Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[2,1]=>1
[[.,.],.]=>[1,2]=>[1,2]=>0
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>11
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>10
[[.,.],[.,.]]=>[3,1,2]=>[1,3,2]=>01
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>10
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>00
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>111
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>110
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,1,3,2]=>101
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>110
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>100
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,4,3,2]=>011
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[1,4,2,3]=>010
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,4,2]=>101
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,2,4,3]=>001
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>110
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>100
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[1,3,2,4]=>010
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>100
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>000
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>1111
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>1110
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,4,1,3,2]=>1101
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>1110
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>1100
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,1,4,3,2]=>1011
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,1,4,2,3]=>1010
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,3,1,4,2]=>1101
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,1,2,4,3]=>1001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>1110
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>1100
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,1,3,2,4]=>1010
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>1100
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>1000
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,5,4,3,2]=>0111
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[1,5,4,2,3]=>0110
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,5,2,4,3]=>0101
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[1,5,3,2,4]=>0110
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[1,5,2,3,4]=>0100
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,1,5,3,2]=>1011
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,1,5,2,3]=>1010
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[1,2,5,3,4]=>0010
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,3,1,5,2]=>1101
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,2,5,3]=>1001
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,4,2,5,3]=>0101
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,2,5,4]=>1001
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,2,3,5,4]=>0001
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>1100
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,1,3,2,5]=>1010
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>1100
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>1000
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[1,4,3,2,5]=>0110
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[1,4,2,3,5]=>0100
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,4,2,5]=>1010
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[1,2,4,3,5]=>0010
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>1000
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[1,3,2,4,5]=>0100
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>11110
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>11101
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>11110
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>11100
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>11011
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,5,1,4,2,3]=>11010
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>11101
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>11001
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>11110
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>11100
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>11010
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>11100
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>11000
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>10111
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,1,5,4,2,3]=>10110
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,1,5,2,4,3]=>10101
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,1,5,3,2,4]=>10110
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,1,5,2,3,4]=>10100
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>11011
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,1,5,2,3]=>11010
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>10011
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,1,2,5,3,4]=>10010
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>11101
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>11001
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>10101
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>11001
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>10001
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>11110
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>11100
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>11010
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>11100
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>11000
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>10110
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,1,4,2,3,5]=>10100
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>11010
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>10010
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>11100
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>11000
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>10100
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>11000
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>10000
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>01111
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[1,6,5,4,2,3]=>01110
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,6,5,2,4,3]=>01101
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[1,6,5,3,2,4]=>01110
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[1,6,5,2,3,4]=>01100
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,6,2,5,4,3]=>01011
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[1,6,2,5,3,4]=>01010
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,6,4,2,5,3]=>01101
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,6,2,3,5,4]=>01001
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[1,6,4,3,2,5]=>01110
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[1,6,4,2,3,5]=>01100
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,6,2,4,3,5]=>01010
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[1,6,3,2,4,5]=>01100
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[1,6,2,3,4,5]=>01000
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>10111
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,1,6,4,2,3]=>10110
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[5,1,6,2,4,3]=>10101
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,1,6,3,2,4]=>10110
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[5,1,6,2,3,4]=>10100
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>00111
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[1,2,6,5,3,4]=>00110
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,6,3,5,4]=>00101
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[1,2,6,4,3,5]=>00110
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[1,2,6,3,4,5]=>00100
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>11011
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,4,1,6,2,3]=>11010
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>10011
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,1,2,6,3,4]=>10010
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>01011
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[1,5,2,6,3,4]=>01010
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>10011
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,1,2,6,3,5]=>10010
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>00011
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[1,2,3,6,4,5]=>00010
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>11101
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>11001
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>10101
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>11001
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>10001
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>01101
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,5,2,3,6,4]=>01001
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>10101
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>00101
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>11001
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>10001
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>01001
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>10001
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>00001
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>11100
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>11010
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>11100
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>11000
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>10110
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,1,4,2,3,6]=>10100
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>11010
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>10010
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>11100
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>11000
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>10100
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>11000
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>10000
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>01110
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[1,5,4,2,3,6]=>01100
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[1,5,2,4,3,6]=>01010
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[1,5,3,2,4,6]=>01100
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[1,5,2,3,4,6]=>01000
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>10110
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,1,5,2,3,6]=>10100
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>00110
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[1,2,5,3,4,6]=>00100
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>11010
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>10010
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>01010
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>10010
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>00010
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>11000
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>10100
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>11000
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>10000
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>01100
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[1,4,2,3,5,6]=>01000
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>10100
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>00100
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>10000
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>111110
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>111101
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>111110
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>111100
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>111011
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,6,5,1,4,2,3]=>111010
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>111101
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>111001
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>111110
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>111100
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>111010
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>111100
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>110111
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,6,1,5,4,2,3]=>110110
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,6,1,5,2,4,3]=>110101
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,6,1,5,3,2,4]=>110110
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,6,1,5,2,3,4]=>110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>111011
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,6,4,1,5,2,3]=>111010
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>110011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,6,1,2,5,3,4]=>110010
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>111101
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>111001
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>110101
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>111001
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>110001
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>111110
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>111100
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>111010
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>111100
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>111000
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>110110
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,6,1,4,2,3,5]=>110100
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>111010
