Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>=>
[.,[.,.]]=>[2,1]=>1=>1
[[.,.],.]=>[1,2]=>0=>0
[.,[.,[.,.]]]=>[3,2,1]=>11=>11
[.,[[.,.],.]]=>[2,3,1]=>10=>01
[[.,.],[.,.]]=>[1,3,2]=>01=>10
[[.,[.,.]],.]=>[2,1,3]=>10=>01
[[[.,.],.],.]=>[1,2,3]=>00=>00
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>111=>111
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>110=>011
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>101=>101
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>110=>011
[.,[[[.,.],.],.]]=>[2,3,4,1]=>100=>001
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>011=>110
[[.,.],[[.,.],.]]=>[1,3,4,2]=>010=>010
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>101=>101
[[[.,.],.],[.,.]]=>[1,2,4,3]=>001=>100
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>110=>011
[[.,[[.,.],.]],.]=>[2,3,1,4]=>100=>001
[[[.,.],[.,.]],.]=>[1,3,2,4]=>010=>010
[[[.,[.,.]],.],.]=>[2,1,3,4]=>100=>001
[[[[.,.],.],.],.]=>[1,2,3,4]=>000=>000
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>1111=>1111
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>1110=>0111
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>1101=>1011
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>1110=>0111
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>1100=>0011
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>1011=>1101
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>1010=>0101
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>1101=>1011
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>1001=>1001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>1110=>0111
[.,[[.,[[.,.],.]],.]]=>[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=>0001
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>0111=>1110
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>0110=>0110
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>0101=>1010
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>0110=>0110
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>0100=>0010
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>1011=>1101
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>1010=>0101
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>0011=>1100
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>0010=>0100
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>1101=>1011
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>1001=>1001
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>0101=>1010
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>1001=>1001
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>0001=>1000
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1110=>0111
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>1100=>0011
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>1010=>0101
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1100=>0011
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>1000=>0001
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>0110=>0110
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>0100=>0010
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>1010=>0101
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>0010=>0100
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>1100=>0011
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>1000=>0001
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>0100=>0010
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1000=>0001
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0000=>0000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>11111=>11111
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>11110=>01111
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>11101=>10111
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>11110=>01111
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>11100=>00111
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>11011=>11011
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>11010=>01011
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>11101=>10111
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>11001=>10011
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>11110=>01111
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>11100=>00111
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>11010=>01011
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>11100=>00111
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>11000=>00011
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>10111=>11101
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>10110=>01101
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>10101=>10101
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>10110=>01101
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>10100=>00101
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>11011=>11011
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>11010=>01011
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>10011=>11001
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>10010=>01001
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>11101=>10111
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>11001=>10011
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>10101=>10101
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>11001=>10011
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>10001=>10001
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>11110=>01111
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>11100=>00111
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>11010=>01011
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>11100=>00111
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>11000=>00011
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>10110=>01101
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>10100=>00101
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>11010=>01011
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>10010=>01001
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>11100=>00111
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>11000=>00011
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>10100=>00101
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>11000=>00011
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>10000=>00001
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>01111=>11110
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>01110=>01110
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>01101=>10110
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>01110=>01110
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>01100=>00110
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>01011=>11010
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>01010=>01010
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>01101=>10110
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>01001=>10010
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>01110=>01110
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>01100=>00110
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>01010=>01010
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>01100=>00110
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>01000=>00010
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>10111=>11101
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>10110=>01101
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>10101=>10101
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>10110=>01101
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>10100=>00101
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>00111=>11100
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>00110=>01100
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>00101=>10100
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>00110=>01100
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>00100=>00100
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>11011=>11011
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>11010=>01011
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>10011=>11001
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>10010=>01001
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>01011=>11010
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>01010=>01010
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>10011=>11001
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>10010=>01001
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>00011=>11000
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>00010=>01000
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>11101=>10111
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>11001=>10011
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>10101=>10101
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>11001=>10011
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>10001=>10001
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>01101=>10110
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>01001=>10010
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>10101=>10101
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>00101=>10100
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>11001=>10011
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>10001=>10001
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>01001=>10010
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>10001=>10001
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>00001=>10000
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>11110=>01111
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>11100=>00111
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>11010=>01011
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>11100=>00111
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>11000=>00011
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>10110=>01101
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>10100=>00101
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>11010=>01011
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>10010=>01001
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>11100=>00111
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>11000=>00011
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>10100=>00101
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>11000=>00011
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>10000=>00001
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>01110=>01110
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>01100=>00110
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>01010=>01010
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>01100=>00110
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>01000=>00010
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>10110=>01101
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>10100=>00101
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>00110=>01100
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>00100=>00100
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>11010=>01011
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>10010=>01001
