Identifier
Mp00018:
Binary trees
—left border symmetry⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
[.,.]=>[.,.]=>[1]=>
[.,[.,.]]=>[.,[.,.]]=>[2,1]=>1
[[.,.],.]=>[[.,.],.]=>[1,2]=>0
[.,[.,[.,.]]]=>[.,[.,[.,.]]]=>[3,2,1]=>11
[.,[[.,.],.]]=>[.,[[.,.],.]]=>[2,3,1]=>01
[[.,.],[.,.]]=>[[.,[.,.]],.]=>[2,1,3]=>10
[[.,[.,.]],.]=>[[.,.],[.,.]]=>[1,3,2]=>01
[[[.,.],.],.]=>[[[.,.],.],.]=>[1,2,3]=>00
[.,[.,[.,[.,.]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>111
[.,[.,[[.,.],.]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>011
[.,[[.,.],[.,.]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>101
[.,[[.,[.,.]],.]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>011
[.,[[[.,.],.],.]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>001
[[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>110
[[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>010
[[.,[.,.]],[.,.]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>101
[[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>100
[[.,[.,[.,.]]],.]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>011
[[.,[[.,.],.]],.]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>001
[[[.,.],[.,.]],.]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>010
[[[.,[.,.]],.],.]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>001
[[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>000
[.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>1111
[.,[.,[.,[[.,.],.]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0111
[.,[.,[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>1011
[.,[.,[[.,[.,.]],.]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>0111
[.,[.,[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0011
[.,[[.,.],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>1101
[.,[[.,.],[[.,.],.]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0101
[.,[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>1011
[.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>1001
[.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0111
[.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0011
[.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0101
[.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0011
[.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0001
[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1110
[[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0110
[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1010
[[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>0110
[[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0010
[[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>1101
[[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>0101
[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>1100
[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0100
[[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>1011
[[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>1001
[[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>1010
[[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>1001
[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1000
[[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>0111
[[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>0011
[[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>0101
[[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>0011
[[.,[[[.,.],.],.]],.]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>0001
[[[.,.],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>0110
[[[.,.],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>0010
[[[.,[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>0101
[[[[.,.],.],[.,.]],.]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>0100
[[[.,[.,[.,.]]],.],.]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>0011
[[[.,[[.,.],.]],.],.]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>0001
[[[[.,.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>0010
[[[[.,[.,.]],.],.],.]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>0001
[[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>01111
[.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>10111
[.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>01111
[.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00111
[.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>11011
[.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>01011
[.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>10111
[.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>10011
[.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>01111
[.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>00111
[.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>01011
[.,[.,[[[.,[.,.]],.],.]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>00111
[.,[.,[[[[.,.],.],.],.]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00011
[.,[[.,.],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>11101
[.,[[.,.],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>01101
[.,[[.,.],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>10101
[.,[[.,.],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>01101
[.,[[.,.],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00101
[.,[[.,[.,.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>11011
[.,[[.,[.,.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>01011
[.,[[[.,.],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>11001
[.,[[[.,.],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>01001
[.,[[.,[.,[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>10111
[.,[[.,[[.,.],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>10011
[.,[[[.,.],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>10101
[.,[[[.,[.,.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>10011
[.,[[[[.,.],.],.],[.,.]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>10001
[.,[[.,[.,[.,[.,.]]]],.]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>01111
[.,[[.,[.,[[.,.],.]]],.]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>00111
[.,[[.,[[.,.],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>01011
[.,[[.,[[.,[.,.]],.]],.]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>00111
[.,[[.,[[[.,.],.],.]],.]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>00011
[.,[[[.,.],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>01101
[.,[[[.,.],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>00101
[.,[[[.,[.,.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>01011
[.,[[[[.,.],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>01001
[.,[[[.,[.,[.,.]]],.],.]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>00111
[.,[[[.,[[.,.],.]],.],.]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>00011
[.,[[[[.,.],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>00101
[.,[[[[.,[.,.]],.],.],.]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>00011
[.,[[[[[.,.],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00001
[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>11110
[[.,.],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>01110
[[.,.],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>10110
[[.,.],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>01110
[[.,.],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00110
[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>11010
[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>01010
[[.,.],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>10110
[[.,.],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>10010
[[.,.],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>01110
[[.,.],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>00110
[[.,.],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>01010
[[.,.],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>00110
[[.,.],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00010
[[.,[.,.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>11101
[[.,[.,.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>01101
[[.,[.,.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>10101
[[.,[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>01101
[[.,[.,.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>00101
[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>11100
[[[.,.],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>01100
[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>10100
[[[.,.],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>01100
[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00100
[[.,[.,[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>11011
[[.,[.,[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>01011
[[.,[[.,.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>11001
[[.,[[.,.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>01001
[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>11010
[[[.,.],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>01010
[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>11001
[[[.,[.,.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>01001
[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>11000
[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>01000
[[.,[.,[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>10111
[[.,[.,[[.,.],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>10011
[[.,[[.,.],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>10101
[[.,[[.,[.,.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>10011
[[.,[[[.,.],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>10001
[[[.,.],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>10110
[[[.,.],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>10010
[[[.,[.,.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>10101
[[[[.,.],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>10100
[[[.,[.,[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>10011
[[[.,[[.,.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>10001
[[[[.,.],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>10010
[[[[.,[.,.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>10001
[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>10000
[[.,[.,[.,[.,[.,.]]]]],.]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>01111
[[.,[.,[.,[[.,.],.]]]],.]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>00111
[[.,[.,[[.,.],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>01011
[[.,[.,[[.,[.,.]],.]]],.]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>00111
[[.,[.,[[[.,.],.],.]]],.]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>00011
[[.,[[.,.],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>01101
[[.,[[.,.],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>00101
[[.,[[.,[.,.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>01011
[[.,[[[.,.],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>01001
[[.,[[.,[.,[.,.]]],.]],.]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>00111
[[.,[[.,[[.,.],.]],.]],.]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>00011
[[.,[[[.,.],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>00101
[[.,[[[.,[.,.]],.],.]],.]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>00011
[[.,[[[[.,.],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>00001
[[[.,.],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>01110
[[[.,.],[.,[[.,.],.]]],.]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>00110
[[[.,.],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>01010
[[[.,.],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>00110
[[[.,.],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>00010
[[[.,[.,.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>01101
[[[.,[.,.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>00101
[[[[.,.],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>01100
[[[[.,.],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>00100
[[[.,[.,[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>01011
[[[.,[[.,.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>01001
[[[[.,.],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>01010
[[[[.,[.,.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>01001
[[[[[.,.],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>01000
[[[.,[.,[.,[.,.]]]],.],.]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>00111
[[[.,[.,[[.,.],.]]],.],.]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>00011
[[[.,[[.,.],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>00101
[[[.,[[.,[.,.]],.]],.],.]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>00011
[[[.,[[[.,.],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>00001
[[[[.,.],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>00110
[[[[.,.],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>00010
[[[[.,[.,.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>00101
[[[[[.,.],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>00100
[[[[.,[.,[.,.]]],.],.],.]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>00011
[[[[.,[[.,.],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>00001
[[[[[.,.],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>00010
[[[[[.,[.,.]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>00001
[[[[[[.,.],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>011111
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>101111
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>011111
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>001111
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>110111
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>010111
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>101111
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>100111