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>110010
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>111100
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>111000
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>110100
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>111000
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>110000
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>101111
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,1,6,5,4,2,3]=>101110
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,1,6,5,2,4,3]=>101101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,1,6,5,3,2,4]=>101110
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,1,6,5,2,3,4]=>101100
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,1,6,2,5,4,3]=>101011
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,1,6,2,5,3,4]=>101010
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,1,6,4,2,5,3]=>101101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,1,6,2,3,5,4]=>101001
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,1,6,4,3,2,5]=>101110
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,1,6,4,2,3,5]=>101100
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,1,6,2,4,3,5]=>101010
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,1,6,3,2,4,5]=>101100
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,1,6,2,3,4,5]=>101000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>110111
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,5,1,6,4,2,3]=>110110
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,5,1,6,2,4,3]=>110101
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,5,1,6,3,2,4]=>110110
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,5,1,6,2,3,4]=>110100
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>100111
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,1,2,6,5,3,4]=>100110
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,1,2,6,3,5,4]=>100101
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,1,2,6,4,3,5]=>100110
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,1,2,6,3,4,5]=>100100
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>111011
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,4,1,6,2,3]=>111010
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>110011
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,1,2,6,3,4]=>110010
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>101011
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,1,5,2,6,3,4]=>101010
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>110011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,1,2,6,3,5]=>110010
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>100011
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,1,2,3,6,4,5]=>100010
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>111101
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>111001
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>110101
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>111001
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>110001
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>101101
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,1,5,2,3,6,4]=>101001
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>110101
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>100101
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>111001
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>110001
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>101001
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>110001
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>111110
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>111100
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>111010
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>111100
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>111000
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>110110
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,5,1,4,2,3,6]=>110100
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>111010
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>110010
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>111100
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>111000
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>110100
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>111000
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>110000
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>101110
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,1,5,4,2,3,6]=>101100
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,1,5,2,4,3,6]=>101010
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,1,5,3,2,4,6]=>101100
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,1,5,2,3,4,6]=>101000
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>110110
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,1,5,2,3,6]=>110100
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>100110
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,1,2,5,3,4,6]=>100100
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>111010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>110010
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>101010
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>110010
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>100010
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>111100
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>111000
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>110100
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>111000
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>110000
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>101100
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,1,4,2,3,5,6]=>101000
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>110100
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>100100
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>111000
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>110000
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>101000
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>110000
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>100000
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>011111
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[1,7,6,5,4,2,3]=>011110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,7,6,5,2,4,3]=>011101
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[1,7,6,5,3,2,4]=>011110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[1,7,6,5,2,3,4]=>011100
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,7,6,2,5,4,3]=>011011
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[1,7,6,2,5,3,4]=>011010
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,7,6,4,2,5,3]=>011101
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,7,6,2,3,5,4]=>011001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[1,7,6,4,3,2,5]=>011110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[1,7,6,4,2,3,5]=>011100
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,7,6,2,4,3,5]=>011010
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[1,7,6,3,2,4,5]=>011100
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[1,7,6,2,3,4,5]=>011000
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,7,2,6,5,4,3]=>010111
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[1,7,2,6,5,3,4]=>010110
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,7,2,6,3,5,4]=>010101
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[1,7,2,6,4,3,5]=>010110
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[1,7,2,6,3,4,5]=>010100
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,7,5,2,6,4,3]=>011011
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[1,7,5,2,6,3,4]=>011010
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,7,2,3,6,5,4]=>010011
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[1,7,2,3,6,4,5]=>010010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,7,5,4,2,6,3]=>011101
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,7,5,2,3,6,4]=>011001
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,7,2,5,3,6,4]=>010101
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[1,7,4,2,3,6,5]=>011001
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,7,2,3,4,6,5]=>010001
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[1,7,5,4,3,2,6]=>011110
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[1,7,5,4,2,3,6]=>011100
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[1,7,5,2,4,3,6]=>011010
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[1,7,5,3,2,4,6]=>011100
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[1,7,5,2,3,4,6]=>011000
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,7,2,5,4,3,6]=>010110
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[1,7,2,5,3,4,6]=>010100
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[1,7,4,2,5,3,6]=>011010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,7,2,3,5,4,6]=>010010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[1,7,4,3,2,5,6]=>011100
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[1,7,4,2,3,5,6]=>011000
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[1,7,2,4,3,5,6]=>010100
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[1,7,3,2,4,5,6]=>011000
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[1,7,2,3,4,5,6]=>010000
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>101111
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,1,7,5,4,2,3]=>101110
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[6,1,7,5,2,4,3]=>101101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,1,7,5,3,2,4]=>101110
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[6,1,7,5,2,3,4]=>101100
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,1,7,2,5,4,3]=>101011
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,1,7,2,5,3,4]=>101010
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[6,1,7,4,2,5,3]=>101101
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[6,1,7,2,3,5,4]=>101001
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,1,7,4,3,2,5]=>101110
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[6,1,7,4,2,3,5]=>101100
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,1,7,2,4,3,5]=>101010
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[6,1,7,3,2,4,5]=>101100
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[6,1,7,2,3,4,5]=>101000
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>001111
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[1,2,7,6,5,3,4]=>001110
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,7,6,3,5,4]=>001101
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[1,2,7,6,4,3,5]=>001110
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[1,2,7,6,3,4,5]=>001100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,2,7,3,6,5,4]=>001011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[1,2,7,3,6,4,5]=>001010
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,2,7,5,3,6,4]=>001101
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,2,7,3,4,6,5]=>001001
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[1,2,7,5,4,3,6]=>001110
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[1,2,7,5,3,4,6]=>001100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,2,7,3,5,4,6]=>001010
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[1,2,7,4,3,5,6]=>001100
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[1,2,7,3,4,5,6]=>001000
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>110111
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,1,7,4,2,3]=>110110
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[6,5,1,7,2,4,3]=>110101
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,1,7,3,2,4]=>110110
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[6,5,1,7,2,3,4]=>110100
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>100111
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,1,2,7,5,3,4]=>100110
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[6,1,2,7,3,5,4]=>100101
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,1,2,7,4,3,5]=>100110
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[6,1,2,7,3,4,5]=>100100
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>010111
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[1,6,2,7,5,3,4]=>010110
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,6,2,7,3,5,4]=>010101
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[1,6,2,7,4,3,5]=>010110
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[1,6,2,7,3,4,5]=>010100
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>100111
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[5,1,2,7,6,3,4]=>100110
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,1,2,7,3,6,4]=>100101
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[5,1,2,7,4,3,6]=>100110
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,1,2,7,3,4,6]=>100100
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[1,2,3,7,6,4,5]=>000110
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,3,7,4,6,5]=>000101
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[1,2,3,7,5,4,6]=>000110
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[1,2,3,7,4,5,6]=>000100
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>111011
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,5,4,1,7,2,3]=>111010
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>110011
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,5,1,2,7,3,4]=>110010
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>101011
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,1,5,2,7,3,4]=>101010
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>110011
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,4,1,2,7,3,5]=>110010