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>01010=>01010
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>10010=>01001
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>00010=>01000
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>11100=>00111
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>11000=>00011
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>10100=>00101
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>11000=>00011
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>10000=>00001
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>01100=>00110
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>01000=>00010
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>10100=>00101
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>00100=>00100
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>11000=>00011
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>10000=>00001
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>01000=>00010
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>10000=>00001
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>00000=>00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>111111=>111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>111110=>011111
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>111101=>101111
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>111110=>011111
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>111100=>001111
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>111011=>110111
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>111010=>010111
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>111101=>101111
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>111001=>100111
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>111110=>011111
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>111100=>001111
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>111010=>010111
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>111100=>001111
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>111000=>000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>110111=>111011
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>110110=>011011
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>110101=>101011
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>110110=>011011
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>110100=>001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>111011=>110111
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>111010=>010111
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>110011=>110011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>110010=>010011
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>111101=>101111
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>111001=>100111
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>110101=>101011
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>111001=>100111
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>110001=>100011
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>111110=>011111
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>111100=>001111
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>111010=>010111
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>111100=>001111
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>111000=>000111
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>110110=>011011
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>110100=>001011
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>111010=>010111
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>110010=>010011
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>111100=>001111
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[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=>000011
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>101111=>111101
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>101110=>011101
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>101101=>101101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>101110=>011101
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>101100=>001101
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>101011=>110101
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>101010=>010101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>101101=>101101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>101001=>100101
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>101110=>011101
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>101100=>001101
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>101010=>010101
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>101100=>001101
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>101000=>000101
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>110111=>111011
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>110110=>011011
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>110101=>101011
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>110110=>011011
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>110100=>001011
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>100111=>111001
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>100110=>011001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>100101=>101001
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>100110=>011001
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>100100=>001001
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>111011=>110111
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>111010=>010111
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>110011=>110011
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>110010=>010011
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>101011=>110101
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>101010=>010101
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>110011=>110011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>110010=>010011
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>100011=>110001
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>100010=>010001
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>111101=>101111
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>111001=>100111
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>110101=>101011
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>111001=>100111
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>110001=>100011
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>101101=>101101
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>101001=>100101
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>110101=>101011
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>100101=>101001
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>111001=>100111
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>110001=>100011
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>101001=>100101
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>110001=>100011
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>100001=>100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>111110=>011111
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>111100=>001111
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>111010=>010111
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>111100=>001111
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>111000=>000111
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>110110=>011011
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>110100=>001011
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>111010=>010111
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>110010=>010011
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>111100=>001111
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[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=>000011
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>101110=>011101
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>101100=>001101
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>101010=>010101
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>101100=>001101
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>101000=>000101
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>110110=>011011
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[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=>001001
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>111010=>010111
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>110010=>010011
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>101010=>010101
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>110010=>010011
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>100010=>010001
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>111100=>001111
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[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=>000011
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>101100=>001101
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>101000=>000101
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>110100=>001011
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>100100=>001001
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>111000=>000111
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>110000=>000011
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>101000=>000101
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>110000=>000011
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>100000=>000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>011111=>111110
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>011110=>011110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>011101=>101110
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>011110=>011110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>011100=>001110
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>011011=>110110
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>011010=>010110
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>011101=>101110
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>011001=>100110
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>011110=>011110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>011100=>001110
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>011010=>010110
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>011100=>001110
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>011000=>000110
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>010111=>111010
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>010110=>011010
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>010101=>101010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>010110=>011010
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>010100=>001010
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>011011=>110110
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>011010=>010110
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>010011=>110010
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>010010=>010010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>011101=>101110
