111
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>0001100=>1110011
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>0001000=>1110111
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>1110100=>0001011
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[2,4,3,1,6,5,7,8]=>1010100=>0101011
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>1100100=>0011011
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>1000100=>0111011
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>1010100=>0101011
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>0010100=>1101011
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>0100100=>1011011
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>1000100=>0111011
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>0000100=>1111011
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>1111000=>0000111
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>1110000=>0001111
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>1101000=>0010111
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>1110000=>0001111
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>1100000=>0011111
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>1011000=>0100111
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>1010000=>0101111
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>1101000=>0010111
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>1001000=>0110111
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>1110000=>0001111
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>1100000=>0011111
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>1010000=>0101111
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>1100000=>0011111
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>1000000=>0111111
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>0111000=>1000111
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>0110000=>1001111
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>0101000=>1010111
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>0100000=>1011111
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>1011000=>0100111
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>1010000=>0101111
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>0011000=>1100111
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]=>1101000=>0010111
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>1001000=>0110111
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>0101000=>1010111
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]=>1001000=>0110111
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>0001000=>1110111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>1110000=>0001111
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>1100000=>0011111
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>1010000=>0101111
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>1100000=>0011111
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>1000000=>0111111
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>0110000=>1001111
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>0100000=>1011111
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>1010000=>0101111
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>0010000=>1101111
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>1100000=>0011111
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>1000000=>0111111
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>0100000=>1011111
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>1000000=>0111111
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>0000000=>1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>11111111=>00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>11111110=>00000001
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>11111100=>00000011
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>11111000=>00000111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>11110000=>00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>11100000=>00011111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>11000000=>00111111
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>10000000=>01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>00000000=>11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>111111111=>000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>111111110=>000000001
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>11111101=>00000010
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>111111100=>000000011
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>111111000=>000000111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>111110000=>000001111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>111100000=>000011111
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[3,5,6,7,8,9,4,2,1]=>11010000=>00101111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>111000000=>000111111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[2,4,5,6,7,8,9,3,1]=>10100000=>01011111
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>110000000=>001111111
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>01000000=>10111111
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>100000000=>011111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>000000000=>111111111
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>11111110=>00000001
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>11111110=>00000001
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>11111110=>00000001
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>11111110=>00000001
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>11111110=>00000001
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>11111110=>00000001
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>11111110=>00000001
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>111111110=>000000001
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[6,8,7,9,5,4,3,2,1]=>11111010=>00000101
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>111111110=>000000001
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[5,8,7,6,9,4,3,2,1]=>11110110=>00001001
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>111111110=>000000001
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[4,8,7,6,5,9,3,2,1]=>11101110=>00010001
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>111111110=>000000001
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[3,8,7,6,5,4,9,2,1]=>11011110=>00100001
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>111111110=>000000001
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[2,8,7,6,5,4,3,9,1]=>10111110=>01000001
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>111111110=>000000001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>01111110=>10000001
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>111111110=>000000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>111111110=>000000001
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,3,5,7,9,10,8,6,4,2]=>010101010=>101010101
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[1,6,7,5,8,4,9,3,10,2]=>011110000=>100001111
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>111100000=>000011111
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,10,9,1]=>101010101=>010101010
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,1,4,6,5,3,8,10,9,7]=>101010101=>010101010
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,1,4,6,5,3,8,7,10,9]=>101010101=>010101010
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,9,8,1,10]=>110101010=>001010101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>101010101=>010101010
[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,10,9,12,11,1]=>10101010101=>01010101010
[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3,8,7,10,12,11,9]=>10101010101=>01010101010
[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,10,9,7,12,11]=>10101010101=>01010101010