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>100011
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,1,2,3,7,4,5]=>100010
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>011011
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[1,6,5,2,7,3,4]=>011010
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,6,2,3,7,5,4]=>010011
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[1,6,2,3,7,4,5]=>010010
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>101011
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,1,6,2,7,3,4]=>101010
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>001011
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[1,2,6,3,7,4,5]=>001010
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>110011
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,7,3,6]=>110010
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>100011
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,1,2,3,7,4,6]=>100010
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>010011
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[1,5,2,3,7,4,6]=>010010
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>100011
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[4,1,2,3,7,5,6]=>100010
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>000011
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[1,2,3,4,7,5,6]=>000010
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>111101
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>111001
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>110101
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>111001
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>110001
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>101101
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,5,2,3,7,4]=>101001
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>110101
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>100101
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>111001
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>110001
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>101001
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>110001
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>100001
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>011101
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,6,5,2,3,7,4]=>011001
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,6,2,5,3,7,4]=>010101
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[1,6,4,2,3,7,5]=>011001
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,6,2,3,4,7,5]=>010001
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>101101
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[5,1,6,2,3,7,4]=>101001
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>001101
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,6,3,4,7,5]=>001001
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>110101
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>100101
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>010101
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>100101
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>000101
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>111001
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>110001
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>101001
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>110001
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>100001
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>011001
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[1,5,2,3,4,7,6]=>010001
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>101001
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>001001
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>110001
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>100001
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>010001
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>100001
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>111100
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>111010
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>111100
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>111000
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>110110
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,5,1,4,2,3,7]=>110100
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>111010
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>110010
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>111100
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>111000
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>110100
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>111000
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>110000
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>101110
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,1,5,4,2,3,7]=>101100
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,1,5,2,4,3,7]=>101010
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,1,5,3,2,4,7]=>101100
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,1,5,2,3,4,7]=>101000
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>110110
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,1,5,2,3,7]=>110100
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>100110
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,1,2,5,3,4,7]=>100100
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>111010
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>110010
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>101010
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>110010
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>100010
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>111100
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>111000
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>110100
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>111000
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>110000
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>101100
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,1,4,2,3,5,7]=>101000
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>110100
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>100100
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>111000
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>110000
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>101000
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>110000
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>100000
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>011110
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[1,6,5,4,2,3,7]=>011100
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[1,6,5,2,4,3,7]=>011010
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[1,6,5,3,2,4,7]=>011100
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[1,6,5,2,3,4,7]=>011000
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,6,2,5,4,3,7]=>010110
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>010100
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[1,6,4,2,5,3,7]=>011010
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[1,6,2,3,5,4,7]=>010010
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[1,6,4,3,2,5,7]=>011100
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[1,6,4,2,3,5,7]=>011000
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[1,6,2,4,3,5,7]=>010100
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[1,6,3,2,4,5,7]=>011000
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[1,6,2,3,4,5,7]=>010000
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>101110
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,1,6,4,2,3,7]=>101100
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[5,1,6,2,4,3,7]=>101010
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,1,6,3,2,4,7]=>101100
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[5,1,6,2,3,4,7]=>101000
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>001110
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[1,2,6,5,3,4,7]=>001100
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,6,3,5,4,7]=>001010
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[1,2,6,4,3,5,7]=>001100
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[1,2,6,3,4,5,7]=>001000
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>110110
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,4,1,6,2,3,7]=>110100
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>100110
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,1,2,6,3,4,7]=>100100
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>010110
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[1,5,2,6,3,4,7]=>010100
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>100110
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[4,1,2,6,3,5,7]=>100100
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>000110
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[1,2,3,6,4,5,7]=>000100
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>111010
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>110010
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>101010
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>110010
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>100010
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>011010
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[1,5,2,3,6,4,7]=>010010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>001010
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>110010
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>100010
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>010010
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>100010
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>000010
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>111000
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>110100
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>111000
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>110000
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>101100
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,1,4,2,3,6,7]=>101000
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>110100
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>100100
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>111000
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>110000
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>101000
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>110000
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>100000
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>011100
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[1,5,4,2,3,6,7]=>011000
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[1,5,2,4,3,6,7]=>010100
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[1,5,3,2,4,6,7]=>011000
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[1,5,2,3,4,6,7]=>010000
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>101100
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,1,5,2,3,6,7]=>101000
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>001100
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[1,2,5,3,4,6,7]=>001000
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>110100
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>100100
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>010100
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>100100
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>110000
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>110000
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>100000
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>010000
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>101000
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>1111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>1111101
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>1111110
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>1111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>1111011
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,1,4,2,3]=>1111010
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>1111101
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>1111001
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>1111110
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>1111100
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>1111010
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>1111100
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>1111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[8,7,6,1,5,4,2,3]=>1110110
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[8,7,6,1,5,2,4,3]=>1110101
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[8,7,6,1,5,3,2,4]=>1110110
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[8,7,6,1,5,2,3,4]=>1110100
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>1111011
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>1110011
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>1111101
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,1,2,5,3]=>1111001
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[8,7,6,1,4,2,5,3]=>1110101
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>1110001
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>1111110
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>1111100
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>1111010
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>1111100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>1111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>1110110
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[8,7,6,1,4,2,3,5]=>1110100
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,1,4,2,5]=>1111010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>1110010