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[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=>100010
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>011110=>011110
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>011100=>001110
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>011010=>010110
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>011100=>001110
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>011000=>000110
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>010110=>011010
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>010100=>001010
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>011010=>010110
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>010010=>010010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>011100=>001110
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>011000=>000110
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>010100=>001010
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>011000=>000110
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>010000=>000010
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>101111=>111101
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>101110=>011101
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>101101=>101101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>101110=>011101
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>101100=>001101
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>101011=>110101
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>101010=>010101
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>101101=>101101
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>101001=>100101
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>101110=>011101
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>101100=>001101
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>101010=>010101
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>101100=>001101
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>101000=>000101
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>001111=>111100
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>001110=>011100
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>001101=>101100
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>001110=>011100
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>001100=>001100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>001011=>110100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>001010=>010100
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>001101=>101100
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>001001=>100100
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>001110=>011100
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>001100=>001100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>001010=>010100
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>001100=>001100
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>001000=>000100
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>110111=>111011
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>110110=>011011
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>110101=>101011
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>110110=>011011
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>110100=>001011
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>100111=>111001
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>100110=>011001
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>100101=>101001
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>100110=>011001
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>100100=>001001
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>010111=>111010
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>010110=>011010
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>010101=>101010
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>010110=>011010
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>010100=>001010
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>100111=>111001
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>100110=>011001
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>100101=>101001
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>100110=>011001
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>100100=>001001
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>000111=>111000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>000110=>011000
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>000101=>101000
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>000110=>011000
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>000100=>001000
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>111011=>110111
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>111010=>010111
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>110011=>110011
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>110010=>010011
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>101011=>110101
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>101010=>010101
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>110011=>110011
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>110010=>010011
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>100011=>110001
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>100010=>010001
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>011011=>110110
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>011010=>010110
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>010011=>110010
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>010010=>010010
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>101011=>110101
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[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=>010100
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>110011=>110011
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>110010=>010011
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>100011=>110001
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>100010=>010001
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>010011=>110010
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>010010=>010010
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>100011=>110001
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>100010=>010001
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>000011=>110000
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>000010=>010000
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>111101=>101111
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>111001=>100111
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>110101=>101011
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>111001=>100111
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>110001=>100011
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>101101=>101101
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>101001=>100101
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>110101=>101011
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>100101=>101001
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>111001=>100111
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>110001=>100011
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>101001=>100101
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>110001=>100011
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>100001=>100001
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>011101=>101110
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[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=>100010
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>101101=>101101
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>101001=>100101
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>001101=>101100
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>001001=>100100
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>110101=>101011
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>100101=>101001
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>010101=>101010
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>100101=>101001
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>000101=>101000
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>111001=>100111
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>110001=>100011
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>101001=>100101
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>110001=>100011
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>100001=>100001
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>011001=>100110
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>010001=>100010
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>101001=>100101
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>001001=>100100
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>110001=>100011
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>100001=>100001
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>010001=>100010
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>100001=>100001
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>000001=>100000
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>111110=>011111
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>111100=>001111
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>111010=>010111
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>111100=>001111
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>111000=>000111
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>110110=>011011
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>110100=>001011
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>111010=>010111
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>110010=>010011
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>111100=>001111
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[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=>000011
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>101110=>011101
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>101100=>001101
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>101010=>010101
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>101100=>001101
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>101000=>000101
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>110110=>011011
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[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=>001001
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>111010=>010111
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>110010=>010011
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>101010=>010101
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>110010=>010011
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>100010=>010001
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>111100=>001111
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[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=>000011