[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[2,1,4,6,5,3,8,7,10,9,12,11]=>10101010101=>01010101010
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,9,8,11,10,1,12]=>11010101010=>00101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>01010101010
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>00000001=>11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>000000001=>111111110
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>10000001=>01111110
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>11000000=>00111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001=>1111111110
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]=>100000001=>011111110
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]=>01000001=>10111110
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[2,3,1,4,5,6,7,9,8]=>10000001=>01111110
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[2,4,3,5,6,7,8,9,1]=>10100000=>01011111
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>11000000=>00111111
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>110000000=>001111111
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>1000000000=>0111111111
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>00000010=>11111101
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>00000100=>11111011
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>00001000=>11110111
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>00010000=>11101111
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>00100000=>11011111
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>00000011=>11111100
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>000000010=>111111101
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>00000110=>11111001
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>000000100=>111111011
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,4,7,6,8,9,5]=>00001100=>11110011
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>000001000=>111110111
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,3,6,5,7,8,9,4]=>00011000=>11100111
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>000010000=>111101111
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[1,2,5,4,6,7,8,9,3]=>00110000=>11001111
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>000100000=>111011111
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>01100000=>10011111
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>001000000=>110111111
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>010000000=>101111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>01111111=>10000000
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>11111100=>00000011
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>01111110=>10000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>011111111=>100000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110=>0000000001
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>111111100=>000000011
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>11111100=>00000011
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>01111110=>10000001
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>011111110=>100000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111=>1000000000
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>111110000=>000001111
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,8,3,9,2,10,1]=>111101000=>000010111
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,7,6,8,5,9,2,10,1]=>111011000=>000100111
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,9,2,10,1]=>111100100=>000011011
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,9,2,10,1]=>111010100=>000101011
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,7,6,8,5,9,4,10,1]=>110111000=>001000111
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,9,4,10,1]=>110110100=>001001011
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,8,7,9,6,10,1]=>111001100=>000110011
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,8,7,9,6,10,1]=>110101100=>001010011
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,10,1]=>111100010=>000011101
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,10,1]=>111010010=>000101101
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[3,2,6,5,7,4,9,8,10,1]=>110110010=>001001101
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[4,3,5,2,7,6,9,8,10,1]=>111001010=>000110101
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,10,1]=>110101010=>001010101
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,7,6,8,5,9,4,10,3]=>101111000=>010000111
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,6,5,8,7,9,4,10,3]=>101110100=>010001011
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,5,4,8,7,9,6,10,3]=>101101100=>010010011
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,10,3]=>101110010=>010001101
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,10,3]=>101101010=>010010101
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,8,7,9,6,10,5]=>110011100=>001100011
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,10,5]=>110011010=>001100101
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,8,7,9,6,10,5]=>101011100=>010100011
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,10,5]=>101011010=>010100101
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,9,8,10,7]=>111000110=>000111001
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,9,8,10,7]=>110100110=>001011001
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,9,8,10,7]=>101100110=>010011001
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,9,8,10,7]=>110010110=>001101001
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,9,8,10,7]=>101010110=>010101001
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9]=>111100001=>000011110
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9]=>111010001=>000101110
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9]=>110110001=>001001110
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[4,3,5,2,7,6,8,1,10,9]=>111001001=>000110110
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,7,6,8,1,10,9]=>110101001=>001010110
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9]=>101110001=>010001110
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[2,1,5,4,7,6,8,3,10,9]=>101101001=>010010110
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,7,6,8,5,10,9]=>110011001=>001100110
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,4,3,7,6,8,5,10,9]=>101011001=>010100110
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,5,2,6,1,8,7,10,9]=>111000101=>000111010
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,6,1,8,7,10,9]=>110100101=>001011010
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[2,1,5,4,6,3,8,7,10,9]=>101100101=>010011010
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7,10,9]=>110010101=>001101010
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>11111100000=>00000011111
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>11111010000=>00000101111
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>11110110000=>00001001111
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>11111001000=>00000110111
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>11110101000=>00001010111
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>11101110000=>00010001111
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>11101101000=>00010010111
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>11110011000=>00001100111
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>11101011000=>00010100111
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>11111000100=>00000111011
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>11110100100=>00001011011
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>11101100100=>00010011011
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>11110010100=>00001101011
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>11101010100=>00010101011
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>11011110000=>00100001111