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>011111
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>001111
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>010111
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>001111
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>111011
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>011011
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>101011
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>011011
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>110111
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>010111
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>110011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>010011
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>101111
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>100111
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>101011
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>100111
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>100011
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>011111
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>001111
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>010111
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>001111
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>000111
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>011011
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>001011
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>010111
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>010011
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>001111
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>000111
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>001011
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>000111
[.,[.,[[[[[.,.],.],.],.],.]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>000011
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>111101
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>011101
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>101101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>011101
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>001101
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>110101
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>010101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>101101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>100101
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>011101
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>001101
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>010101
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>001101
[.,[[.,.],[[[[.,.],.],.],.]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>000101
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>111011
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>011011
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>101011
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>011011
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>001011
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>111001
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>011001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>101001
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>011001
[.,[[[.,.],.],[[[.,.],.],.]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>001001
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>110111
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>010111
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>110011
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>010011
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>110101
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>010101
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>110011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>010011
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>110001
[.,[[[[.,.],.],.],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>010001
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>101111
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>100111
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>101011
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>100111
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>100011
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>101101
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>100101
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>101011
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>101001
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>100111
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>100011
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>100101
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>100011
[.,[[[[[.,.],.],.],.],[.,.]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>011111
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>001111
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>010111
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>001111
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>000111
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>011011
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>001011
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>010111
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>010011
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>001111
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>000111
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>001011
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>000111
[.,[[.,[[[[.,.],.],.],.]],.]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>000011
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>011101
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>001101
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>010101
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>001101
[.,[[[.,.],[[[.,.],.],.]],.]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>000101
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>011011
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>001011
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>011001
[.,[[[[.,.],.],[[.,.],.]],.]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>001001
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>010111
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>010011
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>010101
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>010011
[.,[[[[[.,.],.],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>010001
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>001111
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>000111
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>001011
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>000111
[.,[[[.,[[[.,.],.],.]],.],.]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>000011
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>001101
[.,[[[[.,.],[[.,.],.]],.],.]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>000101
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>001011
[.,[[[[[.,.],.],[.,.]],.],.]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>001001
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>000111
[.,[[[[.,[[.,.],.]],.],.],.]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>000011
[.,[[[[[.,.],[.,.]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>000101
[.,[[[[[.,[.,.]],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>000011
[.,[[[[[[.,.],.],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>111110
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>011110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>101110
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>011110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>001110
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>110110
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>010110
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>101110
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>100110
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>011110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>001110
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>010110
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>001110
[[.,.],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>000110
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>111010
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>011010
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>101010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>011010
[[.,.],[[.,.],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>001010
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>110110
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>010110
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>110010
[[.,.],[[[.,.],.],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>010010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>101110
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>100110
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>101010
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>100110
[[.,.],[[[[.,.],.],.],[.,.]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>100010
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>011110
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>001110
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>010110
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>001110
[[.,.],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>000110
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>011010
[[.,.],[[[.,.],[[.,.],.]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>001010
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>010110
[[.,.],[[[[.,.],.],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>010010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>001110
[[.,.],[[[.,[[.,.],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>000110
[[.,.],[[[[.,.],[.,.]],.],.]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>001010
[[.,.],[[[[.,[.,.]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>000110
[[.,.],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>000010
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>111101
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>011101
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>101101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>011101
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>001101
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>110101
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>010101
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>101101
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>100101
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>011101
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>001101
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>010101
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>001101
[[.,[.,.]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>000101
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>111100
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>011100
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>101100
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>011100
[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>001100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>110100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>010100
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>101100
[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>100100
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>011100
[[[.,.],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>001100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>010100
[[[.,.],.],[[[.,[.,.]],.],.]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>001100
[[[.,.],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>000100
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>111011
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>011011
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>101011
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>011011
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>001011
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>111001
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>011001
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>101001
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>011001
[[.,[[.,.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>001001
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>111010
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>011010
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>101010
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>011010
[[[.,.],[.,.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>001010
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>111001
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>011001
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>101001
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>011001
[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>001001
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>111000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>011000
[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>101000
[[[[.,.],.],.],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>011000
[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>001000
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>110111