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>101100=>001101
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>101000=>000101
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>110100=>001011
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>100100=>001001
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>111000=>000111
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>110000=>000011
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>101000=>000101
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>110000=>000011
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>100000=>000001
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>011110=>011110
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>011100=>001110
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>011010=>010110
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>011100=>001110
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>011000=>000110
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>010110=>011010
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>010100=>001010
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>011010=>010110
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>010010=>010010
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>011100=>001110
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>011000=>000110
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>010100=>001010
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>011000=>000110
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>010000=>000010
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>101110=>011101
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>101100=>001101
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>101010=>010101
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>101100=>001101
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>101000=>000101
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>001110=>011100
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>001100=>001100
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>001010=>010100
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>001100=>001100
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>001000=>000100
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>110110=>011011
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[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=>001001
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>010110=>011010
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>010100=>001010
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>100110=>011001
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>100100=>001001
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>000110=>011000
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>000100=>001000
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>111010=>010111
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>110010=>010011
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>101010=>010101
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>110010=>010011
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>100010=>010001
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>011010=>010110
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>010010=>010010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>101010=>010101
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>001010=>010100
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>110010=>010011
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>100010=>010001
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>010010=>010010
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>100010=>010001
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>000010=>010000
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>111100=>001111
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[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=>000011
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>101100=>001101
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>101000=>000101
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>110100=>001011
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>100100=>001001
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>111000=>000111
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>110000=>000011
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>101000=>000101
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>110000=>000011
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>100000=>000001
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>011100=>001110
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>011000=>000110
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>010100=>001010
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>011000=>000110
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>010000=>000010
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>101100=>001101
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>101000=>000101
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>001100=>001100
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>001000=>000100
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>110100=>001011
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>100100=>001001
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>010100=>001010
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>100100=>001001
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>000100=>001000
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>111000=>000111
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>110000=>000011
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>101000=>000101
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>110000=>000011
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>100000=>000001
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>011000=>000110
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>010000=>000010
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>101000=>000101
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>001000=>000100
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>110000=>000011
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>100000=>000001
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>010000=>000010
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>100000=>000001
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>000000=>000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>1111111=>1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>1111110=>0111111
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>1111101=>1011111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>1111110=>0111111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>1111100=>0011111
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>1111011=>1101111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>1111010=>0101111
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>1111101=>1011111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>1111001=>1001111
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>1111110=>0111111
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>1111100=>0011111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>1111010=>0101111
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>1111100=>0011111
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>1111000=>0001111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>1110111=>1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>1110110=>0110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>1110101=>1010111
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>1110110=>0110111
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>1110100=>0010111
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>1110011=>1100111
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>1110010=>0100111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>1110101=>1010111
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>1110001=>1000111
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>1111110=>0111111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>1111100=>0011111
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>1111010=>0101111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>1111100=>0011111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>1111000=>0001111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>1110110=>0110111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>1110100=>0010111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>1111010=>0101111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>1110010=>0100111
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>1111100=>0011111
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>1111000=>0001111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>1110100=>0010111
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>1111000=>0001111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>1110000=>0000111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>1101111=>1111011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>1101011=>1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>1101010=>0101011
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>1101001=>1001011
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>1101110=>0111011
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>1101100=>0011011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>1101000=>0001011
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>1110100=>0010111
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>1100111=>1110011
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>1100100=>0010011
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>1111010=>0101111
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>1110010=>0100111
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>1110010=>0100111
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>1100010=>0100011
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>1110001=>1000111
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>1110101=>1010111
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>1111001=>1001111
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>1110001=>1000111
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>1110001=>1000111
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>1111110=>0111111
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>1111010=>0101111
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>1110110=>0110111
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>1111000=>0001111
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>1110000=>0000111
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>1100110=>0110011
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>1110010=>0100111
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>1110010=>0100111
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>1111100=>0011111
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>1100100=>0010011
