Identifier
Mp00017:
Binary trees
—to 312-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
[[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>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
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>101
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>110
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>100
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[3,4,2,1]=>011
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,1,3]=>010
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,2,4,1]=>101
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[2,3,4,1]=>001
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>110
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>100
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,3,1,4]=>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
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,4,2,3,1]=>1101
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>1110
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>1100
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,3,4,2,1]=>1011
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,4,1,3]=>1010
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>1101
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>1001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>1110
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>1100
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,3,1,4]=>1010
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>1100
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>1000
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[4,5,3,2,1]=>0111
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[3,5,4,1,2]=>0110
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,5,2,4,1]=>0101
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[3,5,2,1,4]=>0110
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,1,3,4]=>0100
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[4,3,5,2,1]=>1011
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2,5,1,4]=>1010
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>0011
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[2,3,5,1,4]=>0010
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,3,2,5,1]=>1101
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,2,3,5,1]=>1001
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[3,4,2,5,1]=>0101
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[3,2,4,5,1]=>1001
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[2,3,4,5,1]=>0001
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>1100
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>1010
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>1100
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>1000
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[3,4,2,1,5]=>0110
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[2,4,1,3,5]=>0100
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[3,2,4,1,5]=>1010
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[2,3,4,1,5]=>0010
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>1000
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,3,1,4,5]=>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
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>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
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>11011
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>11010
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>11101
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>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
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>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
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>10111
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>10110
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>10101
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>10110
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>10100
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>11011
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>11010
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>10011
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>10010
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>11101
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>11001
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>10101
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>11001
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>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
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>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
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>10110
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>10100
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>11010
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>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
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>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
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>01111
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>01110
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>01101
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>01110
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>01100
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>01011
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>01010
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>01101
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>01001
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>01110
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>01100
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>01010
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>01100
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>01000
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>10111
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>10110
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>10101
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>10110
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>10100
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>00111
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>00110
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>00101
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>00110
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>00100
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>11011
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>11010
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>10011
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>10010
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>01011
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>01010
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>10011
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>10010
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>00011
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>00010
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>11101
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>11001
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>10101
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>11001
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>10001
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>01101
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>01001
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>10101
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>00101
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>11001
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>10001
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>01001
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>10001
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>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
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>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
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>10110
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>10100
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>11010
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>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
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>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
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>01110
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>01100
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>01010
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>01100
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>01000
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>10110
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>10100
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>00110
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>00100
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>11010
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>10010
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>01010
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>10010
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>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
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>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
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>01100
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>01000
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>10100
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>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
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>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
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>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
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>111011
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>111010
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>111101
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>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
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>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
