Identifier
Mp00018:
Binary trees
—left border symmetry⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
[.,.]=>[.,.]=>[1]=>
[.,[.,.]]=>[.,[.,.]]=>[2,1]=>0
[[.,.],.]=>[[.,.],.]=>[1,2]=>1
[.,[.,[.,.]]]=>[.,[.,[.,.]]]=>[3,2,1]=>00
[.,[[.,.],.]]=>[.,[[.,.],.]]=>[2,3,1]=>00
[[.,.],[.,.]]=>[[.,[.,.]],.]=>[2,1,3]=>01
[[.,[.,.]],.]=>[[.,.],[.,.]]=>[1,3,2]=>10
[[[.,.],.],.]=>[[[.,.],.],.]=>[1,2,3]=>11
[.,[.,[.,[.,.]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>000
[.,[.,[[.,.],.]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>000
[.,[[.,.],[.,.]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>000
[.,[[.,[.,.]],.]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>000
[.,[[[.,.],.],.]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>000
[[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>001
[[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>001
[[.,[.,.]],[.,.]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>010
[[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>011
[[.,[.,[.,.]]],.]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>100
[[.,[[.,.],.]],.]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>100
[[[.,.],[.,.]],.]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>101
[[[.,[.,.]],.],.]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>110
[[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>111
[.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0000
[.,[.,[.,[[.,.],.]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0000
[.,[.,[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>0000
[.,[.,[[.,[.,.]],.]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>0000
[.,[.,[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0000
[.,[[.,.],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>0000
[.,[[.,.],[[.,.],.]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0000
[.,[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>0000
[.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0000
[.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0000
[.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0000
[.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0000
[.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0000
[.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0000
[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>0001
[[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0001
[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>0001
[[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>0001
[[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0001
[[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>0010
[[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>0010
[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>0011
[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0011
[[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>0100
[[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>0100
[[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>0101
[[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>0110
[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>0111
[[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1000
[[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1000
[[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1000
[[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1000
[[.,[[[.,.],.],.]],.]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1000
[[[.,.],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>1001
[[[.,.],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1001
[[[.,[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>1010
[[[[.,.],.],[.,.]],.]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1011
[[[.,[.,[.,.]]],.],.]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>1100
[[[.,[[.,.],.]],.],.]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1100
[[[[.,.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1101
[[[[.,[.,.]],.],.],.]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1110
[[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1111
[.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>00000
[.,[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>00000
[.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>00000
[.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>00000
[.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00000
[.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>00000
[.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>00000
[.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>00000
[.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>00000
[.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>00000
[.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>00000
[.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>00000
[.,[.,[[[.,[.,.]],.],.]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>00000
[.,[.,[[[[.,.],.],.],.]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00000
[.,[[.,.],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>00000
[.,[[.,.],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>00000
[.,[[.,.],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>00000
[.,[[.,.],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>00000
[.,[[.,.],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00000
[.,[[.,[.,.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>00000
[.,[[.,[.,.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>00000
[.,[[[.,.],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>00000
[.,[[[.,.],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>00000
[.,[[.,[.,[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>00000
[.,[[.,[[.,.],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>00000
[.,[[[.,.],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>00000
[.,[[[.,[.,.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>00000
[.,[[[[.,.],.],.],[.,.]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>00000
[.,[[.,[.,[.,[.,.]]]],.]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>00000
[.,[[.,[.,[[.,.],.]]],.]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>00000
[.,[[.,[[.,.],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>00000
[.,[[.,[[.,[.,.]],.]],.]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>00000
[.,[[.,[[[.,.],.],.]],.]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>00000
[.,[[[.,.],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>00000
[.,[[[.,.],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>00000
[.,[[[.,[.,.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>00000
[.,[[[[.,.],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>00000
[.,[[[.,[.,[.,.]]],.],.]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>00000
[.,[[[.,[[.,.],.]],.],.]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>00000
[.,[[[[.,.],[.,.]],.],.]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>00000
[.,[[[[.,[.,.]],.],.],.]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>00000
[.,[[[[[.,.],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00000
[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>00001
[[.,.],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>00001
[[.,.],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>00001
[[.,.],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>00001
[[.,.],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00001
[[.,.],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>00001
[[.,.],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>00001
[[.,.],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>00001
[[.,.],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>00001
[[.,.],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>00001
[[.,.],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>00001
[[.,.],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>00001
[[.,.],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>00001
[[.,.],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00001
[[.,[.,.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>00010
[[.,[.,.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>00010
[[.,[.,.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>00010
[[.,[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>00010
[[.,[.,.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>00010
[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>00011
[[[.,.],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>00011
[[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>00011
[[[.,.],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>00011
[[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00011
[[.,[.,[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>00100
[[.,[.,[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>00100
[[.,[[.,.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>00100
[[.,[[.,.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>00100
[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>00101
[[[.,.],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>00101
[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>00110
[[[.,[.,.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>00110
[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>00111
[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>00111
[[.,[.,[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>01000
[[.,[.,[[.,.],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>01000
[[.,[[.,.],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>01000
[[.,[[.,[.,.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>01000
[[.,[[[.,.],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>01000
[[[.,.],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>01001
[[[.,.],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>01001
[[[.,[.,.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>01010
[[[[.,.],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>01011
[[[.,[.,[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>01100
[[[.,[[.,.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>01100
[[[[.,.],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>01101
[[[[.,[.,.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>01110
[[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>01111
[[.,[.,[.,[.,[.,.]]]]],.]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>10000
[[.,[.,[.,[[.,.],.]]]],.]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>10000
[[.,[.,[[.,.],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>10000
[[.,[.,[[.,[.,.]],.]]],.]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>10000
[[.,[.,[[[.,.],.],.]]],.]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>10000
[[.,[[.,.],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>10000
[[.,[[.,.],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>10000
[[.,[[.,[.,.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>10000
[[.,[[[.,.],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>10000
[[.,[[.,[.,[.,.]]],.]],.]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>10000
[[.,[[.,[[.,.],.]],.]],.]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>10000
[[.,[[[.,.],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>10000
[[.,[[[.,[.,.]],.],.]],.]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>10000
[[.,[[[[.,.],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>10000
[[[.,.],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>10001
[[[.,.],[.,[[.,.],.]]],.]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>10001
[[[.,.],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>10001
[[[.,.],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>10001
[[[.,.],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>10001
[[[.,[.,.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>10010
[[[.,[.,.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>10010
[[[[.,.],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>10011
[[[[.,.],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>10011
[[[.,[.,[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>10100
[[[.,[[.,.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>10100
[[[[.,.],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>10101
[[[[.,[.,.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>10110
[[[[[.,.],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>10111
[[[.,[.,[.,[.,.]]]],.],.]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>11000
[[[.,[.,[[.,.],.]]],.],.]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>11000
[[[.,[[.,.],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>11000
[[[.,[[.,[.,.]],.]],.],.]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>11000
[[[.,[[[.,.],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>11000
[[[[.,.],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>11001
[[[[.,.],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>11001
[[[[.,[.,.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>11010
[[[[[.,.],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>11011
[[[[.,[.,[.,.]]],.],.],.]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>11100
[[[[.,[[.,.],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>11100
[[[[[.,.],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>11101
[[[[[.,[.,.]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>11110
[[[[[[.,.],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>000000
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>000000
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>000000