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>1011111=>1111101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>1011110=>0111101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>1011000=>0001101
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>1010111=>1110101
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>1010101=>1010101
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>1010100=>0010101
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>1011011=>1101101
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>1010010=>0100101
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>1011001=>1001101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>1010101=>1010101
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>1011110=>0111101
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>1011100=>0011101
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>1010110=>0110101
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>1011100=>0011101
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>1101111=>1111011
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>1101101=>1011011
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>1101010=>0101011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>1101000=>0001011
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>1001111=>1111001
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>1001100=>0011001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>1001011=>1101001
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>1001010=>0101001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>1001110=>0111001
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>1001000=>0001001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>1110111=>1110111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>1110110=>0110111
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>1110101=>1010111
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>1100111=>1110011
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>1100110=>0110011
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>1010111=>1110101
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>1010101=>1010101
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>1100111=>1110011
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>1000111=>1110001
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>1000100=>0010001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>1111011=>1101111
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>1111010=>0101111
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>1110011=>1100111
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>1110011=>1100111
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>1011011=>1101101
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>1011010=>0101101
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>1010011=>1100101
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>1001011=>1101001
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>1110011=>1100111
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>1010011=>1100101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>1000011=>1100001
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>1111101=>1011111
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>1110101=>1010111
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>1111001=>1001111
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>1110001=>1000111
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>1101101=>1011011
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>1101001=>1001011
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>1110101=>1010111
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>1111001=>1001111
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>1011101=>1011101
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>1010101=>1010101
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>1110101=>1010111
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>1100101=>1010011
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>1010101=>1010101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>1000101=>1010001
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>1111001=>1001111
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>1011001=>1001101
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>1110001=>1000111
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>1100001=>1000011
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>1010001=>1000101
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>1000001=>1000001
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>1110110=>0110111
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>1110100=>0010111
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>1110000=>0000111
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>1101010=>0101011
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>1101000=>0001011
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>1110110=>0110111
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>1110100=>0010111
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>1100110=>0110011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>1111010=>0101111
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>1111100=>0011111
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>1110100=>0010111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>1111000=>0001111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>1110000=>0000111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>1101100=>0011011
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>1101000=>0001011
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>1111000=>0001111
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>1101000=>0001011
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>1011010=>0101101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>1010100=>0010101
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>1010000=>0000101
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>1101100=>0011011
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>1001110=>0111001
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>1110110=>0110111
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>1110100=>0010111
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>1100110=>0110011
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>1010110=>0110101
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>1100110=>0110011
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>1000110=>0110001
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>1111010=>0101111
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>1011010=>0101101
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>1101010=>0101011
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>1001010=>0101001
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>1110010=>0100111
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>1010010=>0100101
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>1100010=>0100011
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>1000010=>0100001
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>1111100=>0011111
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>1111000=>0001111
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>1101100=>0011011
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>1101000=>0001011
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>1111000=>0001111
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>1100000=>0000011
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>1011100=>0011101
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>1011000=>0001101
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>1001100=>0011001
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>1001000=>0001001
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>1110100=>0010111
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>1100100=>0010011
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>1010100=>0010101
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>1000100=>0010001
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>1111000=>0001111
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>1101000=>0001011
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>1110000=>0000111
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>1011000=>0001101
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>1010000=>0000101
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>1101000=>0001011
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>1001000=>0001001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>1110000=>0000111
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>1100000=>0000011
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>1010000=>0000101
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>1100000=>0000011
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>1000000=>0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>0111111=>1111110
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>0111110=>0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>0111101=>1011110
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>0111110=>0111110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>0111100=>0011110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>0111110=>0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>0111100=>0011110
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>0111010=>0101110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>0111100=>0011110
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>0111000=>0001110
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>0110111=>1110110
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>0110110=>0110110
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>0110101=>1010110
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>0110100=>0010110
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>0111010=>0101110
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>0110010=>0100110
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>0110101=>1010110
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>0111001=>1001110
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>0110110=>0110110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>0111100=>0011110
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>0111000=>0001110
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>0101111=>1111010
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>0101101=>1011010
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>0101100=>0011010
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>0101011=>1101010
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>0101010=>0101010
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>0101010=>0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>0101100=>0011010
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>0101000=>0001010
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>0110111=>1110110
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>0110110=>0110110
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>0110101=>1010110