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>1111100
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>1111000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>1110100
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>1111000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>1110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,7,1,6,5,4,3,2]=>1101111
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[8,7,1,6,5,2,4,3]=>1101101
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,7,1,6,5,3,2,4]=>1101110
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,7,1,6,2,5,4,3]=>1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,7,1,6,2,5,3,4]=>1101010
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,7,1,6,2,3,5,4]=>1101001
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,7,1,6,4,3,2,5]=>1101110
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[8,7,1,6,4,2,3,5]=>1101100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,7,1,6,2,3,4,5]=>1101000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>1110111
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[8,7,5,1,6,4,2,3]=>1110110
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[8,7,5,1,6,3,2,4]=>1110110
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,7,5,1,6,2,3,4]=>1110100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[8,7,1,2,6,5,4,3]=>1100111
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[8,7,1,2,6,5,3,4]=>1100110
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[8,7,1,2,6,3,4,5]=>1100100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>1111011
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[8,7,5,4,1,6,2,3]=>1111010
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[8,7,5,1,2,6,4,3]=>1110011
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[8,7,1,5,2,6,3,4]=>1101010
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,7,4,1,2,6,5,3]=>1110011
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[8,7,1,2,3,6,5,4]=>1100011
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[8,7,1,2,3,6,4,5]=>1100010
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>1111101
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>1111001
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[8,7,4,1,5,2,6,3]=>1110101
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[8,7,3,1,2,4,6,5]=>1110001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[8,7,1,2,3,4,6,5]=>1100001
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>1111110
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>1111100
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>1111010
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>1111000
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>1110110
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[8,7,5,1,4,2,3,6]=>1110100
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>1111010
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[8,7,5,1,2,4,3,6]=>1110010
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>1111100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>1111000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>1110000
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>1100110
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,1,5,2,6]=>1111010
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[8,7,1,4,2,5,3,6]=>1101010
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>1111100
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>1110000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[8,7,1,4,3,2,5,6]=>1101100
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[8,7,1,2,4,3,5,6]=>1100100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>1111000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[8,7,1,3,2,4,5,6]=>1101000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>1110000
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>1100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,1,7,6,5,4,3,2]=>1011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[8,1,7,6,5,4,2,3]=>1011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[8,1,7,6,5,2,4,3]=>1011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[8,1,7,6,5,3,2,4]=>1011110
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[8,1,7,6,2,5,4,3]=>1011011
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[8,1,7,6,4,2,5,3]=>1011101
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[8,1,7,6,4,3,2,5]=>1011110
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[8,1,7,6,4,2,3,5]=>1011100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[8,1,7,6,2,4,3,5]=>1011010
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,1,7,6,2,3,4,5]=>1011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,1,7,2,6,5,4,3]=>1010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,1,7,2,6,3,5,4]=>1010101
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[8,1,7,2,6,4,3,5]=>1010110
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,1,7,2,6,3,4,5]=>1010100
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[8,1,7,2,3,6,5,4]=>1010011
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[8,1,7,2,3,6,4,5]=>1010010
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,1,7,5,4,2,6,3]=>1011101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[8,1,7,2,5,3,6,4]=>1010101
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[8,1,7,5,4,3,2,6]=>1011110
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[8,1,7,5,2,4,3,6]=>1011010
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,1,7,5,3,2,4,6]=>1011100
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[8,1,7,2,5,4,3,6]=>1010110
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[8,1,7,2,5,3,4,6]=>1010100
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[8,1,7,2,3,4,5,6]=>1010000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,6,1,7,5,4,3,2]=>1101111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[8,6,1,7,5,4,2,3]=>1101110
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[8,6,1,7,5,2,4,3]=>1101101
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[8,6,1,7,5,2,3,4]=>1101100
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[8,6,1,7,2,5,4,3]=>1101011
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[8,6,1,7,4,2,5,3]=>1101101
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[8,6,1,7,2,3,5,4]=>1101001
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,6,1,7,4,3,2,5]=>1101110
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[8,6,1,7,4,2,3,5]=>1101100
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,6,1,7,2,3,4,5]=>1101000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,1,2,7,6,5,4,3]=>1001111
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[8,1,2,7,6,3,5,4]=>1001101
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,1,2,7,6,3,4,5]=>1001100
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[8,1,2,7,3,6,5,4]=>1001011
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[8,1,2,7,3,6,4,5]=>1001010
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[8,1,2,7,3,4,6,5]=>1001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,1,2,7,5,4,3,6]=>1001110
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[8,1,2,7,5,3,4,6]=>1001100
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,1,2,7,3,4,5,6]=>1001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>1110111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[8,6,5,1,7,4,2,3]=>1110110
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[8,6,5,1,7,2,4,3]=>1110101
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[8,6,5,1,7,3,2,4]=>1110110
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,6,1,2,7,5,4,3]=>1100111
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[8,6,1,2,7,5,3,4]=>1100110
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,6,1,2,7,3,5,4]=>1100101
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[8,6,1,2,7,4,3,5]=>1100110
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[8,6,1,2,7,3,4,5]=>1100100
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[8,1,6,2,7,3,5,4]=>1010101
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[8,1,6,2,7,4,3,5]=>1010110
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,1,6,2,7,3,4,5]=>1010100
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[8,5,1,2,7,6,4,3]=>1100111
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[8,5,1,2,7,6,3,4]=>1100110
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[8,5,1,2,7,3,4,6]=>1100100
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[8,1,2,3,7,6,5,4]=>1000111
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[8,1,2,3,7,5,4,6]=>1000110
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[8,1,2,3,7,4,5,6]=>1000100
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,1,7,2,3]=>1111010
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[8,6,1,5,2,7,4,3]=>1101011
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[8,6,4,1,2,7,5,3]=>1110011
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[8,6,4,1,2,7,3,5]=>1110010
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[8,1,6,5,2,7,4,3]=>1011011
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[8,5,4,1,2,7,6,3]=>1110011
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[8,5,4,1,2,7,3,6]=>1110010
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,5,1,2,3,7,4,6]=>1100010
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[8,1,5,2,3,7,4,6]=>1010010
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,4,1,2,3,7,5,6]=>1100010
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[8,1,2,3,4,7,6,5]=>1000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[8,1,2,3,4,7,5,6]=>1000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>1111101
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,1,2,7,3]=>1111001
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>1111001
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,6,4,1,5,2,7,3]=>1110101
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,6,1,2,5,3,7,4]=>1100101
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,6,4,1,2,3,7,5]=>1110001
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[8,6,3,1,2,4,7,5]=>1110001
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[8,6,1,2,3,4,7,5]=>1100001
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,1,6,5,2,3,7,4]=>1011001
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[8,1,6,2,5,3,7,4]=>1010101
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[8,5,1,6,4,2,7,3]=>1101101
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[8,5,4,1,6,2,7,3]=>1110101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[8,1,5,2,6,3,7,4]=>1010101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[8,1,2,3,6,4,7,5]=>1000101
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[8,5,4,1,2,3,7,6]=>1110001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[8,5,1,4,2,3,7,6]=>1101001
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[8,1,2,5,3,4,7,6]=>1001001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[8,4,3,1,2,5,7,6]=>1110001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[8,1,4,2,3,5,7,6]=>1010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[8,3,1,2,4,5,7,6]=>1100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[8,1,2,3,4,5,7,6]=>1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>1111110
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>1111100
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>1111010
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>1111100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>1111000
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>1110110
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>1110010
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>1111100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>1110100
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>1110000
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>1101110
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,6,1,5,2,4,3,7]=>1101010
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,6,1,5,3,2,4,7]=>1101100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[8,6,1,5,2,3,4,7]=>1101000
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>1110110
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>[8,6,1,2,5,4,3,7]=>1100110
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,4,1,2,5,3,7]=>1110010
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[8,6,1,4,2,5,3,7]=>1101010
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[8,6,1,2,3,5,4,7]=>1100010
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>1111100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>1110100
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>1111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>1110000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>1101100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,6,1,4,2,3,5,7]=>1101000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,6,3,1,4,2,5,7]=>1110100
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[8,6,1,2,4,3,5,7]=>1100100
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>1100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,1,6,5,4,3,2,7]=>1011110
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[8,1,6,5,2,3,4,7]=>1011000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,1,6,2,5,3,4,7]=>1010100
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[8,1,6,4,2,5,3,7]=>1011010
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,1,6,2,3,5,4,7]=>1010010
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[8,1,6,4,2,3,5,7]=>1011000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,1,6,2,4,3,5,7]=>1010100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[8,1,6,3,2,4,5,7]=>1011000
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,1,6,2,3,4,5,7]=>1010000