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>110111
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>110110
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>110101
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>110110
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>111011
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>111010
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>110011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>110010
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>111101
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>111001
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>110101
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>111001
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>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
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>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
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>110110
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>110100
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>111010
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>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
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>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
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>101111
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>101110
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>101101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>101110
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,3,6,5,1,2,4]=>101100
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>101011
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>101010
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>101101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>101001
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>101110
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>101100
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>101010
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>101100
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>101000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>110111
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>110110
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>110101
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>110110
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,3,2,6,1,4,5]=>110100
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>100111
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,3,4,6,5,1,2]=>100110
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,3,4,6,2,5,1]=>100101
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,3,4,6,2,1,5]=>100110
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,2,3,6,1,4,5]=>100100
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>111011
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>111010
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>110011
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>110010
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>101011
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,3,4,2,6,1,5]=>101010
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>110011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,3,2,4,6,1,5]=>110010
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>100011
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>100010
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>111101
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>111001
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>110101
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>111001
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>110001
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>101101
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,3,5,2,4,6,1]=>101001
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>110101
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>100101
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>111001
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>110001
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>101001
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>110001
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>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
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>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
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,5,3,4,2,1,6]=>110110
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>110100
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>111010
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>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
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>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
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>101110
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,3,5,4,1,2,6]=>101100
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,3,5,2,4,1,6]=>101010
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,3,5,2,1,4,6]=>101100
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,5,1,3,4,6]=>101000
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>110110
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,5,1,4,6]=>110100
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>100110
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,4,6]=>100100
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>111010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,2,3,5,1,6]=>110010
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>101010
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>110010
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,5,1,6]=>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
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>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
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>101100
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>101000
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>110100
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>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
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>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
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>011111
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[5,7,6,4,3,1,2]=>011110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[5,7,6,4,2,3,1]=>011101
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[5,7,6,4,2,1,3]=>011110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[4,7,6,5,1,2,3]=>011100
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>011011
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>011010
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>011101
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>011001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>011110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>011100
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>011010
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>011100
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>011000
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>010111
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>010110
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>010101
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>010110
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>010100
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>011011
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>011010
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>010011
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>010010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>011101
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>011001
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>010101
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>011001
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>010001
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>011110
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>011100
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>011010
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>011100
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>011000
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>010110
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>010100
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>011010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>010010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>011100
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>011000
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>010100
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>011000
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>010000
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>101111
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>101110
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>101101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>101110
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>101100
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>101011
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>101010
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>101101
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>101001
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>101110
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>101100
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>101010
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>101100
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>101000
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>001111
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>001110
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>001101
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>001110
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>001100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>001011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>001010
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>001101