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>0110110=>0110110
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>0100111=>1110010
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>0100110=>0110010
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>0100100=>0010010
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>0111011=>1101110
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>0101010=>0101010
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>0110011=>1100110
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>0110010=>0100110
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>0100011=>1100010
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>0111101=>1011110
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>0111001=>1001110
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>0110101=>1010110
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>0101101=>1011010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>0110101=>1010110
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>0111001=>1001110
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>0111100=>0011110
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>0101010=>0101010
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>0100110=>0110010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>0101010=>0101010
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>0110100=>0010110
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>0111000=>0001110
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>1011110=>0111101
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>1011101=>1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>1011110=>0111101
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>1011100=>0011101
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>1011010=>0101101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>1011101=>1011101
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>1011110=>0111101
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>1011100=>0011101
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>1011100=>0011101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>1011000=>0001101
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>1010111=>1110101
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>1010110=>0110101
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>1010101=>1010101
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>1010100=>0010101
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>1010011=>1100101
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>1010010=>0100101
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>1010101=>1010101
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>1010001=>1000101
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>1011010=>0101101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>1011100=>0011101
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>1011000=>0001101
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>1010110=>0110101
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>1010100=>0010101
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>1011010=>0101101
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>1011000=>0001101
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>1010000=>0000101
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>0011111=>1111100
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>0011100=>0011100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>0011101=>1011100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>0011110=>0111100
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>0011010=>0101100
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>0011100=>0011100
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>0011000=>0001100
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>0010111=>1110100
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>0010110=>0110100
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>0010101=>1010100
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>0010100=>0010100
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>0011011=>1101100
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>0011010=>0101100
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>0010010=>0100100
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>0011101=>1011100
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>0010101=>1010100
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>0011001=>1001100
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>0011010=>0101100
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>0011000=>0001100
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>0010110=>0110100
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>0011100=>0011100
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>1101111=>1111011
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>1101110=>0111011
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>1101101=>1011011
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>1101110=>0111011
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>1101100=>0011011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>1101011=>1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>1101010=>0101011
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>1101101=>1011011
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>1101001=>1001011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>1101110=>0111011
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>1101100=>0011011
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>1101010=>0101011
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>1101100=>0011011
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>1101000=>0001011
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>1001111=>1111001
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>1001101=>1011001
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>1001110=>0111001
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>1001100=>0011001
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>1001101=>1011001
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>1001000=>0001001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>0101111=>1111010
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>0101101=>1011010
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>0101010=>0101010
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>0101101=>1011010
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>0101110=>0111010
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>0101010=>0101010
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>0101100=>0011010
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>1001111=>1111001
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>1001110=>0111001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>1001101=>1011001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>0001111=>1111000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>0001110=>0111000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>0001101=>1011000
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>0001110=>0111000
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>0001100=>0011000
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>0001011=>1101000
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>0001010=>0101000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>0001101=>1011000
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>0001001=>1001000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>0001110=>0111000
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>0001100=>0011000
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>0001010=>0101000
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>0001100=>0011000
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>0001000=>0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>1110110=>0110111
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>1110101=>1010111
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>1110110=>0110111
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>1110100=>0010111
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>1100111=>1110011
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>1100110=>0110011
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>1100101=>1010011
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>1100110=>0110011
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>1100100=>0010011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>1010111=>1110101
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>1010101=>1010101
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>1010110=>0110101
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>1010100=>0010101
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>1100111=>1110011
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>1100110=>0110011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>1100101=>1010011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>1100110=>0110011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>1100100=>0010011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>1000111=>1110001
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>1000110=>0110001
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>1000101=>1010001
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>1000110=>0110001
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>1000100=>0010001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>0110110=>0110110
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>0110100=>0010110
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>0100111=>1110010
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>0100110=>0110010
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>0100101=>1010010
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>0100110=>0110010
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>0100100=>0010010
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>1010110=>0110101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>1010101=>1010101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>1010110=>0110101
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>1010100=>0010101
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>0010110=>0110100
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>0010101=>1010100
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>0010110=>0110100
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>0010100=>0010100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>1100111=>1110011
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>1100110=>0110011
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>1100101=>1010011
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>1100110=>0110011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>1100100=>0010011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>1000111=>1110001
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>1000110=>0110001
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>1000110=>0110001