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>000000
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>000000
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>000000
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>000000
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>000000
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>000000
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>000000
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>000000
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>000000
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>000000
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>000000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>000000
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>000000
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>000000
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>000000
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>000000
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>000000
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>000000
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>000000
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>000000
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>000000
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>000000
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>000000
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>000000
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>000000
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>000000
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>000000
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>000000
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>000000
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>000000
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>000000
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>000000
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>000000
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>000000
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>000000
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>000000
[.,[.,[[[[[.,.],.],.],.],.]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>000000
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>000000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>000000
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>000000
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>000000
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>000000
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>000000
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[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>000000
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>000000
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>000000
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[.,[[.,.],[[[.,.],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>000000
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>000000
[.,[[.,.],[[[[.,.],.],.],.]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>000000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>000000
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>000000
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>000000
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>000000
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>000000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>000000
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>000000
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>000000
[.,[[[.,.],.],[[[.,.],.],.]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>000000
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>000000
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>000000
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>000000
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>000000
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>000000
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>000000
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>000000
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>000000
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>000000
[.,[[[[.,.],.],.],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>000000
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>000000
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>000000
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>000000
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>000000
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[.,[[[[[.,[.,.]],.],.],.],.]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>000000
[.,[[[[[[.,.],.],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>000000
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>000001
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>000001
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>000001
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>000001
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>000001
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>000001
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>000001
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>000001
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>000001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>000001
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>000001
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>000001
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>000001
[[.,.],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>000001
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>000001
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>000001
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>000001
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>000001
[[.,.],[[.,.],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>000001
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>000001
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>000001
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>000001
[[.,.],[[[.,.],.],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>000001
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>000001
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>000001
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>000001
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>000001
[[.,.],[[[[.,.],.],.],[.,.]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>000001
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>000001
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>000001
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>000001
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>000001
[[.,.],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>000001
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>000001
[[.,.],[[[.,.],[[.,.],.]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>000001
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>000001
[[.,.],[[[[.,.],.],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>000001
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>000001
[[.,.],[[[.,[[.,.],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>000001
[[.,.],[[[[.,.],[.,.]],.],.]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>000001
[[.,.],[[[[.,[.,.]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>000001
[[.,.],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>000001
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>000010
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>000010
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>000010
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>000010
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>000010
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>000010
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>000010
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>000010
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>000010
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>000010
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>000010
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>000010
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>000010
[[.,[.,.]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>000010
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>000011
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>000011
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>000011
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>000011
[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>000011
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>000011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>000011
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>000011
[[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>000011
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>000011
[[[.,.],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>000011
[[[.,.],.],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>000011
[[[.,.],.],[[[.,[.,.]],.],.]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>000011
[[[.,.],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>000011
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>000100
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>000100
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>000100
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>000100
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>000100
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>000100
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>000100
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>000100
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>000100
[[.,[[.,.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>000100
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>000101
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>000101
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>000101
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>000101
[[[.,.],[.,.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>000101
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>000110
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>000110
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>000110
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>000110
[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>000110
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>000111
[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>000111
[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>000111
[[[[.,.],.],.],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>000111
[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>000111
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>001000
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>001000
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>001000
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>001000
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>001000
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>001000
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>001000
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>001000
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>001000
[[.,[[[.,.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>001000
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>001001
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>001001
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>001001
[[[.,.],[[.,.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>001001
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>001010
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>001010
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>001011
[[[[.,.],.],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>001011
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>001100
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>001100
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>001100
[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>001100
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>001101
[[[[.,.],[.,.]],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>001101
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>001110
[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>001110
[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>001111
[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>001111
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>010000
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>010000
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>010000
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>010000
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>010000
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>010000
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>010000
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>010000
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>010000
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>010000
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>010000
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>010000
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>010000
[[.,[[[[.,.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>010000