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>010111
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>110011
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>010011
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>110101
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>010101
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>110011
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>010011
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>110001
[[.,[[[.,.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>010001
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>110110
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>010110
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>110010
[[[.,.],[[.,.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>010010
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>110101
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>010101
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>110100
[[[[.,.],.],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>010100
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>110011
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>010011
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>110001
[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>010001
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>110010
[[[[.,.],[.,.]],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>010010
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>110001
[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>010001
[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>110000
[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>010000
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>101111
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>100111
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>101011
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>100111
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>100011
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>101101
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>100101
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>101011
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>101001
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>100111
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>100011
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>100101
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>100011
[[.,[[[[.,.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>100001
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>101110
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>100110
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>101010
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>100110
[[[.,.],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>100010
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>101101
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>100101
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>101100
[[[[.,.],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>100100
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>101011
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>101001
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>101010
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>101001
[[[[[.,.],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>101000
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>100111
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>100011
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>100101
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>100011
[[[.,[[[.,.],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>100001
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>100110
[[[[.,.],[[.,.],.]],.],[.,.]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>100010
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>100101
[[[[[.,.],.],[.,.]],.],[.,.]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>100100
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>100011
[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>100001
[[[[[.,.],[.,.]],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>100010
[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>100001
[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>100000
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>011111
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>001111
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>010111
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>001111
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>000111
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>011011
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>001011
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>010111
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>010011
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>001111
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>000111
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>001011
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>000111
[[.,[.,[[[[.,.],.],.],.]]],.]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>000011
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>011101
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>001101
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>010101
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>001101
[[.,[[.,.],[[[.,.],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>000101
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>011011
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>001011
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>011001
[[.,[[[.,.],.],[[.,.],.]]],.]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>001001
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>010111
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>010011
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>010101
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>010011
[[.,[[[[.,.],.],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>010001
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>001111
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>000111
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>001011
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>000111
[[.,[[.,[[[.,.],.],.]],.]],.]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>000011
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>001101
[[.,[[[.,.],[[.,.],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>000101
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>001011
[[.,[[[[.,.],.],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>001001
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>000111
[[.,[[[.,[[.,.],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>000011
[[.,[[[[.,.],[.,.]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>000101
[[.,[[[[.,[.,.]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>000011
[[.,[[[[[.,.],.],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>000001
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>011110
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>001110
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>010110
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>001110
[[[.,.],[.,[[[.,.],.],.]]],.]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>000110
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>011010
[[[.,.],[[.,.],[[.,.],.]]],.]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>001010
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>010110
[[[.,.],[[[.,.],.],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>010010
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>001110
[[[.,.],[[.,[[.,.],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>000110
[[[.,.],[[[.,.],[.,.]],.]],.]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>001010
[[[.,.],[[[.,[.,.]],.],.]],.]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>000110
[[[.,.],[[[[.,.],.],.],.]],.]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>000010
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>011101
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>001101
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>010101
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>001101
[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>000101
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>011100
[[[[.,.],.],[.,[[.,.],.]]],.]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>001100
[[[[.,.],.],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>010100
[[[[.,.],.],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>001100
[[[[.,.],.],[[[.,.],.],.]],.]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>000100
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>011011
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>001011
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>011001
[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>001001
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>011010
[[[[.,.],[.,.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>001010
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>011001
[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>001001
[[[[[.,.],.],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>011000
[[[[[.,.],.],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>001000
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>010111
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>010011
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>010101
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>010011
[[[.,[[[.,.],.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>010001
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>010110
[[[[.,.],[[.,.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>010010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>010101
[[[[[.,.],.],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>010100
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>010011
[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>010001
[[[[[.,.],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>010010
[[[[[.,[.,.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>010001
[[[[[[.,.],.],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>010000
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>001111
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>000111
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>001011
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>000111
[[[.,[.,[[[.,.],.],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>000011
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>001101
[[[.,[[.,.],[[.,.],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>000101
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>001011
[[[.,[[[.,.],.],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>001001
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>000111
[[[.,[[.,[[.,.],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>000011
[[[.,[[[.,.],[.,.]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>000101
[[[.,[[[.,[.,.]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>000011
[[[.,[[[[.,.],.],.],.]],.],.]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>000001
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>001110
[[[[.,.],[.,[[.,.],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>000110
[[[[.,.],[[.,.],[.,.]]],.],.]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>001010
[[[[.,.],[[.,[.,.]],.]],.],.]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>000110
[[[[.,.],[[[.,.],.],.]],.],.]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>000010
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>001101
[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>000101
[[[[[.,.],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>001100
[[[[[.,.],.],[[.,.],.]],.],.]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>000100
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>001011
[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>001001
[[[[[.,.],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>001010
[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>001001
[[[[[[.,.],.],.],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>001000
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>000111
[[[[.,[.,[[.,.],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>000011
[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>000101
[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>000011
[[[[.,[[[.,.],.],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>000001
[[[[[.,.],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>000110
[[[[[.,.],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>000010
[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>000101
[[[[[[.,.],.],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>000100
[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>000011
[[[[[.,[[.,.],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>000001
[[[[[[.,.],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>000010
[[[[[[.,[.,.]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>000001
[[[[[[[.,.],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>0111111
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>1011111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>0111111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>0011111
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>1101111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>0101111