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>001001
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>001110
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>001100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>001010
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>001100
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>001000
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>110111
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>110110
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>110101
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>110110
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>110100
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>100111
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>100110
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>100101
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>100110
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>100100
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>010111
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>010110
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>010101
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>010110
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>010100
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>100111
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>100110
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>100101
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>100110
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>100100
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>000111
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>000110
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>000101
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>000110
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>000100
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>111011
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>111010
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>110011
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>110010
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>101011
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>101010
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>110011
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>110010
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>100011
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>100010
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>011011
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>011010
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>010011
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>010010
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>101011
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>101010
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>001011
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>001010
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>110011
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>110010
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>100011
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>100010
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>010011
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>010010
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>100011
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>100010
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>000011
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>000010
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,7,1]=>111101
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,7,1]=>111001
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,5,3,4,2,7,1]=>110101
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,7,1]=>111001
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,7,1]=>110001
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>101101
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,3,5,2,4,7,1]=>101001
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>110101
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,3,4,5,2,7,1]=>100101
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>111001
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,7,1]=>110001
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>101001
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>110001
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>100001
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>011101
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[4,6,5,2,3,7,1]=>011001
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>010101
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>011001
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>010001
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>101101
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>101001
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>001101
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>001001
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>110101
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>100101
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>010101
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>100101
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>000101
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,7,1]=>111001
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,7,1]=>110001
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[5,3,4,2,6,7,1]=>101001
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>110001
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>100001
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>011001
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>010001
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>101001
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>001001
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,7,1]=>110001
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>100001
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>010001
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,7,1]=>100001
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,7,1]=>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
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>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
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>110110
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>110100
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>111010
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>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
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>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
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>101110
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>101100
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>101010
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>101100
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>101000
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>110110
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>110100
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>100110
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>100100
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>111010
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>110010
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>101010
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>110010
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>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
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>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
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>101100
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>101000
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>110100
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>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
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>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
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>011110
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>011100
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>011010
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>011100
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>011000
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>010110
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>010100
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>011010
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>010010
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>011100
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>011000
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>010100
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>011000
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>010000
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>101110
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>101100
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>101010
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>101100
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>101000
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>001110
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>001100
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>001010
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>001100
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>001000
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>110110
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>110100
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>100110
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>100100
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>010110
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>010100
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>100110
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>100100
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>000110
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>000100
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>111010
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>110010
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>101010