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>010001
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>010001
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>010001
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>010001
[[[.,.],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>010001
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>010010
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>010010
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>010011
[[[[.,.],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>010011
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>010100
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>010100
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>010101
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>010110
[[[[[.,.],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>010111
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>011000
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>011000
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>011000
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>011000
[[[.,[[[.,.],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>011000
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>011001
[[[[.,.],[[.,.],.]],.],[.,.]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>011001
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>011010
[[[[[.,.],.],[.,.]],.],[.,.]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>011011
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>011100
[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>011100
[[[[[.,.],[.,.]],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>011101
[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>011110
[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>011111
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>100000
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>100000
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>100000
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>100000
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>100000
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>100000
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>100000
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>100000
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>100000
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>100000
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>100000
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>100000
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>100000
[[.,[.,[[[[.,.],.],.],.]]],.]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>100000
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>100000
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>100000
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>100000
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>100000
[[.,[[.,.],[[[.,.],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>100000
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>100000
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>100000
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>100000
[[.,[[[.,.],.],[[.,.],.]]],.]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>100000
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>100000
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>100000
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>100000
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>100000
[[.,[[[[.,.],.],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>100000
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>100000
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>100000
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>100000
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>100000
[[.,[[.,[[[.,.],.],.]],.]],.]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>100000
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>100000
[[.,[[[.,.],[[.,.],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>100000
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>100000
[[.,[[[[.,.],.],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>100000
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>100000
[[.,[[[.,[[.,.],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>100000
[[.,[[[[.,.],[.,.]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>100000
[[.,[[[[.,[.,.]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>100000
[[.,[[[[[.,.],.],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>100000
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>100001
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>100001
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>100001
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>100001
[[[.,.],[.,[[[.,.],.],.]]],.]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>100001
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>100001
[[[.,.],[[.,.],[[.,.],.]]],.]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>100001
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>100001
[[[.,.],[[[.,.],.],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>100001
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>100001
[[[.,.],[[.,[[.,.],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>100001
[[[.,.],[[[.,.],[.,.]],.]],.]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>100001
[[[.,.],[[[.,[.,.]],.],.]],.]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>100001
[[[.,.],[[[[.,.],.],.],.]],.]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>100001
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>100010
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>100010
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>100010
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>100010
[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>100010
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>100011
[[[[.,.],.],[.,[[.,.],.]]],.]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>100011
[[[[.,.],.],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>100011
[[[[.,.],.],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>100011
[[[[.,.],.],[[[.,.],.],.]],.]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>100011
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>100100
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>100100
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>100100
[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>100100
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>100101
[[[[.,.],[.,.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>100101
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>100110
[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>100110
[[[[[.,.],.],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>100111
[[[[[.,.],.],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>100111
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>101000
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>101000
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>101000
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>101000
[[[.,[[[.,.],.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>101000
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>101001
[[[[.,.],[[.,.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>101001
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>101011
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>101100
[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>101100
[[[[[.,.],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>101101
[[[[[.,[.,.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>101110
[[[[[[.,.],.],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>101111
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>110000
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>110000
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>110000
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>110000
[[[.,[.,[[[.,.],.],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>110000
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>110000
[[[.,[[.,.],[[.,.],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>110000
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>110000
[[[.,[[[.,.],.],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>110000
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>110000
[[[.,[[.,[[.,.],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>110000
[[[.,[[[.,.],[.,.]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>110000
[[[.,[[[.,[.,.]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>110000
[[[.,[[[[.,.],.],.],.]],.],.]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>110000
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>110001
[[[[.,.],[.,[[.,.],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>110001
[[[[.,.],[[.,.],[.,.]]],.],.]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>110001
[[[[.,.],[[.,[.,.]],.]],.],.]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>110001
[[[[.,.],[[[.,.],.],.]],.],.]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>110001
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>110010
[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>110010
[[[[[.,.],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>110011
[[[[[.,.],.],[[.,.],.]],.],.]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>110011
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>110100
[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>110100
[[[[[.,.],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>110101
[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>110110
[[[[[[.,.],.],.],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>110111
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>111000
[[[[.,[.,[[.,.],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>111000
[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>111000
[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>111000
[[[[.,[[[.,.],.],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>111000
[[[[[.,.],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>111001
[[[[[.,.],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>111001
[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>111010
[[[[[[.,.],.],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>111011
[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>111100
[[[[[.,[[.,.],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>111100
[[[[[[.,.],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>111101
[[[[[[.,[.,.]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>111110
[[[[[[[.,.],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>0000000
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>0000000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>0000000
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>0000000
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>0000000
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>0000000
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>0000000
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>0000000
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>0000000
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>0000000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>0000000
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>0000000
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>0000000
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>0000000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>0000000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>0000000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>0000000
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>0000000
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>0000000
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>0000000
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>0000000
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>0000000
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>0000000
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>0000000
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>0000000
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>0000000
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>0000000
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>0000000
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>0000000
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>0000000
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>0000000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>0000000
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>0000000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>0000000
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>0000000
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>0000000
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>0000000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>0000000
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>0000000
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>0000000
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>0000000
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>0000000
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>0000000
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>0000000
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>0000000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>0000000