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[8,5,1,6,4,3,2,7]=>1101110
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[8,5,1,6,4,2,3,7]=>1101100
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,5,1,6,3,2,4,7]=>1101100
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,1,2,6,5,4,3,7]=>1001110
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[8,1,2,6,3,4,5,7]=>1001000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,5,4,1,6,2,3,7]=>1110100
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,1,5,2,6,4,3,7]=>1010110
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[8,4,1,2,6,5,3,7]=>1100110
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,4,1,2,6,3,5,7]=>1100100
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[8,1,2,3,6,5,4,7]=>1000110
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[8,1,2,3,6,4,5,7]=>1000100
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[8,1,5,4,2,6,3,7]=>1011010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,4,1,5,2,6,3,7]=>1101010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[8,4,3,1,2,6,5,7]=>1110010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[8,1,4,2,3,6,5,7]=>1010010
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[8,3,1,2,4,6,5,7]=>1100010
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[8,1,2,3,4,6,5,7]=>1000010
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>1111100
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>1111000
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>1110000
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>1100100
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>1111000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>1110000
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>1100000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>1011100
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[8,1,5,4,2,3,6,7]=>1011000
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[8,1,5,3,2,4,6,7]=>1011000
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,1,5,2,3,4,6,7]=>1010000
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[8,4,1,5,3,2,6,7]=>1101100
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>1001100
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[8,1,2,5,3,4,6,7]=>1001000
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[8,1,2,3,5,4,6,7]=>1000100
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>1111000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[8,4,1,3,2,5,6,7]=>1101000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>1110000
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>1100000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>1011000
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>1010000
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>1001000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>1110000
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>1100000
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>1010000
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>1100000
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>1000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[1,8,7,6,5,4,2,3]=>0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[1,8,7,6,5,2,4,3]=>0111101
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[1,8,7,6,5,3,2,4]=>0111110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[1,8,7,6,5,2,3,4]=>0111100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[1,8,7,6,2,5,4,3]=>0111011
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[1,8,7,6,4,2,5,3]=>0111101
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[1,8,7,6,4,3,2,5]=>0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[1,8,7,6,4,2,3,5]=>0111100
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[1,8,7,6,2,4,3,5]=>0111010
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[1,8,7,6,3,2,4,5]=>0111100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[1,8,7,6,2,3,4,5]=>0111000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[1,8,7,2,6,5,4,3]=>0110111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[1,8,7,2,6,5,3,4]=>0110110
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[1,8,7,2,6,3,5,4]=>0110101
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[1,8,7,2,6,3,4,5]=>0110100
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[1,8,7,2,3,6,4,5]=>0110010
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[1,8,7,4,2,3,6,5]=>0111001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[1,8,7,5,4,3,2,6]=>0111110
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[1,8,7,5,3,2,4,6]=>0111100
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[1,8,7,2,5,4,3,6]=>0110110
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[1,8,7,2,5,3,4,6]=>0110100
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[1,8,7,4,3,2,5,6]=>0111100
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[1,8,7,4,2,3,5,6]=>0111000
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[1,8,7,3,2,4,5,6]=>0111000
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[1,8,7,2,3,4,5,6]=>0110000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[1,8,2,7,6,5,4,3]=>0101111
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[1,8,2,7,6,4,3,5]=>0101110
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[1,8,2,7,6,3,4,5]=>0101100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[1,8,2,7,3,6,5,4]=>0101011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[1,8,2,7,3,6,4,5]=>0101010
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[1,8,2,7,5,3,6,4]=>0101101
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[1,8,2,7,3,4,6,5]=>0101001
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[1,8,2,7,5,4,3,6]=>0101110
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[1,8,2,7,5,3,4,6]=>0101100
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[1,8,2,7,3,5,4,6]=>0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[1,8,2,7,4,3,5,6]=>0101100
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[1,8,2,7,3,4,5,6]=>0101000
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[1,8,6,2,7,3,4,5]=>0110100
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[1,8,2,3,7,6,5,4]=>0100111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[1,8,2,3,7,6,4,5]=>0100110
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[1,8,6,5,2,7,3,4]=>0111010
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[1,8,6,2,3,7,4,5]=>0110010
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[1,8,2,6,3,7,4,5]=>0101010
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[1,8,5,2,3,7,6,4]=>0110011
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[1,8,5,2,3,7,4,6]=>0110010
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[1,8,2,3,4,7,6,5]=>0100011
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[1,8,2,3,4,7,5,6]=>0100010
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[1,8,5,4,2,3,7,6]=>0111001
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[1,8,2,5,3,4,7,6]=>0101001
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[1,8,4,2,3,5,7,6]=>0110001
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[1,8,2,3,4,5,7,6]=>0100001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[1,8,6,5,4,3,2,7]=>0111110
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[1,8,6,5,3,2,4,7]=>0111100
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[1,8,6,2,5,3,4,7]=>0110100
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[1,8,6,4,2,3,5,7]=>0111000
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[1,8,6,2,4,3,5,7]=>0110100
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[1,8,6,3,2,4,5,7]=>0111000
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[1,8,6,2,3,4,5,7]=>0110000
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[1,8,2,6,3,5,4,7]=>0101010
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[1,8,2,6,3,4,5,7]=>0101000
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[1,8,2,3,6,5,4,7]=>0100110
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[1,8,5,4,2,6,3,7]=>0111010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[1,8,2,5,3,6,4,7]=>0101010
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[1,8,2,3,4,6,5,7]=>0100010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[1,8,5,4,3,2,6,7]=>0111100
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[1,8,5,4,2,3,6,7]=>0111000
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[1,8,5,3,2,4,6,7]=>0111000
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[1,8,2,5,3,4,6,7]=>0101000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[1,8,4,2,5,3,6,7]=>0110100
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[1,8,2,3,5,4,6,7]=>0100100
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[1,8,4,3,2,5,6,7]=>0111000
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[1,8,4,2,3,5,6,7]=>0110000
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[1,8,2,4,3,5,6,7]=>0101000
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[1,8,3,2,4,5,6,7]=>0110000
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[1,8,2,3,4,5,6,7]=>0100000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,1,8,6,5,4,3,2]=>1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[7,1,8,6,5,4,2,3]=>1011110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[7,1,8,6,5,2,4,3]=>1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,1,8,6,5,3,2,4]=>1011110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[7,1,8,6,5,2,3,4]=>1011100
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[7,1,8,6,2,5,4,3]=>1011011
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[7,1,8,6,2,5,3,4]=>1011010
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[7,1,8,6,4,3,2,5]=>1011110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[7,1,8,6,4,2,3,5]=>1011100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[7,1,8,6,2,4,3,5]=>1011010
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[7,1,8,6,3,2,4,5]=>1011100
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[7,1,8,6,2,3,4,5]=>1011000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[7,1,8,2,6,5,4,3]=>1010111
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[7,1,8,2,6,3,5,4]=>1010101
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[7,1,8,2,6,4,3,5]=>1010110
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[7,1,8,2,3,6,5,4]=>1010011
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[7,1,8,2,5,3,6,4]=>1010101
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[7,1,8,5,4,3,2,6]=>1011110
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[7,1,8,5,4,2,3,6]=>1011100
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[7,1,8,5,3,2,4,6]=>1011100
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[7,1,8,5,2,3,4,6]=>1011000
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[7,1,8,2,5,4,3,6]=>1010110
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[7,1,8,4,2,5,3,6]=>1011010
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[7,1,8,2,3,4,5,6]=>1010000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[1,2,8,7,6,5,3,4]=>0011110
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[1,2,8,7,6,4,3,5]=>0011110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[1,2,8,7,6,3,4,5]=>0011100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[1,2,8,7,5,3,6,4]=>0011101
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[1,2,8,7,3,4,6,5]=>0011001
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[1,2,8,7,5,4,3,6]=>0011110
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[1,2,8,7,3,5,4,6]=>0011010
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[1,2,8,7,3,4,5,6]=>0011000
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[1,2,8,3,7,6,5,4]=>0010111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[1,2,8,3,7,4,6,5]=>0010101
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[1,2,8,3,7,4,5,6]=>0010100
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[1,2,8,6,3,7,5,4]=>0011011
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[1,2,8,6,3,7,4,5]=>0011010
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[1,2,8,3,4,7,6,5]=>0010011
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[1,2,8,6,3,4,7,5]=>0011001
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[1,2,8,3,6,4,7,5]=>0010101
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[1,2,8,3,4,5,7,6]=>0010001
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[1,2,8,6,5,4,3,7]=>0011110
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[1,2,8,6,4,3,5,7]=>0011100
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[1,2,8,6,3,4,5,7]=>0011000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[1,2,8,3,6,5,4,7]=>0010110
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[1,2,8,3,6,4,5,7]=>0010100
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[1,2,8,5,3,6,4,7]=>0011010
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[1,2,8,3,4,6,5,7]=>0010010
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[1,2,8,5,4,3,6,7]=>0011100
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[1,2,8,5,3,4,6,7]=>0011000
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[1,2,8,3,5,4,6,7]=>0010100
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[1,2,8,4,3,5,6,7]=>0011000
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[1,2,8,3,4,5,6,7]=>0010000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,1,8,5,4,3,2]=>1101111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[7,6,1,8,5,4,2,3]=>1101110
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[7,6,1,8,5,3,2,4]=>1101110
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[7,6,1,8,5,2,3,4]=>1101100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[7,6,1,8,2,5,4,3]=>1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,6,1,8,2,5,3,4]=>1101010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[7,6,1,8,4,2,5,3]=>1101101