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>11011101000=>00100010111
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>11011011000=>00100100111
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>11011100100=>00100011011
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>11011010100=>00100101011
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>11100111000=>00011000111
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>11100110100=>00011001011
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>11010111000=>00101000111
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>11010110100=>00101001011
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>11110001100=>00001110011
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>11101001100=>00010110011
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>11011001100=>00100110011
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>11100101100=>00011010011
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>11010101100=>00101010011
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>11111000010=>00000111101
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>11110100010=>00001011101
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>11101100010=>00010011101
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>11110010010=>00001101101
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>11101010010=>00010101101
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>11011100010=>00100011101
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>11011010010=>00100101101
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>11100110010=>00011001101
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>11010110010=>00101001101
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>11110001010=>00001110101
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>11101001010=>00010110101
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>11011001010=>00100110101
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>11100101010=>00011010101
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>11010101010=>00101010101
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>10111110000=>01000001111
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>10111101000=>01000010111
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>10111011000=>01000100111
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>10111100100=>01000011011
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>10111010100=>01000101011
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>10110111000=>01001000111
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>10110110100=>01001001011
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>10111001100=>01000110011
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>10110101100=>01001010011
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>10111100010=>01000011101
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>10111010010=>01000101101
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>10110110010=>01001001101
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>10111001010=>01000110101
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>10110101010=>01001010101
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>11001111000=>00110000111
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>11001110100=>00110001011
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>11001101100=>00110010011
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>11001110010=>00110001101
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>11001101010=>00110010101
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>10101111000=>01010000111
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>10101110100=>01010001011
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>10101101100=>01010010011
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>10101110010=>01010001101
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>10101101010=>01010010101
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>11100011100=>00011100011
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>11100011010=>00011100101
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>11010011100=>00101100011
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>11010011010=>00101100101
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>10110011100=>01001100011
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>10110011010=>01001100101
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>11001011100=>00110100011
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>11001011010=>00110100101
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>10101011100=>01010100011
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>10101011010=>01010100101
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>11110000110=>00001111001
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>11101000110=>00010111001
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>11011000110=>00100111001
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,7,6,8,1,11,10,12,9]=>11100100110=>00011011001
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>11010100110=>00101011001
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>10111000110=>01000111001
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>10110100110=>01001011001
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>11001100110=>00110011001
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>10101100110=>01010011001
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>11100010110=>00011101001
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>11010010110=>00101101001
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>10110010110=>01001101001
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>11001010110=>00110101001
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>10101010110=>01010101001
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>11111000001=>00000111110
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>11110100001=>00001011110
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>11101100001=>00010011110
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>11110010001=>00001101110
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>11101010001=>00010101110
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>11011100001=>00100011110
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>11011010001=>00100101110
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>11100110001=>00011001110
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>11010110001=>00101001110
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>11110001001=>00001110110
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>[4,3,6,5,7,2,9,8,10,1,12,11]=>11101001001=>00010110110
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[3,2,6,5,7,4,9,8,10,1,12,11]=>11011001001=>00100110110
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>[4,3,5,2,7,6,9,8,10,1,12,11]=>11100101001=>00011010110
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>11010101001=>00101010110
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>10111100001=>01000011110
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>10111010001=>01000101110
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>10110110001=>01001001110
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>10111001001=>01000110110
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>10110101001=>01001010110
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>11001110001=>00110001110
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>11001101001=>00110010110
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>10101110001=>01010001110
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>10101101001=>01010010110
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>11100011001=>00011100110
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>11010011001=>00101100110