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>110010
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>100010
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>011010
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>010010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>001010
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>110010
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>100010
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>010010
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>100010
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>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
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>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
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>101100
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>101000
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>110100
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>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
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>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
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>011100
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>011000
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>010100
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>011000
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>010000
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>101100
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>101000
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>001100
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>001000
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>110100
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>100100
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>010100
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>100100
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>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
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>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
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>011000
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>010000
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>101000
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>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
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>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
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>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
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>1111011
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>1111010
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>1111101
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>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
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>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
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[8,7,6,3,5,4,1,2]=>1110110
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,7,6,3,5,2,4,1]=>1110101
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>1110110
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[8,7,6,2,5,1,3,4]=>1110100
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>1111010
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>1110011
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>1111101
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[8,7,6,4,2,3,5,1]=>1111001
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>1110101
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>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
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>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
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>1110110
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[8,7,6,2,4,1,3,5]=>1110100
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>1111010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>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
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>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
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[8,7,5,6,4,3,2,1]=>1101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[8,7,4,6,5,3,1,2]=>1101110
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[8,7,4,6,5,2,3,1]=>1101101
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[8,7,4,6,5,2,1,3]=>1101110
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>1101010
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>1101110
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[8,7,3,6,4,1,2,5]=>1101100
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[3,5,7,6,8,4,2,1]=>[8,7,3,6,2,4,1,5]=>1101010
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[8,7,2,6,1,3,4,5]=>1101000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[8,7,5,4,6,3,2,1]=>1110111
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[8,7,4,3,6,5,1,2]=>1110110
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[8,7,3,2,6,1,4,5]=>1110100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,4,5,6,3,2,1]=>1100111
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[8,7,2,3,6,1,4,5]=>1100100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[8,7,5,4,3,6,2,1]=>1111011
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>1111010
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[8,7,4,2,3,6,1,5]=>1110010
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[8,7,3,2,4,6,1,5]=>1110010
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[8,7,3,4,5,6,2,1]=>1100011
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[8,7,2,3,4,6,1,5]=>1100010
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[8,7,5,4,3,2,6,1]=>1111101
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,7,4,3,5,2,6,1]=>1110101
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[8,7,4,3,2,5,6,1]=>1111001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[3,4,5,6,8,7,2,1]=>[8,7,2,3,4,5,6,1]=>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
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>1111000
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>1110110
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>1111010
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[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
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[8,7,4,5,3,2,1,6]=>1101110
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[8,7,3,5,2,4,1,6]=>1101010
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[8,7,2,5,1,3,4,6]=>1101000
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>1100110
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[3,4,6,7,5,8,2,1]=>[8,7,2,3,5,1,4,6]=>1100100
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[8,7,3,4,2,5,1,6]=>1101010
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[8,7,2,3,4,5,1,6]=>1100010
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[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
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[3,6,5,4,7,8,2,1]=>[8,7,3,4,2,1,5,6]=>1101100
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>[8,7,2,4,1,3,5,6]=>1101000
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>[8,7,3,2,4,1,5,6]=>1110100
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[8,7,2,3,4,1,5,6]=>1100100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>1111000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[3,5,4,6,7,8,2,1]=>[8,7,2,3,1,4,5,6]=>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
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,6,7,5,4,3,2,1]=>1011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[8,5,7,6,4,3,1,2]=>1011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,5,7,6,4,2,3,1]=>1011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[8,5,7,6,4,2,1,3]=>1011110
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[8,4,7,6,5,1,2,3]=>1011100
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[8,4,7,6,3,1,2,5]=>1011100
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[2,6,5,7,8,4,3,1]=>[8,4,7,6,2,1,3,5]=>1011100
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[8,3,7,6,1,2,4,5]=>1011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[8,5,7,4,6,3,2,1]=>1010111
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[8,4,7,3,6,5,1,2]=>1010110
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>1010101
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[8,3,7,2,6,1,4,5]=>1010100
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>[8,5,7,4,3,6,2,1]=>1011011
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[2,5,4,7,8,6,3,1]=>[8,4,7,3,2,6,1,5]=>1011010
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[8,3,7,2,4,6,1,5]=>1010010
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>[8,5,7,4,3,2,6,1]=>1011101
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[8,4,7,5,2,3,6,1]=>1011001
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[8,4,7,3,5,2,6,1]=>1010101
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[2,4,5,6,8,7,3,1]=>[8,3,7,2,4,5,6,1]=>1010001
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[8,5,7,4,3,2,1,6]=>1011110
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[2,5,6,7,4,8,3,1]=>[8,3,7,5,1,2,4,6]=>1011000
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[8,4,7,3,5,2,1,6]=>1010110
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>[8,3,7,2,5,1,4,6]=>1010100
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[2,5,4,7,6,8,3,1]=>[8,4,7,3,2,5,1,6]=>1011010
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[8,4,7,3,2,1,5,6]=>1011100
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[8,3,7,4,1,2,5,6]=>1011000
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>[8,3,7,2,4,1,5,6]=>1010100
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,6,5,7,4,3,2,1]=>1101111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[3,2,7,8,6,5,4,1]=>[8,5,4,7,6,3,1,2]=>1101110
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[3,2,5,7,8,6,4,1]=>[8,4,3,7,2,6,1,5]=>1101010
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[8,4,3,7,5,1,2,6]=>1101100
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[8,3,2,7,1,4,5,6]=>1101000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,5,6,7,4,3,2,1]=>1001111