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[7,6,1,8,2,3,5,4]=>1101001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,1,8,4,3,2,5]=>1101110
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[7,6,1,8,4,2,3,5]=>1101100
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[7,6,1,8,3,2,4,5]=>1101100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[7,6,1,8,2,3,4,5]=>1101000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,1,2,8,6,5,4,3]=>1001111
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[7,1,2,8,6,4,3,5]=>1001110
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[7,1,2,8,3,6,5,4]=>1001011
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,1,2,8,3,6,4,5]=>1001010
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[7,1,2,8,5,3,4,6]=>1001100
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,1,2,8,3,5,4,6]=>1001010
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[7,1,2,8,3,4,5,6]=>1001000
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[1,7,2,8,6,5,3,4]=>0101110
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[1,7,2,8,6,3,5,4]=>0101101
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[1,7,2,8,3,6,5,4]=>0101011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[1,7,2,8,3,6,4,5]=>0101010
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[1,7,2,8,5,3,6,4]=>0101101
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[1,7,2,8,5,4,3,6]=>0101110
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[1,7,2,8,5,3,4,6]=>0101100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[1,7,2,8,3,5,4,6]=>0101010
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[1,7,2,8,4,3,5,6]=>0101100
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[1,7,2,8,3,4,5,6]=>0101000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[6,1,2,8,7,5,3,4]=>1001110
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[6,1,2,8,7,4,3,5]=>1001110
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,1,2,8,7,3,4,5]=>1001100
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[6,1,2,8,3,7,4,5]=>1001010
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[6,1,2,8,5,3,7,4]=>1001101
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[6,1,2,8,3,4,7,5]=>1001001
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[6,1,2,8,5,3,4,7]=>1001100
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[6,1,2,8,3,5,4,7]=>1001010
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,1,2,8,4,3,5,7]=>1001100
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[6,1,2,8,3,4,5,7]=>1001000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>0001111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[1,2,3,8,7,6,4,5]=>0001110
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[1,2,3,8,7,4,6,5]=>0001101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[1,2,3,8,7,5,4,6]=>0001110
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[1,2,3,8,7,4,5,6]=>0001100
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,2,3,8,4,7,6,5]=>0001011
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[1,2,3,8,4,7,5,6]=>0001010
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[1,2,3,8,6,4,7,5]=>0001101
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[1,2,3,8,4,5,7,6]=>0001001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[1,2,3,8,6,5,4,7]=>0001110
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[1,2,3,8,6,4,5,7]=>0001100
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[1,2,3,8,4,6,5,7]=>0001010
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[1,2,3,8,5,4,6,7]=>0001100
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[1,2,3,8,4,5,6,7]=>0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,5,1,8,4,3,2]=>1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[7,6,5,1,8,4,2,3]=>1110110
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[7,6,5,1,8,2,4,3]=>1110101
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[7,6,5,1,8,3,2,4]=>1110110
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[7,6,5,1,8,2,3,4]=>1110100
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,1,2,8,5,4,3]=>1100111
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,1,6,2,8,5,4,3]=>1010111
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[7,1,6,2,8,3,5,4]=>1010101
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[7,1,6,2,8,4,3,5]=>1010110
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[7,1,6,2,8,3,4,5]=>1010100
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,5,1,2,8,6,4,3]=>1100111
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[7,5,1,2,8,3,4,6]=>1100100
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,1,2,3,8,6,5,4]=>1000111
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[7,1,2,3,8,5,4,6]=>1000110
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[7,1,2,3,8,4,5,6]=>1000100
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[1,7,6,2,8,5,4,3]=>0110111
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[1,7,6,2,8,3,4,5]=>0110100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[1,7,2,3,8,6,5,4]=>0100111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[1,7,2,3,8,6,4,5]=>0100110
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[1,7,2,3,8,4,5,6]=>0100100
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[6,1,7,2,8,5,4,3]=>1010111
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[6,1,7,2,8,3,5,4]=>1010101
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,1,7,2,8,3,4,5]=>1010100
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[1,2,7,3,8,6,5,4]=>0010111
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[1,2,7,3,8,6,4,5]=>0010110
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[1,2,7,3,8,5,4,6]=>0010110
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[1,2,7,3,8,4,5,6]=>0010100
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[6,5,1,2,8,7,4,3]=>1100111
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[6,5,1,2,8,7,3,4]=>1100110
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[6,5,1,2,8,3,7,4]=>1100101
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[6,5,1,2,8,4,3,7]=>1100110
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,5,1,2,8,3,4,7]=>1100100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[6,1,2,3,8,7,5,4]=>1000111
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[6,1,2,3,8,7,4,5]=>1000110
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[6,1,2,3,8,4,7,5]=>1000101
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[6,1,2,3,8,5,4,7]=>1000110
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,1,2,3,8,4,5,7]=>1000100
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[1,6,2,3,8,7,4,5]=>0100110
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[1,6,2,3,8,5,4,7]=>0100110
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[1,6,2,3,8,4,5,7]=>0100100
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,1,2,3,8,7,6,4]=>1000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[5,1,2,3,8,7,4,6]=>1000110
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,1,2,3,8,4,7,6]=>1000101
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,1,2,3,8,4,6,7]=>1000100
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[1,2,3,4,8,7,5,6]=>0000110
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[1,2,3,4,8,5,7,6]=>0000101
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[1,2,3,4,8,6,5,7]=>0000110
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[1,2,3,4,8,5,6,7]=>0000100
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,1,8,3,2]=>1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,1,8,2,3]=>1111010
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[7,6,5,1,2,8,4,3]=>1110011
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6]=>[7,6,5,1,2,8,3,4]=>1110010
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[7,6,1,2,3,8,5,4]=>1100011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[7,6,1,2,3,8,4,5]=>1100010
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[7,1,6,2,3,8,5,4]=>1010011
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,1,6,2,3,8,4,5]=>1010010
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[7,5,1,6,2,8,4,3]=>1101011
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[7,1,2,6,3,8,4,5]=>1001010
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[7,5,4,1,2,8,3,6]=>1110010
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[7,5,1,2,3,8,6,4]=>1100011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[7,5,1,2,3,8,4,6]=>1100010
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[7,1,2,3,4,8,6,5]=>1000011
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[7,1,2,3,4,8,5,6]=>1000010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[1,7,6,5,2,8,4,3]=>0111011
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[1,7,6,5,2,8,3,4]=>0111010
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[1,7,2,6,3,8,5,4]=>0101011
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[1,7,2,6,3,8,4,5]=>0101010
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[1,7,2,3,4,8,6,5]=>0100011
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[1,7,2,3,4,8,5,6]=>0100010
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,1,7,5,2,8,3,4]=>1011010
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[1,2,7,6,3,8,5,4]=>0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[1,2,7,6,3,8,4,5]=>0011010
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[1,2,7,3,4,8,6,5]=>0010011
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[1,2,7,3,4,8,5,6]=>0010010
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,5,1,7,2,8,4,3]=>1101011
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[6,5,1,7,2,8,3,4]=>1101010
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,1,2,7,3,8,5,4]=>1001011
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[1,6,2,7,3,8,5,4]=>0101011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[1,6,2,7,3,8,4,5]=>0101010
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[5,1,2,7,3,8,6,4]=>1001011
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[5,1,2,7,3,8,4,6]=>1001010
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[1,2,3,7,4,8,6,5]=>0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[1,2,3,7,4,8,5,6]=>0001010
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,4,1,2,8,3,7]=>1110010
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>1100010
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[6,4,1,2,3,8,7,5]=>1100011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,4,1,2,3,8,5,7]=>1100010
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[6,1,2,3,4,8,7,5]=>1000011
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,1,2,3,4,8,5,7]=>1000010
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[1,6,5,2,3,8,4,7]=>0110010
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[1,6,2,3,4,8,7,5]=>0100011
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[1,6,2,3,4,8,5,7]=>0100010
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[5,1,6,2,3,8,4,7]=>1010010
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[1,2,6,3,4,8,7,5]=>0010011
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[1,2,6,3,4,8,5,7]=>0010010
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[5,4,1,2,3,8,7,6]=>1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[5,4,1,2,3,8,6,7]=>1100010
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[5,1,2,3,4,8,7,6]=>1000011
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[5,1,2,3,4,8,6,7]=>1000010
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[1,5,2,3,4,8,6,7]=>0100010
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[4,1,2,3,5,8,7,6]=>1000011
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[4,1,2,3,5,8,6,7]=>1000010
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,8,6,7]=>0000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,1,8,2]=>1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,1,2,8,3]=>1111001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,6,5,1,4,2,8,3]=>1110101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,1,2,8,4]=>1111001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,6,5,1,2,3,8,4]=>1110001
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,6,1,5,4,2,8,3]=>1101101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[7,6,1,5,2,3,8,4]=>1101001
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,6,4,1,5,2,8,3]=>1110101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,6,4,1,2,3,8,5]=>1110001
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,6,3,1,2,4,8,5]=>1110001
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,6,1,2,3,4,8,5]=>1100001
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,1,6,5,2,3,8,4]=>1011001
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,6,2,5,3,8,4]=>1010101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,2,6,5,3,8,4]=>1001101
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[7,1,2,6,3,4,8,5]=>1001001
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[7,5,4,1,6,2,8,3]=>1110101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,2,6,3,8,4]=>1010101
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,4,1,2,6,3,8,5]=>1100101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,5,3,1,2,4,8,6]=>1110001
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,1,5,2,3,4,8,6]=>1010001
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,4,1,5,2,3,8,6]=>1101001
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[7,1,2,5,3,4,8,6]=>1001001
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,4,1,2,3,5,8,6]=>1100001
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,3,1,2,4,5,8,6]=>1100001
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,1,2,3,4,5,8,6]=>1000001
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[1,7,6,5,4,2,8,3]=>0111101
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[1,7,6,2,5,3,8,4]=>0110101
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[1,7,2,6,3,4,8,5]=>0101001