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>10110011001=>01001100110
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>11001011001=>00110100110
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>10101011001=>01010100110
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>11110000101=>00001111010
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>11101000101=>00010111010
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>11011000101=>00100111010
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>[4,3,5,2,7,6,8,1,10,9,12,11]=>11100100101=>00011011010
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>11010100101=>00101011010
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>10111000101=>01000111010
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>10110100101=>01001011010
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>11001100101=>00110011010
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>10101100101=>01010011010
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>[4,3,5,2,6,1,8,7,10,9,12,11]=>11100010101=>00011101010
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>11010010101=>00101101010
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>10110010101=>01001101010
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>11001010101=>00110101010
[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,10,9,2]=>011010101=>100101010
[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,10,9,12,11,2]=>01101010101=>10010101010
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>10111111=>01000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>11011111=>00100000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>11101111=>00010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>11110111=>00001000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>11111011=>00000100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>11111101=>00000010
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>00111111=>11000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>101111111=>010000000
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>10011111=>01100000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>110111111=>001000000
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[3,4,2,1,9,8,7,6,5]=>11001111=>00110000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>111011111=>000100000
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[4,5,3,2,1,9,8,7,6]=>11100111=>00011000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]=>111101111=>000010000
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[5,6,4,3,2,1,9,8,7]=>11110011=>00001100
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>111110111=>000001000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[6,7,5,4,3,2,1,9,8]=>11111001=>00000110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>111111011=>000000100
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>111111101=>000000010
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>11111100=>00000011
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>11111000=>00000111
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>11110000=>00001111
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>11100000=>00011111
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>11000000=>00111111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>10000000=>01111111
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>111111100=>000000011
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>111111000=>000000111
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>111110000=>000001111
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>111100000=>000011111
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>111000000=>000111111
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>01100000=>10011111
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>110000000=>001111111
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>01000000=>10111111
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>100000000=>011111111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[4,9,8,7,6,5,3,2,1]=>11101111=>00010000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[3,9,8,7,6,5,4,2,1]=>11011111=>00100000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>10111111=>01000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[6,10,9,8,7,5,4,3,2,1]=>111110111=>000001000
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,8,7,5,10,9]=>101010101=>010101010
[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[2,4,3,1,6,5,8,10,9,7]=>101010101=>010101010
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7,10,9]=>101010101=>010101010
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,3,6,8,7,5,10,9]=>101010101=>010101010
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,5,8,10,9,7]=>101010101=>010101010
[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5,10,12,11,9]=>10101010101=>01010101010
[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,8,7,5,10,9,12,11]=>10101010101=>01010101010
[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5,8,10,9,7,12,11]=>10101010101=>01010101010
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,4,3,1,6,5,8,7,10,12,11,9]=>10101010101=>01010101010
[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7,10,9,12,11]=>10101010101=>01010101010
[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5,10,12,11,9]=>10101010101=>01010101010
[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,1,4,3,6,8,7,5,10,9,12,11]=>10101010101=>01010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,3,6,5,8,10,9,7,12,11]=>10101010101=>01010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,5,8,7,10,12,11,9]=>10101010101=>01010101010
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>10000001=>01111110
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000=>0111111111
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]=>10000010=>01111101
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[2,1,3,4,5,6,8,9,7]=>10000010=>01111101
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[2,3,4,5,6,8,9,7,1]=>10000010=>01111101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>100000001=>011111110
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]=>10100000=>01011111
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[3,2,1,5,4,6,7,8,9]=>11010000=>00101111
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]=>11111010=>00000101
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>11000000=>00111111
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>10000000=>01111111
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>10000000=>01111111
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>10000000=>01111111
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>100000000=>011111111
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[2,4,3,1,5,6,7,8,9]=>10100000=>01011111
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[2,3,5,4,1,6,7,8,9]=>10010000=>01101111
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[2,3,4,6,5,1,7,8,9]=>10001000=>01110111
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[2,3,4,5,7,6,1,8,9]=>10000100=>01111011
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[2,3,4,5,6,8,7,1,9]=>10000010=>01111101
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>100000000=>011111111
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]=>00100000=>11011111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>00010000=>11101111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>00001000=>11110111
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]=>00000100=>11111011
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>00000010=>11111101
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>010000000=>101111111
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]=>001000000=>110111111
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>000100000=>111011111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>000010000=>111101111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>000001000=>111110111