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[8,3,4,7,6,1,2,5]=>1001100
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>[8,4,5,7,3,6,2,1]=>1001011
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[8,3,4,7,2,6,1,5]=>1001010
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[8,4,5,7,3,2,6,1]=>1001101
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,3,4,7,2,5,6,1]=>1001001
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[8,2,3,7,1,4,5,6]=>1001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,6,5,4,7,3,2,1]=>1110111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[8,5,4,3,7,6,1,2]=>1110110
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[8,5,4,3,7,2,6,1]=>1110101
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,6,4,5,7,3,2,1]=>1100111
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[8,5,6,4,7,3,2,1]=>1010111
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,4,5,3,7,2,6,1]=>1010101
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[8,5,4,6,7,3,2,1]=>1100111
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,4,5,6,7,3,2,1]=>1000111
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[8,3,4,5,7,6,1,2]=>1000110
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[2,3,4,7,6,8,5,1]=>[8,3,4,5,7,2,1,6]=>1000110
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[8,2,3,4,7,1,5,6]=>1000100
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[8,6,5,4,3,7,2,1]=>1111011
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[8,5,4,3,2,7,1,6]=>1111010
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[3,5,4,2,7,8,6,1]=>[8,5,3,4,2,7,1,6]=>1101010
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[8,6,4,3,5,7,2,1]=>1110011
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[8,3,5,2,4,7,1,6]=>1010010
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[8,3,4,5,2,7,1,6]=>1001010
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[8,5,4,3,6,7,2,1]=>1110011
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[4,3,2,5,7,8,6,1]=>[8,4,3,2,5,7,1,6]=>1110010
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[3,4,2,5,8,7,6,1]=>[8,5,3,4,6,7,2,1]=>1100011
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[8,4,2,3,5,7,1,6]=>1100010
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[3,2,4,5,7,8,6,1]=>[8,3,2,4,5,7,1,6]=>1100010
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[8,3,4,5,6,7,2,1]=>1000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[8,2,3,4,5,7,1,6]=>1000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[8,6,5,4,3,2,7,1]=>1111101
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[8,6,5,3,4,2,7,1]=>1110101
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[8,6,5,3,2,4,7,1]=>1111001
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[8,6,4,5,3,2,7,1]=>1101101
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,6,4,3,5,2,7,1]=>1110101
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[8,6,4,3,2,5,7,1]=>1111001
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[8,6,4,2,3,5,7,1]=>1110001
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[3,4,5,6,2,8,7,1]=>[8,6,2,3,4,5,7,1]=>1100001
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[8,5,6,4,3,2,7,1]=>1011101
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[8,4,6,3,5,2,7,1]=>1010101
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>[8,3,6,2,4,5,7,1]=>1010001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[8,5,4,6,3,2,7,1]=>1101101
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[8,5,4,3,6,2,7,1]=>1110101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,4,5,3,6,2,7,1]=>1010101
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>[8,4,3,5,6,2,7,1]=>1100101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[8,3,4,5,6,2,7,1]=>1000101
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[8,5,4,3,2,6,7,1]=>1111001
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>[8,5,4,2,3,6,7,1]=>1110001
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[8,4,5,3,2,6,7,1]=>1011001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[8,4,3,2,5,6,7,1]=>1110001
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[8,4,2,3,5,6,7,1]=>1100001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[8,3,4,2,5,6,7,1]=>1010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>[8,3,2,4,5,6,7,1]=>1100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,6,7,1]=>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
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>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
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>1110110
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[4,6,7,5,3,2,8,1]=>[8,6,5,2,4,1,3,7]=>1110100
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>1111100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>1110100
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>1110000
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>1101010
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[8,6,2,5,1,3,4,7]=>1101000
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[8,6,4,3,5,2,1,7]=>1110110
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[8,6,2,3,5,1,4,7]=>1100100
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[8,6,4,3,2,5,1,7]=>1111010
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[4,5,3,7,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>1110010
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>1111100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>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
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>1101100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,6,2,4,1,3,5,7]=>1101000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>1110100
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[8,6,2,3,4,1,5,7]=>1100100
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>1100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[8,5,6,4,3,2,1,7]=>1011110
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[2,6,5,7,4,3,8,1]=>[8,4,6,5,2,1,3,7]=>1011100
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>[8,3,6,5,1,2,4,7]=>1011000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[8,3,6,2,5,1,4,7]=>1010100
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[8,3,6,2,4,1,5,7]=>1010100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[8,3,6,2,1,4,5,7]=>1011000
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[8,4,3,6,5,1,2,7]=>1101100
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[3,2,5,7,6,4,8,1]=>[8,4,3,6,2,5,1,7]=>1101010
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,4,3,6,2,1,5,7]=>1101100
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[8,3,2,6,1,4,5,7]=>1101000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[8,4,5,6,3,2,1,7]=>1001110
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[8,2,3,6,1,4,5,7]=>1001000
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[8,4,2,3,6,1,5,7]=>1100100
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[8,4,5,3,6,2,1,7]=>1010110
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[8,4,3,5,6,2,1,7]=>1100110
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[8,3,4,5,6,2,1,7]=>1000110
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[8,5,4,3,2,6,1,7]=>1111010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,3,2,4,6,1,7]=>1110010
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[8,5,2,3,4,6,1,7]=>1100010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,4,3,5,2,6,1,7]=>1101010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[8,3,4,2,5,6,1,7]=>1010010
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[8,3,2,4,5,6,1,7]=>1100010
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,6,1,7]=>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
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[3,4,6,5,2,7,8,1]=>[8,5,2,3,4,1,6,7]=>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
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[8,4,5,3,2,1,6,7]=>1011100
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[2,4,6,5,3,7,8,1]=>[8,3,5,2,4,1,6,7]=>1010100
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[8,3,5,2,1,4,6,7]=>1011000
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[3,2,5,6,4,7,8,1]=>[8,3,2,5,1,4,6,7]=>1101000
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>1001100
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[8,2,3,5,1,4,6,7]=>1001000
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[8,4,2,3,5,1,6,7]=>1100100
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[8,2,3,4,5,1,6,7]=>1000100
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>1111000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[8,4,2,3,1,5,6,7]=>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
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[8,3,4,2,1,5,6,7]=>1011000
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[8,2,4,1,3,5,6,7]=>1010000
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>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
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>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
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[7,8,6,5,4,3,2,1]=>0111111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[6,8,7,5,4,3,1,2]=>0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[6,8,7,5,4,2,3,1]=>0111101
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[6,8,7,5,4,2,1,3]=>0111110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[5,8,7,6,4,1,2,3]=>0111100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[6,8,7,5,3,4,2,1]=>0111011
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[6,8,7,5,3,2,4,1]=>0111101
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[6,8,7,5,3,2,1,4]=>0111110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[5,8,7,6,3,1,2,4]=>0111100
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[5,8,7,6,2,3,1,4]=>0111010
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[5,8,7,6,2,1,3,4]=>0111100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[4,8,7,6,1,2,3,5]=>0111000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[6,8,7,4,5,3,2,1]=>0110111
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[5,8,7,3,6,2,4,1]=>0110101
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[4,8,7,2,6,1,3,5]=>0110100
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>[5,8,7,3,2,6,1,4]=>0111010