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>1000100=>0010001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>0100101=>1010010
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>0100110=>0110010
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>0100100=>0010010
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>1000110=>0110001
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>1000100=>0010001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>0000110=>0110000
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>0000101=>1010000
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>0000110=>0110000
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>0000100=>0010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>1111011=>1101111
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>1111010=>0101111
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>1110011=>1100111
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>1101011=>1101011
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>1101010=>0101011
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>1110011=>1100111
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>1100011=>1100011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>1100010=>0100011
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>1011011=>1101101
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>1011010=>0101101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>1010011=>1100101
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>1101011=>1101011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>1101010=>0101011
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>1001011=>1101001
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>1110011=>1100111
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>1100011=>1100011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>1100010=>0100011
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>1010011=>1100101
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>1010010=>0100101
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>1100011=>1100011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>1000011=>1100001
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>0101010=>0101010
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>0110010=>0100110
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>0100011=>1100010
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>0100010=>0100010
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>0011010=>0101100
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>0010011=>1100100
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>0010010=>0100100
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>0101010=>0101010
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>0001011=>1101000
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>0001010=>0101000
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>1110011=>1100111
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>1110010=>0100111
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>1100011=>1100011
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>1100011=>1100011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>1100010=>0100011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>1000011=>1100001
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>1000010=>0100001
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>0110011=>1100110
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>0110010=>0100110
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>0100011=>1100010
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>0100010=>0100010
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>0010010=>0100100
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>1100011=>1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>1100010=>0100011
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>1000010=>0100001
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>0100010=>0100010
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>0000011=>1100000
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>0000010=>0100000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>1111101=>1011111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>1111001=>1001111
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>1110101=>1010111
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>1111001=>1001111
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>1110001=>1000111
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>1101101=>1011011
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>1101001=>1001011
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>1110101=>1010111
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>1111001=>1001111
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>1110001=>1000111
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>1100001=>1000011
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>1011101=>1011101
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>1011001=>1001101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>1010101=>1010101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>1001101=>1011001
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>1001001=>1001001
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>1010101=>1010101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>1111001=>1001111
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>1110001=>1000111
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>1101001=>1001011
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>1110001=>1000111
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>1100001=>1000011
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>1011001=>1001101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>1010001=>1000101
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>1100001=>1000011
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>1000001=>1000001
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>0111001=>1001110
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>0101101=>1011010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>1011001=>1001101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>1010101=>1010101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>1011001=>1001101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>1010001=>1000101
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>1001101=>1011001
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>1001101=>1011001
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>0001101=>1011000
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>0001001=>1001000
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>1100101=>1010011
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>1010101=>1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>1100101=>1010011
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>1000101=>1010001
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>1010101=>1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>0010101=>1010100
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>0100101=>1010010
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>1000101=>1010001
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>0000101=>1010000
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>1111001=>1001111
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>1110001=>1000111
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>1101001=>1001011
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>1011001=>1001101
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>1010001=>1000101
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>1101001=>1001011
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>0101001=>1001010
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,3,4,5,2,6,8,7]=>0100001=>1000010
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>1011001=>1001101
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>1010001=>1000101
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>0011001=>1001100
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>1001001=>1001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>1110001=>1000111
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>1100001=>1000011
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>1000001=>1000001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>0110001=>1000110
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>0100001=>1000010
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>1010001=>1000101
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>0010001=>1000100
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>1000001=>1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>0000001=>1000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>1111110=>0111111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>1111100=>0011111
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>1111010=>0101111
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>1111100=>0011111
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>1111000=>0001111
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>1110110=>0110111
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>1110100=>0010111
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>1110010=>0100111
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>1111100=>0011111
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>1111000=>0001111
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>1110100=>0010111
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>1110000=>0000111
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>1101010=>0101011
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>1101000=>0001011
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>1100110=>0110011
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>1110010=>0100111
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>1101010=>0101011
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>1110010=>0100111
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>1111100=>0011111
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>1111000=>0001111
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>1111000=>0001111
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>1011000=>0001101
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>1010100=>0010101
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>1101110=>0111011
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>1101100=>0011011
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>1101010=>0101011
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>1001110=>0111001
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>1001100=>0011001
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>1001010=>0101001
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>1001100=>0011001
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>1001000=>0001001
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>1100100=>0010011
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>1000110=>0110001
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>1111010=>0101111
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>1110010=>0100111