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[1,7,2,3,6,4,8,5]=>0100101
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[1,7,5,2,3,4,8,6]=>0110001
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[1,7,2,5,3,4,8,6]=>0101001
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[1,7,4,2,3,5,8,6]=>0110001
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[1,7,2,3,4,5,8,6]=>0100001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[6,1,7,5,4,2,8,3]=>1011101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[6,1,7,2,5,3,8,4]=>1010101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>[6,1,7,2,3,4,8,5]=>1010001
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[1,2,7,6,5,3,8,4]=>0011101
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[1,2,7,6,3,4,8,5]=>0011001
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[1,2,7,3,6,4,8,5]=>0010101
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[1,2,7,3,4,5,8,6]=>0010001
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[6,5,1,7,4,2,8,3]=>1101101
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[6,5,1,7,2,3,8,4]=>1101001
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,1,2,7,5,3,8,4]=>1001101
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[6,1,2,7,3,4,8,5]=>1001001
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[1,6,2,7,3,4,8,5]=>0101001
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,1,2,7,3,4,8,6]=>1001001
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[1,2,3,7,6,4,8,5]=>0001101
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[1,2,3,7,4,5,8,6]=>0001001
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,5,4,1,7,2,8,3]=>1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,5,1,2,7,3,8,4]=>1100101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[6,1,5,2,7,3,8,4]=>1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[6,4,1,2,7,3,8,5]=>1100101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[6,1,2,3,7,4,8,5]=>1000101
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[1,6,5,2,7,3,8,4]=>0110101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[1,6,2,3,7,4,8,5]=>0100101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[1,2,6,3,7,4,8,5]=>0010101
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[5,4,1,2,7,3,8,6]=>1100101
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,7,5,8,6]=>0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,1,2,8,7]=>1111001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[6,5,1,2,3,4,8,7]=>1100001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[6,1,5,2,3,4,8,7]=>1010001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[6,1,4,2,3,5,8,7]=>1010001
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[6,1,2,3,4,5,8,7]=>1000001
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[1,6,2,5,3,4,8,7]=>0101001
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[1,6,2,3,4,5,8,7]=>0100001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[5,1,6,4,2,3,8,7]=>1011001
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[1,2,6,3,4,5,8,7]=>0010001
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[5,4,1,6,2,3,8,7]=>1101001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[1,5,2,6,3,4,8,7]=>0101001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[4,1,2,6,3,5,8,7]=>1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[1,2,3,6,4,5,8,7]=>0001001
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[5,1,2,3,4,6,8,7]=>1000001
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[1,5,2,3,4,6,8,7]=>0100001
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[1,2,5,3,4,6,8,7]=>0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,3,1,2,5,6,8,7]=>1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[4,1,2,3,5,6,8,7]=>1000001
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[1,4,2,3,5,6,8,7]=>0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[3,1,2,4,5,6,8,7]=>1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>1111100
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,1,3,2,8]=>1111010
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>1111100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>1111000
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>1110110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[7,6,5,1,4,2,3,8]=>1110100
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,1,4,2,8]=>1111010
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>1110010
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>1111100
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>1111000
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>1110000
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,6,1,5,2,4,3,8]=>1101010
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[7,6,4,1,5,2,3,8]=>1110100
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>1100110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,1,5,2,8]=>1111010
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,6,4,1,2,5,3,8]=>1110010
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[7,6,1,2,3,5,4,8]=>1100010
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>1111100
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>1111000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>1111000
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>1111000
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>1100000
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[7,1,6,5,4,3,2,8]=>1011110
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[7,1,6,5,4,2,3,8]=>1011100
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,1,6,5,2,4,3,8]=>1011010
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,1,6,2,5,4,3,8]=>1010110
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,1,6,2,5,3,4,8]=>1010100
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,2,3,1,8]=>[7,1,6,4,2,5,3,8]=>1011010
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,1,6,4,2,3,5,8]=>1011000
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[7,1,6,2,3,4,5,8]=>1010000
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[7,5,1,6,4,3,2,8]=>1101110
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[7,5,1,6,3,2,4,8]=>1101100
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,1,2,6,5,4,3,8]=>1001110
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[7,1,2,6,5,3,4,8]=>1001100
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,1,2,6,3,5,4,8]=>1001010
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[7,1,2,6,4,3,5,8]=>1001100
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,1,2,6,3,4,5,8]=>1001000
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[7,5,4,1,6,3,2,8]=>1110110
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[7,5,4,1,6,2,3,8]=>1110100
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,1,5,2,6,4,3,8]=>1010110
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[7,1,5,2,6,3,4,8]=>1010100
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[7,4,1,2,6,5,3,8]=>1100110
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>1000110
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[7,1,2,3,6,4,5,8]=>1000100
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[7,5,1,4,2,6,3,8]=>1101010
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[7,5,3,1,2,6,4,8]=>1110010
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[7,1,5,4,2,6,3,8]=>1011010
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,1,5,2,3,6,4,8]=>1010010
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[7,4,1,5,2,6,3,8]=>1101010
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[7,1,2,3,4,6,5,8]=>1000010
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>1111100
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[7,5,4,3,1,2,6,8]=>1111000
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,5,1,4,2,3,6,8]=>1101000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,1,2,4,3,6,8]=>1100100
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>1111000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>1110000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[7,5,1,3,2,4,6,8]=>1101000
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>1100000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>1011000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,4,1,5,3,2,6,8]=>1101100
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,1,4,2,5,3,6,8]=>1010100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>1100100
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>1000100
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>1111000
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>1100000
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>1011000
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[7,1,4,2,3,5,6,8]=>1010000
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>1001000
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>1110000
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>1100000
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>1010000
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>1100000
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>1000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8]=>0111110
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[1,7,6,5,4,2,3,8]=>0111100
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[1,7,6,5,2,4,3,8]=>0111010
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[1,7,6,3,2,4,5,8]=>0111000
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[1,7,6,2,3,4,5,8]=>0110000
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[1,7,2,6,5,4,3,8]=>0101110
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[1,7,2,6,3,5,4,8]=>0101010
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[1,7,2,6,4,3,5,8]=>0101100
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[1,7,2,3,6,4,5,8]=>0100100
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[1,7,2,5,3,6,4,8]=>0101010
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[1,7,5,4,3,2,6,8]=>0111100
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[1,7,2,5,3,4,6,8]=>0101000
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[1,7,4,2,5,3,6,8]=>0110100
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[1,7,2,3,5,4,6,8]=>0100100
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[4,3,5,6,7,1,2,8]=>[1,7,3,2,4,5,6,8]=>0110000
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[1,7,2,3,4,5,6,8]=>0100000
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[6,1,7,5,3,2,4,8]=>1011100
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[6,1,7,4,2,5,3,8]=>1011010
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[6,1,7,3,2,4,5,8]=>1011000
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[6,1,7,2,3,4,5,8]=>1010000
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[1,2,7,6,5,4,3,8]=>0011110
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[1,2,7,6,3,4,5,8]=>0011000
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[1,2,7,5,3,6,4,8]=>0011010
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[1,2,7,3,4,6,5,8]=>0010010
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[1,2,7,5,3,4,6,8]=>0011000
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[1,2,7,4,3,5,6,8]=>0011000
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[1,2,7,3,4,5,6,8]=>0010000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[6,5,1,7,4,3,2,8]=>1101110
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[6,1,2,7,5,4,3,8]=>1001110
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[6,1,2,7,3,4,5,8]=>1001000
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[1,6,2,7,3,5,4,8]=>0101010
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[1,6,2,7,3,4,5,8]=>0101000
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[5,1,2,7,6,3,4,8]=>1001100
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[5,1,2,7,3,6,4,8]=>1001010
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[5,1,2,7,3,4,6,8]=>1001000
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,6,5,4,8]=>0001110
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[1,2,3,7,6,4,5,8]=>0001100
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[1,2,3,7,4,6,5,8]=>0001010
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[1,2,3,7,5,4,6,8]=>0001100
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[1,2,3,7,4,5,6,8]=>0001000
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[6,5,4,1,7,2,3,8]=>1110100
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[6,1,5,2,7,3,4,8]=>1010100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[6,4,1,2,7,3,5,8]=>1100100
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[6,1,2,3,7,5,4,8]=>1000110
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[6,1,2,3,7,4,5,8]=>1000100
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[1,6,5,2,7,4,3,8]=>0110110
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[1,6,2,3,7,4,5,8]=>0100100
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[5,1,6,2,7,4,3,8]=>1010110
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[5,4,1,2,7,6,3,8]=>1100110
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[5,1,2,3,7,6,4,8]=>1000110
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[1,5,2,3,7,4,6,8]=>0100100
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,6,5,8]=>0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[1,2,3,4,7,5,6,8]=>0000100
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[6,5,3,1,2,7,4,8]=>1110010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[6,1,5,4,2,7,3,8]=>1011010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[6,4,1,5,2,7,3,8]=>1101010
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[6,1,2,3,4,7,5,8]=>1000010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[1,6,2,5,3,7,4,8]=>0101010
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[5,1,6,2,3,7,4,8]=>1010010