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[5,8,7,3,4,6,2,1]=>0110011
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,6,5,4,8,7,3,2]=>[6,8,7,4,3,2,5,1]=>0111101
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[5,8,7,3,4,2,6,1]=>0110101
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[5,8,7,3,2,4,6,1]=>0111001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[6,8,7,4,3,2,1,5]=>0111110
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[4,8,7,2,5,1,3,6]=>0110100
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[5,8,7,3,2,1,4,6]=>0111100
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,5,6,4,7,8,3,2]=>[4,8,7,3,1,2,5,6]=>0111000
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>[4,8,7,2,1,3,5,6]=>0111000
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[3,8,7,1,2,4,5,6]=>0110000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[6,8,5,7,4,3,2,1]=>0101111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>[5,8,4,7,6,3,1,2]=>0101110
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[5,8,4,7,6,2,3,1]=>0101101
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[4,8,3,7,6,1,2,5]=>0101100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[5,8,4,7,3,6,2,1]=>0101011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>0101010
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[4,8,3,7,2,5,6,1]=>0101001
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[4,8,3,7,5,1,2,6]=>0101100
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[4,8,3,7,2,5,1,6]=>0101010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[4,8,3,7,2,1,5,6]=>0101100
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[3,8,2,7,1,4,5,6]=>0101000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[6,8,5,4,7,3,2,1]=>0110111
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[5,8,4,3,7,6,1,2]=>0110110
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[5,8,4,3,7,2,6,1]=>0110101
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[5,8,4,3,7,2,1,6]=>0110110
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[4,8,3,2,7,1,5,6]=>0110100
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[3,8,2,4,7,1,5,6]=>0100100
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[6,8,5,4,3,7,2,1]=>0111011
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[5,8,6,3,4,7,2,1]=>0110011
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[4,8,3,5,2,7,1,6]=>0101010
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[5,8,4,3,6,7,2,1]=>0110011
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[4,8,3,5,6,7,2,1]=>0100011
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[6,8,5,4,3,2,7,1]=>0111101
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[5,8,4,6,3,2,7,1]=>0101101
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[5,8,4,3,6,2,7,1]=>0110101
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[5,8,4,3,2,6,7,1]=>0111001
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[3,8,2,4,5,6,7,1]=>0100001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[6,8,5,4,3,2,1,7]=>0111110
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[5,8,6,4,2,1,3,7]=>0111100
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,5,6,7,4,3,8,2]=>[4,8,6,5,1,2,3,7]=>0111000
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,4,6,5,7,3,8,2]=>[4,8,6,2,3,1,5,7]=>0110100
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[4,8,6,2,1,3,5,7]=>0111000
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[3,8,6,1,2,4,5,7]=>0110000
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[4,8,3,6,2,5,1,7]=>0101010
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,3,6,5,7,4,8,2]=>[4,8,3,6,2,1,5,7]=>0101100
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[3,8,2,6,1,4,5,7]=>0101000
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>[4,8,3,2,6,1,5,7]=>0110100
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[4,8,3,5,2,6,1,7]=>0101010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[5,8,4,3,2,1,6,7]=>0111100
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[4,8,5,2,1,3,6,7]=>0111000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[4,8,3,2,5,1,6,7]=>0110100
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[3,8,2,4,5,1,6,7]=>0100100
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[4,8,3,2,1,5,6,7]=>0111000
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[3,8,2,1,4,5,6,7]=>0110000
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[2,8,1,3,4,5,6,7]=>0100000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[7,6,8,5,4,3,2,1]=>1011111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[6,5,8,7,4,3,1,2]=>1011110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[6,5,8,7,4,2,3,1]=>1011101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[6,5,8,7,4,2,1,3]=>1011110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[5,4,8,7,6,1,2,3]=>1011100
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[6,5,8,7,3,4,2,1]=>1011011
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[5,4,8,7,2,6,1,3]=>1011010
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[6,5,8,7,3,2,4,1]=>1011101
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[2,1,5,6,8,7,4,3]=>[5,4,8,7,2,3,6,1]=>1011001
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[6,5,8,7,3,2,1,4]=>1011110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[5,4,8,7,3,1,2,6]=>1011100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[5,4,8,7,2,3,1,6]=>1011010
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[5,4,8,7,2,1,3,6]=>1011100
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[4,3,8,7,1,2,5,6]=>1011000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[6,5,8,4,7,3,2,1]=>1010111
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[5,4,8,3,7,6,1,2]=>1010110
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[5,4,8,3,7,2,6,1]=>1010101
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[2,1,4,7,6,8,5,3]=>[5,4,8,3,7,2,1,6]=>1010110
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[4,3,8,2,7,1,5,6]=>1010100
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[6,5,8,4,3,7,2,1]=>1011011
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>[5,4,8,3,2,7,1,6]=>1011010
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[4,3,8,2,5,7,1,6]=>1010010
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[2,1,6,5,4,8,7,3]=>[6,5,8,4,3,2,7,1]=>1011101
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[2,1,5,6,4,8,7,3]=>[5,4,8,6,2,3,7,1]=>1011001
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[5,4,8,3,6,2,7,1]=>1010101
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[5,4,8,3,2,6,7,1]=>1011001
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[4,3,8,2,5,6,7,1]=>1010001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[2,1,7,6,5,4,8,3]=>[6,5,8,4,3,2,1,7]=>1011110
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[2,1,6,7,5,4,8,3]=>[5,4,8,6,3,1,2,7]=>1011100
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[5,4,8,6,2,3,1,7]=>1011010
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[5,4,8,6,2,1,3,7]=>1011100
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[4,3,8,6,1,2,5,7]=>1011000
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[5,4,8,3,6,2,1,7]=>1010110
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[4,3,8,2,6,1,5,7]=>1010100
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[5,4,8,3,2,6,1,7]=>1011010
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[4,3,8,5,1,2,6,7]=>1011000
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[4,3,8,2,1,5,6,7]=>1011000
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[3,2,8,1,4,5,6,7]=>1010000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[6,7,8,5,4,3,2,1]=>0011111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[5,6,8,7,4,3,1,2]=>0011110
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>[5,6,8,7,4,2,1,3]=>0011110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[4,5,8,7,6,1,2,3]=>0011100
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[4,5,8,7,2,3,6,1]=>0011001
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[5,6,8,7,3,2,1,4]=>0011110
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[4,5,8,7,2,3,1,6]=>0011010
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[3,4,8,7,1,2,5,6]=>0011000
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[5,6,8,4,7,3,2,1]=>0010111
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[4,5,8,3,7,6,1,2]=>0010110
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[4,5,8,3,7,2,6,1]=>0010101
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,2,4,7,6,8,5,3]=>[4,5,8,3,7,2,1,6]=>0010110
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[3,4,8,2,7,1,5,6]=>0010100
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[5,6,8,4,3,7,2,1]=>0011011
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>[4,5,8,3,2,7,1,6]=>0011010
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[4,5,8,3,6,7,2,1]=>0010011
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[5,6,8,4,3,2,7,1]=>0011101
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[3,4,8,2,5,6,7,1]=>0010001
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[5,6,8,4,3,2,1,7]=>0011110
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[3,4,8,6,1,2,5,7]=>0011000
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,2,5,4,7,6,8,3]=>[4,5,8,3,2,6,1,7]=>0011010
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[4,5,8,3,2,1,6,7]=>0011100
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[3,4,8,2,1,5,6,7]=>0011000
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[2,3,8,1,4,5,6,7]=>0010000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[7,6,5,8,4,3,2,1]=>1101111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[6,5,4,8,7,3,1,2]=>1101110
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[6,5,4,8,7,2,3,1]=>1101101
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[6,5,4,8,7,2,1,3]=>1101110
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[6,5,4,8,3,7,2,1]=>1101011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[5,4,3,8,2,7,1,6]=>1101010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[6,5,4,8,3,2,7,1]=>1101101
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[5,4,3,8,2,6,7,1]=>1101001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[6,5,4,8,3,2,1,7]=>1101110
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[5,4,3,8,2,1,6,7]=>1101100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[4,3,2,8,1,5,6,7]=>1101000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[7,5,6,8,4,3,2,1]=>1001111