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>0000000
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>0000000
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>0000000
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>0000000
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>0000000
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>0000000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>0000000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>0000000
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>0000000
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>0000000
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>0000000
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>0000000
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>0000000
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>0000000
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>0000000
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>0000000
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>0000000
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>0000000
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>0000000
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>0000000
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>0000000
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>0000000
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>0000000
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>0000000
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>0000000
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>0000000
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>0000000
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>0000000
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>0000000
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>0000000
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>0000000
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>0000000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>0000000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>0000000
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>0000000
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>0000000
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>0000000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>0000000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>0000000
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>0000000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>0000000
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>0000000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>0000000
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>0000000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>0000000
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>0000000
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>0000000
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>0000000
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>0000000
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>0000000
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>0000000
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>0000000
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>0000000
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>0000000
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>0000000
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>0000000
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>0000000
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>0000000
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[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>0000000
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[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>0000000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>0000000
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>0000000
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>0000000
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>0000000
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>0000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>0000001
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>0000001
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0000001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>0000001
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>0000001
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>0000001
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>0000001
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>0000001
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>0000001
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>0000001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>0000001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>0000001
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>0000001
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>0000001
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>0000001
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>0000001
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>0000001
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>0000001
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>0000001
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>0000001
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>0000001
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>0000001
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>0000001
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>0000001
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>0000001
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>0000001
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>0000001
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>0000001
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>0000001
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>0000001
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>0000001
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>0000001
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>0000001
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>0000001
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>0000001
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>0000001
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>0000001
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>0000001
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>0000001
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>0000001
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>0000001
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>0000001
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>0000001
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>0000001
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>0000001
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>0000001
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>0000001
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>0000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>0000010
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>0000010
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>0000010
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>0000010
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>0000010
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>0000010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>0000010
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>0000011
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>0000011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>0000011
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>0000011
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>0000011
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>0000011
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>0000011
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>0000011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>0000011
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>0000011
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>0000011
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>0000100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>0000100
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>0000100
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>0000100
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>0000100
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>0000101
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>0000101
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>0000101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>0000101
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>0000101
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>0000101
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>0000110
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>0000110
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>0000110
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>0000110
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>0000110
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>0000110
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>0000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>0000111
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>0000111
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>0000111
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>0000111
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>0000111
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>0000111
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>0000111
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>0000111
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>0000111
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>0000111
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>0000111
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0000111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>0001000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>0001000
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>0001000
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>0001000
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>0001000
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>0001000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>0001000
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>0001000
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>0001000
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>0001000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>0001000
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>0001000
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>0001000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>0001000
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>0001000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>0001001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>0001001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>0001010
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>0001010
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>0001010
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>0001011
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>0001011
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>0001100
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>0001100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>0001100
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>0001101
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>0001110
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>0001111
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>0001111
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>0001111
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>0001111
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>0001111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>0010000
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>0010000
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>0010000
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>0010000
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>0010000
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>0010000
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>0010000
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>0010000
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>0010000
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>0010000
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>0010000
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>0010000
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>0010000
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>0010000
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>0010000
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>0010000
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>0010000
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>0010000
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>0010000
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>0010000
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>0010001
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>0010001
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>0010001
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>0010010