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]=>000000100=>111111011
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>000000010=>111111101
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,3,4,5,6,7,9,8,2]=>01000001=>10111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>11111101=>00000010
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1]=>11100000=>00011111
[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[5,4,3,2,6,7,8,9,1]=>11110000=>00001111
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>11111000=>00000111
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1]=>11111100=>00000011
[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,10,1]=>111000000=>000111111
[.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]=>[5,4,3,2,6,7,8,9,10,1]=>111100000=>000011111
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]=>[6,5,4,3,2,7,8,9,10,1]=>111110000=>000001111
[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[7,6,5,4,3,2,8,9,10,1]=>111111000=>000000111
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[8,7,6,5,4,3,2,9,10,1]=>111111100=>000000011
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>01111101=>10000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7]=>11111010=>00000101
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000=>1111111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]=>001111111=>110000000
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]=>01011111=>10100000
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>10111110=>01000001
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>011111110=>100000001
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[2,8,7,9,6,5,4,3,1]=>10111110=>01000001
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[1,3,4,5,2,6,7,8,9]=>01000000=>10111111
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[1,2,4,5,3,6,7,8,9]=>00100000=>11011111
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[2,1,4,5,3,6,7,8,9]=>10100000=>01011111
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>01010000=>10101111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[8,7,6,5,4,3,2,10,9,1]=>111111101=>000000010
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>10100000=>01011111
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[1,3,4,5,6,7,8,2,9]=>01000000=>10111111
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>000000011=>111111100
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>11111000=>00000111
[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]=>[6,5,7,8,4,3,2,1,9]=>11111000=>00000111
[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.]=>[6,5,4,7,8,3,2,1,9]=>11111000=>00000111
[[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.]=>[6,5,4,3,7,8,2,1,9]=>11111000=>00000111
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9]=>11111000=>00000111
[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]=>[5,4,3,2,1,7,8,9,6]=>11110100=>00001011
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>111111000=>000000111
[[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]=>[4,3,2,1,6,7,8,9,5]=>11101000=>00010111
[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[7,6,8,9,5,4,3,2,1,10]=>111111000=>000000111
[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.]=>[7,6,5,8,9,4,3,2,1,10]=>111111000=>000000111
[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.]=>[7,6,5,4,8,9,3,2,1,10]=>111111000=>000000111
[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.]=>[7,6,5,4,3,8,9,2,1,10]=>111111000=>000000111
[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]=>[7,6,5,4,3,2,8,9,1,10]=>111111000=>000000111
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>00000111=>11111000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>00001111=>11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]=>00011111=>11100000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>00000101=>11111010
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]=>000000111=>111111000
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,4,6,5,9,8,7]=>00001011=>11110100
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]=>000001111=>111110000
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]=>00010111=>11101000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]=>000011111=>111100000
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,2,4,3,9,8,7,6,5]=>00101111=>11010000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]=>000111111=>111000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]=>000000101=>111111010
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>1111111110=>0000000001
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[1,9,8,10,7,6,5,4,3,2]=>011111110=>100000001
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[2,8,9,7,6,5,4,3,1]=>10111110=>01000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>1111111110=>0000000001
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>11111100=>00000011
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>11000000=>00111111
[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10,11]=>1000000000=>0111111111
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9,10]=>110000000=>001111111
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>11000000=>00111111
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>11111100=>00000011
[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]=>[6,5,8,7,4,3,2,1,9]=>11111010=>00000101
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>11111100=>00000011
[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]=>[6,7,5,8,4,3,2,1,9]=>11111000=>00000111
[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]=>[4,3,2,1,8,9,7,6,5]=>11101110=>00010001
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[2,3,1,5,4,6,7,8,9]=>10010000=>01101111
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>11100000=>00011111
[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]=>[4,3,2,1,6,7,8,9,10,5]=>111010000=>000101111
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>11000000=>00111111
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]=>11110110=>00001001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10]=>111111010=>000000101
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>10011111=>01100000
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>10111110=>01000001
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>10000001=>01111110
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>01000000=>10111111
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>111111100=>000000011
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,4,5,6,7,8,3,9,2]=>01100000=>10011111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>0000000010=>1111111101
[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[2,1,3,5,6,7,8,9,4]=>10010000=>01101111
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[5,6,4,3,2,1,7,8,9]=>11110000=>00001111
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>111100000=>000011111
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[6,7,5,4,3,2,1,8,9,10,11]=>1111100000=>0000011111
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[6,7,5,4,3,2,1,8,9,10]=>111110000=>000001111
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[5,6,4,3,2,7,1,8,9]=>11110000=>00001111
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]=>[1,2,5,6,7,4,8,9,3]=>00110000=>11001111
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>11111000=>00000111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[7,6,5,4,3,2,1,9,10,8]=>111111010=>000000101
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.
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 bottoms
Description
The descent bottoms of a permutation as a binary word.
Map
complement
Description
Send a binary word to the word obtained by interchanging the two letters.
searching the database
Sorry, this map was not found in the database.