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[6,4,5,8,7,3,1,2]=>1001110
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[6,4,5,8,7,2,3,1]=>1001101
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[6,4,5,8,7,2,1,3]=>1001110
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[5,3,4,8,7,1,2,6]=>1001100
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[6,4,5,8,3,2,7,1]=>1001101
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[5,3,4,8,2,6,1,7]=>1001010
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[4,2,3,8,1,5,6,7]=>1001000
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[6,7,5,8,4,3,2,1]=>0101111
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>[5,6,4,8,7,2,1,3]=>0101110
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[5,6,4,8,3,7,2,1]=>0101011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[4,5,3,8,2,7,1,6]=>0101010
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[5,6,4,8,3,2,1,7]=>0101110
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[4,5,3,8,6,1,2,7]=>0101100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[4,5,3,8,2,6,1,7]=>0101010
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[4,5,3,8,2,1,6,7]=>0101100
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[3,4,2,8,1,5,6,7]=>0101000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[6,5,7,8,4,3,2,1]=>1001111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[5,4,6,8,7,3,1,2]=>1001110
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[4,3,5,8,7,1,2,6]=>1001100
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[3,2,4,8,1,5,6,7]=>1001000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[5,6,7,8,4,3,2,1]=>0001111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[4,5,6,8,7,3,1,2]=>0001110
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[4,5,6,8,7,2,1,3]=>0001110
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[3,4,5,8,7,1,2,6]=>0001100
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[4,5,6,8,3,7,2,1]=>0001011
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[3,4,5,8,2,7,1,6]=>0001010
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[3,4,5,8,2,6,7,1]=>0001001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[4,5,6,8,3,2,1,7]=>0001110
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[3,4,5,8,6,1,2,7]=>0001100
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[2,3,4,8,1,5,6,7]=>0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[7,6,5,4,8,3,2,1]=>1110111
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[6,5,4,3,8,7,1,2]=>1110110
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[6,5,4,3,8,2,7,1]=>1110101
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[6,5,4,3,8,2,1,7]=>1110110
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[5,4,3,2,8,1,6,7]=>1110100
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[7,6,4,5,8,3,2,1]=>1100111
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[6,5,3,4,8,7,1,2]=>1100110
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[6,5,3,4,8,2,7,1]=>1100101
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[6,5,3,4,8,2,1,7]=>1100110
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,4,2,3,8,1,6,7]=>1100100
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[7,5,6,4,8,3,2,1]=>1010111
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[6,4,5,3,8,7,1,2]=>1010110
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[6,4,5,3,8,2,7,1]=>1010101
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[6,4,5,3,8,2,1,7]=>1010110
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[7,5,4,6,8,3,2,1]=>1100111
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[6,4,3,5,8,7,1,2]=>1100110
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[6,4,3,5,8,2,7,1]=>1100101
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[6,4,3,5,8,2,1,7]=>1100110
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,3,2,4,8,1,6,7]=>1100100
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[7,4,5,6,8,3,2,1]=>1000111
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[6,3,4,5,8,7,1,2]=>1000110
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[6,3,4,5,8,2,7,1]=>1000101
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[6,3,4,5,8,2,1,7]=>1000110
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,2,3,4,8,1,6,7]=>1000100
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[6,7,5,4,8,3,2,1]=>0110111
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[5,6,4,3,8,2,7,1]=>0110101
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[4,5,3,2,8,1,6,7]=>0110100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[5,7,4,6,8,3,2,1]=>0100111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[4,6,3,5,8,7,1,2]=>0100110
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[4,6,3,5,8,2,7,1]=>0100101
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[4,6,3,5,8,2,1,7]=>0100110
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[3,5,2,4,8,1,6,7]=>0100100
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[6,5,7,4,8,3,2,1]=>1010111
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[5,4,6,3,8,7,1,2]=>1010110
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[5,4,6,3,8,2,7,1]=>1010101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[5,4,6,3,8,2,1,7]=>1010110
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[4,3,5,2,8,1,6,7]=>1010100
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[5,6,7,4,8,3,2,1]=>0010111
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[4,5,6,3,8,7,1,2]=>0010110
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[4,5,6,3,8,2,7,1]=>0010101
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[4,5,6,3,8,2,1,7]=>0010110
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[6,5,4,7,8,3,2,1]=>1100111
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[5,4,3,6,8,7,1,2]=>1100110
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[5,4,3,6,8,2,7,1]=>1100101
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[4,3,2,5,8,1,6,7]=>1100100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[6,4,5,7,8,3,2,1]=>1000111
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[5,3,4,6,8,2,1,7]=>1000110
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[4,2,3,5,8,1,6,7]=>1000100
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[5,6,4,7,8,3,2,1]=>0100111
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[4,5,3,6,8,2,7,1]=>0100101
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[4,5,3,6,8,2,1,7]=>0100110
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[5,4,6,7,8,3,2,1]=>1000111
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[4,3,5,6,8,7,1,2]=>1000110
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[3,2,4,5,8,1,6,7]=>1000100
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[4,5,6,7,8,3,2,1]=>0000111
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[3,4,5,6,8,7,1,2]=>0000110
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[3,4,5,6,8,2,7,1]=>0000101
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[3,4,5,6,8,2,1,7]=>0000110
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[2,3,4,5,8,1,6,7]=>0000100
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[7,6,5,4,3,8,2,1]=>1111011
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[6,5,4,3,2,8,1,7]=>1111010
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[7,6,5,3,4,8,2,1]=>1110011
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[6,5,3,4,2,8,1,7]=>1101010
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[7,6,4,3,5,8,2,1]=>1110011
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[7,6,3,4,5,8,2,1]=>1100011
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[6,5,2,3,4,8,1,7]=>1100010
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[7,5,6,4,3,8,2,1]=>1011011
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[6,4,5,3,2,8,1,7]=>1011010
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[6,3,5,2,4,8,1,7]=>1010010
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[7,5,4,6,3,8,2,1]=>1101011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[6,4,3,5,2,8,1,7]=>1101010
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[7,4,5,6,3,8,2,1]=>1001011
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[7,5,4,3,6,8,2,1]=>1110011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[6,4,3,2,5,8,1,7]=>1110010
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[7,5,3,4,6,8,2,1]=>1100011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[6,4,2,3,5,8,1,7]=>1100010
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[7,3,4,5,6,8,2,1]=>1000011
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[6,2,3,4,5,8,1,7]=>1000010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[6,7,5,4,3,8,2,1]=>0111011
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[5,6,4,3,2,8,1,7]=>0111010
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[4,6,3,5,2,8,1,7]=>0101010
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>[5,7,4,3,6,8,2,1]=>0110011
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[4,7,3,5,6,8,2,1]=>0100011
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]=>[6,5,7,4,3,8,2,1]=>1011011
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[2,1,4,5,3,8,7,6]=>[5,4,7,3,6,8,2,1]=>1010011
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[5,6,7,4,3,8,2,1]=>0011011
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[4,5,6,3,2,8,1,7]=>0011010
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[4,5,7,3,6,8,2,1]=>0010011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[4,5,3,6,2,8,1,7]=>0101010
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[5,4,6,7,3,8,2,1]=>1001011
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[2,1,3,5,4,7,8,6]=>[4,3,5,6,2,8,1,7]=>1001010
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[4,5,6,7,3,8,2,1]=>0001011
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[3,4,5,6,2,8,1,7]=>0001010
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[6,5,4,3,7,8,2,1]=>1110011
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[5,4,3,2,6,8,1,7]=>1110010
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[6,5,3,4,7,8,2,1]=>1100011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[5,3,2,4,6,8,1,7]=>1100010
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[6,3,4,5,7,8,2,1]=>1000011
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[5,2,3,4,6,8,1,7]=>1000010
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[4,6,3,5,7,8,2,1]=>0100011