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>1101010=>0101011
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>1101010=>0101011
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>1110010=>0100111
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>1111000=>0001111
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>1101100=>0011011
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>1100100=>0010011
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>1111000=>0001111
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>1110000=>0000111
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>1101000=>0001011
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>1100000=>0000011
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>1011000=>0001101
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>1101100=>0011011
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>1100100=>0010011
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>1010100=>0010101
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>1111000=>0001111
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>1101000=>0001011
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>1011000=>0001101
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>0111000=>0001110
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>0110100=>0010110
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>0101010=>0101010
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>0101000=>0001010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>0101010=>0101010
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>0110010=>0100110
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>0111000=>0001110
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>0101100=>0011010
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>0110100=>0010110
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>0111000=>0001110
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>0100000=>0000010
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>1011000=>0001101
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>1010100=>0010101
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>0011010=>0101100
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>0011000=>0001100
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>0011000=>0001100
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>0011000=>0001100
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>1101010=>0101011
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>1101100=>0011011
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>1101000=>0001011
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>1001100=>0011001
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>1001100=>0011001
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>1001000=>0001001
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>0101010=>0101010
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>0101100=>0011010
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>0101000=>0001010
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>1001100=>0011001
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>0001110=>0111000
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>0001100=>0011000
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>0001010=>0101000
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>0001100=>0011000
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>0001000=>0001000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>1110110=>0110111
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>1110100=>0010111
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>1100110=>0110011
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>1100100=>0010011
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>1000110=>0110001
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>1000100=>0010001
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>0110110=>0110110
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>0110100=>0010110
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>0100100=>0010010
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>1010100=>0010101
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>0010100=>0010100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>1100110=>0110011
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>1000100=>0010001
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>0100110=>0110010
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>0000110=>0110000
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>0000100=>0010000
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>1111010=>0101111
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>1110010=>0100111
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>1101010=>0101011
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>1011010=>0101101
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>1010010=>0100101
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>1101010=>0101011
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>1100010=>0100011
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>1010010=>0100101
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>0101010=>0101010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>0110010=>0100110
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>0100010=>0100010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>1101010=>0101011
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>1001010=>0101001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>0101010=>0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>0001010=>0101000
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>1110010=>0100111
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>1100010=>0100011
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>1000010=>0100001
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>0110010=>0100110
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>0100010=>0100010
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>0100010=>0100010
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>0000010=>0100000
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>1111000=>0001111
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>1111000=>0001111
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>1110000=>0000111
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>1101100=>0011011
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>1110100=>0010111
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>1111000=>0001111
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>1100000=>0000011
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>1010100=>0010101
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>1010000=>0000101
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>1110100=>0010111
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>1111000=>0001111
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>1110000=>0000111
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>1101000=>0001011
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>0111000=>0001110
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>0110100=>0010110
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>0111000=>0001110
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>0110000=>0000110
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>0101000=>0001010
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>0110100=>0010110
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>0111000=>0001110
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>1011000=>0001101
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>1010100=>0010101
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>0011100=>0011100
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>0011000=>0001100
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>0010000=>0000100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>1101000=>0001011
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>0101000=>0001010
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>0001000=>0001000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>1110100=>0010111
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>1100100=>0010011
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>1000100=>0010001
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>1010100=>0010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>0010100=>0010100
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>0100100=>0010010
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>1000100=>0010001
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>0000100=>0010000
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>1111000=>0001111
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>1110000=>0000111
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>1101000=>0001011
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>1110000=>0000111
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>1100000=>0000011
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>1011000=>0001101
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>1010000=>0000101
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>1101000=>0001011
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>1001000=>0001001
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>1110000=>0000111
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>1100000=>0000011
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>1010000=>0000101
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>1100000=>0000011
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>1000000=>0000001
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>0101000=>0001010
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>0100000=>0000010
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>0101000=>0001010
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>0001000=>0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>1110000=>0000111
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>1100000=>0000011
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>1010000=>0000101
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>1100000=>0000011
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>1000000=>0000001
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>0110000=>0000110
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>0100000=>0000010
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>1010000=>0000101
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>0010000=>0000100
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>1100000=>0000011
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>1000000=>0000001
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>0100000=>0000010
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>1000000=>0000001
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>0000000=>0000000
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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
reverse
Description
Return the reversal of a binary word.
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