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>0010011
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>0010101
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>0010101
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>0011000
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>0011000
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>0011000
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>0011000
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>0011000
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>0011001
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>0011100
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>0011100
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>0011100
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>0011111
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>0011111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>0100000
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>0100000
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>0100000
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>0100000
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>0100000
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>0100000
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>0100000
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>0100000
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>0100000
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>0100000
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>0100000
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>0100001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>0100010
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>0100010
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>0100010
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>0100011
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>0100011
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>0100110
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>0101000
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>0101000
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>0101000
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>0101001
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>0101010
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>0101011
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>0101110
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>0101111
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>0110000
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>0110000
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>0110000
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>0110001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>0110010
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>0110100
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>0110110
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>0111000
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>0111000
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>0111010
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>0111011
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>0111110
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>0111111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>1000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>1000000
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>1000000
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>1000000
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>1000000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>1000000
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>1000000
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>1000000
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>1000000
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>1000000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>1000000
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>1000000
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>1000000
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>1000000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>1000000
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>1000000
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>1000000
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>1000000
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>1000000
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>1000000
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>1000000
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>1000000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>1000000
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>1000000
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>1000000
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>1000000
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>1000000
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>1000000
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>1000000
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>1000000
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>1000000
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>1000000
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>1000000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>1000000
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>1000000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>1000000
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>1000000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>1000000
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>1000000
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>1000000
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>1000000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>1000000
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>1000001
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>1000001
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>1000001
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>1000001
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>1000001
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>1000001
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>1000001
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>1000001
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>1000001
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>1000001
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>1000010
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>1000010
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>1000011
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>1000011
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>1000011
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>1000011
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>1000011
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>1000011
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>1000011
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>1000101
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>1000110
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>1001000
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>1001000
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>1001000
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>1001000
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>1001000
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>1001001
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>1001001
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>1001001
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>1001100
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>1001100
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>1001101
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>1001110
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>1001111
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>1001111
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>1010000
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>1010000
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>1010000
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>1010001
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>1010100
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>1010100
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>1010101
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>1010111
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>1011000
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>1011000
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>1011000
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>1011001
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>1011010
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>1011011
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>1011101
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>1011111
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>1100000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>1100000
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>1100000
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>1100000
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>1100000
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>1100000
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>1100000
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>1100000
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>1100000
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>1100000
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>1100000
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>1100000
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>1100001
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>1100001
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>1100001
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>1100001
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>1100011
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>1100011
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>1100100
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>1100100
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>1100110
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>1101000
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>1101000
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>1101000
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>1101000
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>1101001
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>1101010
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>1101011
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>1101100
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>1101110
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>1101111
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>1110000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>1110000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>1110000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>1110000
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>1110000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>1110000
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>1110000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>1110000
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>1110000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>1110000
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>1110000
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>1110000
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>1110000
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>1110000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>1110001
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>1110001
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>1110001
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>1110001
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>1110001
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>1110010
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>1110010
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>1110011
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>1110100
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>1110100
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>1110101
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>1110111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>1111000
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>1111000
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>1111000
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>1111000
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>1111000
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>1111001
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>1111001
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>1111010
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>1111011
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>1111100
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>1111100
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>1111101
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>1111110
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>1111111
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
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
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