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[1,2,6,3,4,7,5,8]=>0010010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[5,4,1,6,2,7,3,8]=>1101010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[5,1,2,6,3,7,4,8]=>1001010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[1,5,2,6,3,7,4,8]=>0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[1,2,3,6,4,7,5,8]=>0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[5,4,3,1,2,7,6,8]=>1110010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[1,5,4,2,3,7,6,8]=>0110010
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[1,5,2,3,4,7,6,8]=>0100010
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[1,2,5,3,4,7,6,8]=>0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[4,3,1,2,5,7,6,8]=>1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[4,1,2,3,5,7,6,8]=>1000010
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[1,4,2,3,5,7,6,8]=>0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[3,1,2,4,5,7,6,8]=>1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>1111000
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>1111000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>1110000
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>1101100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>1111000
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[6,4,1,5,2,3,7,8]=>1101000
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[6,1,2,5,3,4,7,8]=>1001000
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[6,4,3,1,5,2,7,8]=>1110100
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>1000100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>1111000
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>1110000
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>1110000
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>1100000
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[6,1,2,4,3,5,7,8]=>1001000
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>1110000
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[6,2,1,3,4,5,7,8]=>1100000
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>1000000
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[1,6,5,4,3,2,7,8]=>0111100
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[1,6,5,3,2,4,7,8]=>0111000
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[1,6,2,5,3,4,7,8]=>0101000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>[1,6,4,2,5,3,7,8]=>0110100
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[1,6,4,3,2,5,7,8]=>0111000
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[1,6,2,3,4,5,7,8]=>0100000
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[5,1,6,4,3,2,7,8]=>1011100
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,1,6,4,2,3,7,8]=>1011000
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[5,1,6,2,4,3,7,8]=>1010100
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,1,6,3,2,4,7,8]=>1011000
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[4,5,6,2,1,3,7,8]=>[5,1,6,2,3,4,7,8]=>1010000
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[1,2,6,3,4,5,7,8]=>0010000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[5,4,1,6,3,2,7,8]=>1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,4,1,6,2,3,7,8]=>1101000
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[1,2,3,6,4,5,7,8]=>0001000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[5,4,3,1,6,2,7,8]=>1110100
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[1,5,4,2,6,3,7,8]=>0110100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[1,2,5,3,6,4,7,8]=>0010100
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[4,3,1,2,6,5,7,8]=>1100100
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[4,1,2,3,6,5,7,8]=>1000100
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[1,4,2,3,6,5,7,8]=>0100100
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>1110000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>1101000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>1110000
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>1100000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>1010000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>1101000
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>1110000
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>1100000
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>1010000
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>1100000
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>0101000
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>0100000
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>0010000
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>1001000
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[1,4,2,5,3,6,7,8]=>0101000
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1100000
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1100000
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0100000
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>11111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>11111100
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>11111000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>11100000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>11000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>111111110
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>11111101
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>111111100
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>111111000
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>111110000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>111100000
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[9,8,1,7,2,3,4,5,6]=>11010000
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>111000000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[9,1,8,2,3,4,5,6,7]=>10100000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>110000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[1,9,2,3,4,5,6,7,8]=>01000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>11111110
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>11111110
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>11111110
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>11111110
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>11111110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>11111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>111111110
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>111111110
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>111111110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>111111110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>111111110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>111111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9]=>01111110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>111100000
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[3,1,2,4,5,6,7,9,8]=>10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>11000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>10100000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>11000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>110000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,7,8]=>00000010
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,7,8]=>00000100
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,9,5,6,7,8]=>00001000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[1,2,3,9,4,5,6,7,8]=>00010000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[1,2,9,3,4,5,6,7,8]=>00100000
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,8,9]=>000000010
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,7,6,8]=>00000110
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,7,8,9]=>000000100
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[7,6,8,9,1,2,3,4,5]=>[1,2,3,4,9,6,5,7,8]=>00001100
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,8,9]=>000001000
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[6,5,7,8,9,1,2,3,4]=>[1,2,3,9,5,4,6,7,8]=>00011000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,8,9]=>000010000
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[5,4,6,7,8,9,1,2,3]=>[1,2,9,4,3,5,6,7,8]=>00110000
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[1,2,3,10,4,5,6,7,8,9]=>000100000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>[1,9,3,2,4,5,6,7,8]=>01100000
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[1,2,10,3,4,5,6,7,8,9]=>001000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>11111100
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,2,3]=>01111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>111111100
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>11111100
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[1,9,8,7,6,5,3,2,4]=>01111110
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[1,9,8,7,6,5,2,4,3]=>01111101
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,2,3]=>011111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>111110000
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>11111100000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[8,1,9,7,6,5,4,3,2]=>10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[8,7,1,9,6,5,4,3,2]=>11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,1,9,5,4,3,2]=>11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,1,9,4,3,2]=>11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,1,9,3,2]=>11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,1,9,2]=>11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1,10,8,7,6,5,4,3,2]=>101111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[8,1,2,9,7,6,5,4,3]=>10011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,1,10,7,6,5,4,3,2]=>110111111
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,3,4,2,1,5]=>[8,7,1,2,9,6,5,4,3]=>11001111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,1,10,3,2]=>111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>111111101
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>11110111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>11101111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,3,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>11011111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[9,1,8,7,6,5,4,3,2]=>10111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,3,2]=>111111101
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>111110111
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>111101111
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>101111111
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[10,1,9,2,8,3,7,4,6,5]=>101010101
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[9,1,2,3,4,5,6,8,7]=>10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,1,2,3,4,5,7,6,8]=>10000010
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,6,7]=>10000010
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>11000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>10000000
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>10000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>000000010
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[1,9,2,3,4,5,6,8,7]=>01000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,1,8,2]=>11111101
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>11111000
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>001111111
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[7,8,2,3,4,5,6,9,1]=>[9,1,2,3,4,7,5,6,8]=>10000100
[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]=>[4,5,6,3,7,8,9,2,1]=>[9,8,4,1,2,3,5,6,7]=>11100000
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[6,2,3,4,5,7,8,9,10,1]=>[10,1,2,3,5,4,6,7,8,9]=>100010000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[8,1,9,2,3,4,5,6,7]=>10100000
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[1,8,2,3,4,5,6,7,9]=>01000000
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>11111000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>1111111110
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,8,6,9,7]=>00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>000000111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>000011111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>000111111
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[9,8,10,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,3,2,4]=>011111110
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>11111100
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,1,2,9]=>111111100
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>11111100
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>11100000
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>11000000
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[1,9,7,6,5,4,3,2,8]=>01111110
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[8,1,2,3,4,5,6,9,7]=>10000001
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>01000000
[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[9,3,4,5,6,7,2,1,8]=>[8,7,1,2,3,4,5,9,6]=>11000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,11,9,10]=>0000000010
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,7,6]=>10000011
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>[10,1,2,3,4,5,6,9,8,7]=>100000011
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[9,2,3,4,5,6,1,7,8]=>[7,1,2,3,4,5,6,9,8]=>10000001
[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[9,8,2,3,4,5,6,1,7]=>[8,1,2,3,4,5,9,7,6]=>10000011
[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[3,4,5,2,1,6,7,8,9]=>[5,4,1,2,3,6,7,8,9]=>11000000
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[9,8,7,6,5,2,1,3,4]=>11111100
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the 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 maximal element of the Sylvester class.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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