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>1011111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>1001111
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>0111111
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>0011111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>0101111
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>0011111
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>0001111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>0110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>1010111
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>0110111
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>0010111
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>1100111
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>0100111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>1010111
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>1000111
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>0111111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>0011111
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>0101111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>0011111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>0001111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>0110111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>0010111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>0101111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>0100111
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>0011111
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>0001111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>0010111
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>0001111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>0000111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>1111011
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>0111011
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>1001011
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>0111011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>0001011
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>0010111
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>1110011
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>1100111
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>0101011
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>1100111
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>0100111
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>1010111
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>1001011
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>0111111
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>0110111
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>0010111
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>0011111
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>0001111
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>0001111
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>0000111
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>0011111
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>0000111
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>0011011
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>0010011
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>0000111
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>0111101
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>0101101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>0001101
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>1110101
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>1010101
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>0110101
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>0010101
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>1101101
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>1100101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>1011101
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>1001101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>1010101
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>0011101
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>0001101
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>0110101
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>0010101
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>0100101
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>0011101
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>1111011
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>1011011
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>0111011
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>0011011
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>1101011
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>1011011
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>0111011
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>0011011
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>1111001
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>1011001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>1101001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>0111001
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>0011001
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>0001001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>1110111
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>1110011
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>1110101
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>1010101
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>1110011
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>1110001
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>1010001
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>0110001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>1101111
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>0101111
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>0100111
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>1101101
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>0101101
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>1100101
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>1101011
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>1101001
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>0101001
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>1100111
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>1100101
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>1100011
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>0100011
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>1100001
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>0100001
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>1011111
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>1001111
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>1001011
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>1000011
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>1001101
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>1010101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>1010101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>1010001
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>1001111
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>1001101
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>1000101
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>0111111
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>0101111
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>0000111
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>0111011
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[2,6,7,5,4,8,3,1]=>0011011
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>0010111
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>0110011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>0101111
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>0011111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>0001111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>0000111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>0011011
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>0010111
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>0000111
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>0101101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>0010101
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>0000101
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>0111011
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>0011011
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>0111001
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>0101001
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>0110111
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>0010111
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>0110011
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>0110101
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>0110011
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>0110001
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>0010001
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>0101111
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>0100111
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>0101101
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>0101011
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>0101001
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>0100111
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>0100101
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>0100011
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>0100001
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>0011111
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>0000111
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>0011011
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>0000111
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>0000011
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>0011101
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>0011001
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>0001001
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>0010111
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>0010101
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>0010001
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>0001111
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>0000011
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>0001101
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>0001011
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>0001001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>0000111
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>0000101
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>0000011
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>1011110
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>0111110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0011110
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>1101110
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>0101110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>0011110
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>0101110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>0011110
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>0001110
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>1110110
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>1010110
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>0101110
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>1100110
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>1001110
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>0011110
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>0001110
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>0101110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>0011110
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>1011010
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>1101010
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>0101010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>0111010
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>0011010
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>0001010
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>1110110
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>0110110
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>0110110
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>1110010
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>0110010
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>0101010
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>1100110
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>1011110
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>1001110
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>1001110
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>1011010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>1010110
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>1000110
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>0001110
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>0001110
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>0101010
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>0110010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>0101010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>0011110
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>0001110
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>0010110
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>0001110
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>0000110
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>0001110
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>1111101
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>0111101
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>0111101
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>0011101
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>1101101
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>0101101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>1011101
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>0111101
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>0011101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>0001101
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>1110101
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>0110101
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>1010101
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>0110101
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>0010101
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>0100101
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>1010101
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>0111101
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>0011101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>0011101
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>0110101
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>0010101
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>0101101
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>0011101
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>0001101
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>0000101
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>0111100
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>1011100
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>0011100
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>1101100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>1011100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>0111100
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>0001100
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>1110100
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>0110100
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>0110100
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>1101100
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>0011100
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>0001100
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>1111011
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>0111011
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>1011011
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>0111011
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>0011011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>0101011
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>1011011
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>1001011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>0111011
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>0011011
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>0101011
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>0011011
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>0001011
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>1111001
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>0111001
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>0011001
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>0101001
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>1011001
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>0111001
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>0101001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>1111010
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>0111010
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>0111010
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>0101010
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>1011010
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>0111010
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>0011010
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>0101010
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>1111001
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>0111001
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>0111001
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>1011001
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>0111001
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>0011001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>0111000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>1011000
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>0111000
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>0011000
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>1101000
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>0101000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>1011000
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>1001000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>0111000
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>0011000
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>0101000
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>0011000
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>0110111
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>1010111
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>0110111
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>0010111
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>1110011
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>0110011
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>1010011
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>0010011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>1110101
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>0110101
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>1010101
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>0110101
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>0010101
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>1110011
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>0110011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>1010011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>0110011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>0010011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>1110001
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>0110001
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>1010001
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>0110001
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>0010001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>1110110
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>1010110
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>0010110
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>1110010
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>1010010
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>0010010
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>1110101
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>0110101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>1010101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>0110101
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>0010101
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>1110100
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>1010100
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>0010100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>1110011
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>1010011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>0010011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>1110001
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>1010001
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>0010001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>1110010
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>1010010
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>0010010
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>1110001
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>1010001
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>0010001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>0110000
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>1010000
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>0110000
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>0010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>1101111
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>0101111
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>1100111
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>1101011
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>0101011
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>1100111
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>0100111
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>1100011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>0100011
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>1101101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>1100101
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>1101011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>0101011
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>1101001
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>1100111
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>1100011
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>1100101
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>1100011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>1100001
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>0100001
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>0100110
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>0101010
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>1100110
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>1100010
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>0100010
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>0101101
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>1100100
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>0101010
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>1100111
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>0100111
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>1100011
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>0100011
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>1100101
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>0100101
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>1100011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>1100001
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>0100001
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>0100010
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>1100011
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>1100001
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>0100001
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>1100000
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>0100000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>1011111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>1001111
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>1010111
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>1001111
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>1000111
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>1011011
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>1001011
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>1010111
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>1010011
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>1000111
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>1000011
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>1010101
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>1001101
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>1000101
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>1001001
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>1010101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>1001111
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>1000111
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>1000111
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>1000011
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>1001101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>1000101
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>1001011
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>1000111
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>1000011
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>1000011
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>1000001
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>1000110
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>1001101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>1010101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>1001101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>1000101
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>1001100
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>1001100
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>1001001
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>1010111
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>1010011
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>1010011
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>1010001
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>1010100
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>1010001
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>1010000
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>1001111
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>1000111
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>1000111
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>1000110
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>1001011
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>1001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>1000111
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>1000101
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>1000001
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>1000101
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>1000100
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>1000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>0111111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>0011111
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>0101111
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>0011111
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>0001111
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>0110111
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>0010111
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>0100111
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>0010111
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>0000111
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>0110011
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>0011111
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>0001111
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>0001111
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>0000111
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>0011011
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>0010111
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>0000111
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>0011101
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>0111011
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>0011011
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>0011011
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>0110111
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>0110011
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>0110001
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>0101111
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>0100111
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>0101011
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>0100111
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>0101011
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>0101001
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>0100111
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>0100011
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>0011111
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>0001111
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>0000111
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>0010011
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>0001111
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>0000111
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>0001011
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>0000011
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>0001101
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>0011011
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>0010011
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>0010101
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>0001111
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>0001011
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>0000011
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>0001101
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>0000111
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>0001110
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>0010110
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>0101010
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>0110010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>0101010
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>0100110
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>0001110
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>0000110
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>0011010
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>0010110
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>0000010
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>0101101
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>0011101
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>0011100
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>0101100
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>0011100
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>0001100
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>0110100
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>0101100
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>0001100
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>0001011
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>0101001
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>0011001
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>0001001
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>0101010
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>0011010
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>0001010
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>0011001
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[1,3,4,5,2,6,8,7]=>0001001
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>0011000
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>0001000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>0110111
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>0010111
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>0010011
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>0110101
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>0010101
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>0010011
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>0110001
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>0010001
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>0110110
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>0110010
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>0010010
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>0110011
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>0010011
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>0110001
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>0010001
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>0110010
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>0010010
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>0110001
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>0010001
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>0110000
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>0010000
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>0101111
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>0100111
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>0101101
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>0101011
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>0101001
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>0100011
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>0100101
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>0101010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>0100110
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>0100010
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>0100100
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>0101001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>0101000
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>0100111
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>0100101
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>0100011
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>0100001
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>0100110
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>0100101
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>0100100
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>0100001
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>0100010
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>0100000
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>0011111
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>0000111
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>0011011
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>0010111
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>0010011
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>0001011
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>0000011
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>0001101
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>0000101
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>0011011
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>0011001
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>0010111
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>0001111
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>0000111
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>0000111
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>0000011
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>0001101
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>0000011
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>0001110
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>0000110
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>0001010
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>0010010
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>0011100
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>0001100
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>0000100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>0001011
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>0011001
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>0001001
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>0011001
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>0010111
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>0010011
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>0010101
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>0010011
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>0010001
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>0010010
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>0010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>0010100
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>0010001
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>0010001
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>0010000
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>0001111
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>0000111
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>0001011
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>0000111
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>0000011
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>0001101
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>0000101
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>0001011
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>0001001
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>0000111
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>0000011
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>0000101
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>0000011
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>0000001
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>0001110
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>0000110
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>0001010
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>0000110
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>0000010
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>0001101
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>0000101
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>0000100
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>0001011
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>0001001
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>0001010
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>0000111
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>0000011
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>0000101
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>0000011
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>0000001
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>0000110
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>0000010
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>0000101
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>0000100
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>0000011
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>0000001
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>0000010
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>0000001
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>0000000
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
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 word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
searching the database
Sorry, this map was not found in the database.