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[3,5,2,4,6,8,1,7]=>0100010
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[2,1,4,3,5,7,8,6]=>[4,3,5,2,6,8,1,7]=>1010010
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]=>[4,5,6,3,7,8,2,1]=>0010011
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[5,4,3,6,7,8,2,1]=>1100011
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[4,3,2,5,6,8,1,7]=>1100010
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[4,2,3,5,6,8,1,7]=>1000010
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[3,4,2,5,6,8,1,7]=>0100010
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>[4,3,5,6,7,8,2,1]=>1000011
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>[3,2,4,5,6,8,1,7]=>1000010
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[3,4,5,6,7,8,2,1]=>0000011
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[2,3,4,5,6,8,1,7]=>0000010
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,8,1]=>1111101
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[7,6,5,4,2,3,8,1]=>1111001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[7,6,5,3,4,2,8,1]=>1110101
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[7,6,5,3,2,4,8,1]=>1111001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[7,6,5,2,3,4,8,1]=>1110001
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[7,6,4,5,3,2,8,1]=>1101101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[7,6,3,5,2,4,8,1]=>1101001
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[7,6,4,3,5,2,8,1]=>1110101
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[3,4,6,5,2,1,8,7]=>[7,6,3,4,5,2,8,1]=>1100101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[7,6,4,2,3,5,8,1]=>1110001
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[7,6,3,2,4,5,8,1]=>1110001
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[7,6,2,3,4,5,8,1]=>1100001
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[7,5,6,4,3,2,8,1]=>1011101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[7,4,6,3,5,2,8,1]=>1010101
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>[7,4,3,6,2,5,8,1]=>1101001
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[7,4,5,6,3,2,8,1]=>1001101
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[4,3,2,6,5,1,8,7]=>[7,5,4,3,6,2,8,1]=>1110101
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[7,5,3,4,6,2,8,1]=>1100101
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[7,4,5,3,6,2,8,1]=>1010101
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[7,5,4,3,2,6,8,1]=>1111001
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[7,5,4,2,3,6,8,1]=>1110001
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[7,5,3,2,4,6,8,1]=>1110001
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[7,5,2,3,4,6,8,1]=>1100001
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[7,4,3,5,2,6,8,1]=>1101001
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[7,4,3,2,5,6,8,1]=>1110001
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[7,4,2,3,5,6,8,1]=>1100001
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[7,2,3,4,5,6,8,1]=>1000001
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>[6,7,5,4,3,2,8,1]=>0111101
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>[5,7,6,3,2,4,8,1]=>0111001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[6,5,7,4,3,2,8,1]=>1011101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[5,4,7,6,2,3,8,1]=>1011001
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[5,4,7,3,6,2,8,1]=>1010101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[5,4,7,3,2,6,8,1]=>1011001
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[4,3,7,2,5,6,8,1]=>1010001
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>[3,4,7,2,5,6,8,1]=>0010001
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[6,5,4,7,3,2,8,1]=>1101101
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[6,4,5,7,3,2,8,1]=>1001101
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[2,1,3,5,6,4,8,7]=>[4,3,5,7,2,6,8,1]=>1001001
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[4,5,6,7,3,2,8,1]=>0001101
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[3,4,5,7,2,6,8,1]=>0001001
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[6,5,4,3,7,2,8,1]=>1110101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[6,5,3,4,7,2,8,1]=>1100101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[6,4,5,3,7,2,8,1]=>1010101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[6,4,3,5,7,2,8,1]=>1100101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[6,3,4,5,7,2,8,1]=>1000101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>[4,6,3,5,7,2,8,1]=>0100101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[5,4,6,3,7,2,8,1]=>1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[4,5,6,3,7,2,8,1]=>0010101
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[4,5,3,6,7,2,8,1]=>0100101
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[4,3,5,6,7,2,8,1]=>1000101
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[3,4,5,6,7,2,8,1]=>0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[6,5,4,3,2,7,8,1]=>1111001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[6,5,4,2,3,7,8,1]=>1110001
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[6,5,3,4,2,7,8,1]=>1101001
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[4,3,5,2,1,6,8,7]=>[6,5,3,2,4,7,8,1]=>1110001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>[6,5,2,3,4,7,8,1]=>1100001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[6,3,5,2,4,7,8,1]=>1010001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>[6,3,4,5,2,7,8,1]=>1001001
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[6,2,3,4,5,7,8,1]=>1000001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[5,4,6,3,2,7,8,1]=>1011001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[4,3,6,2,5,7,8,1]=>1010001
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[4,5,6,3,2,7,8,1]=>0011001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[4,3,5,6,2,7,8,1]=>1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[3,4,5,6,2,7,8,1]=>0001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[5,4,3,2,6,7,8,1]=>1110001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[3,4,2,1,5,6,8,7]=>[5,4,2,3,6,7,8,1]=>1100001
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[5,3,2,4,6,7,8,1]=>1100001
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[5,2,3,4,6,7,8,1]=>1000001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[4,5,3,2,6,7,8,1]=>0110001
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[3,5,2,4,6,7,8,1]=>0100001
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[4,3,5,2,6,7,8,1]=>1010001
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[3,4,5,2,6,7,8,1]=>0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[4,3,2,5,6,7,8,1]=>1100001
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[4,2,3,5,6,7,8,1]=>1000001
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]=>[3,4,2,5,6,7,8,1]=>0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[3,2,4,5,6,7,8,1]=>1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[2,3,4,5,6,7,8,1]=>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
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,6,5,4,2,3,1,8]=>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
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,4,2,1,8]=>1110110
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[7,6,5,3,2,4,1,8]=>1111010
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>1110010
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>1111100
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[7,6,5,2,3,1,4,8]=>1110100
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[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
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[7,6,3,5,2,4,1,8]=>1101010
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[7,6,4,3,5,2,1,8]=>1110110
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>1100110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[5,4,3,7,6,2,1,8]=>[7,6,4,3,2,5,1,8]=>1111010
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>1110010
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>1110010
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[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
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>[7,6,3,4,2,1,5,8]=>1101100
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[4,3,6,5,7,2,1,8]=>[7,6,3,2,4,1,5,8]=>1110100
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[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
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[7,5,6,4,3,2,1,8]=>1011110
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[7,3,6,2,5,1,4,8]=>1010100
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>[7,3,6,2,1,4,5,8]=>1011000
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,5,4,6,3,2,1,8]=>1101110
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[3,2,6,5,7,4,1,8]=>[7,4,3,6,2,1,5,8]=>1101100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[7,3,2,6,1,4,5,8]=>1101000
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,4,5,6,3,2,1,8]=>1001110
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>[7,3,4,6,2,1,5,8]=>1001100
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[7,3,2,4,6,1,5,8]=>1100100
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,3,4,5,6,2,1,8]=>1000110
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[7,5,4,3,2,6,1,8]=>1111010
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[7,5,4,2,3,6,1,8]=>1110010
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[7,5,3,4,2,6,1,8]=>1101010
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>1110010
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,4,3,5,2,6,1,8]=>1101010
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[3,4,2,5,7,6,1,8]=>[7,4,2,3,5,6,1,8]=>1100010
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[7,2,3,4,5,6,1,8]=>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
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[7,5,2,3,4,1,6,8]=>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
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[7,5,2,3,1,4,6,8]=>1101000
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>1100000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[7,3,5,2,1,4,6,8]=>1011000
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[7,4,3,5,2,1,6,8]=>1101100
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[7,4,2,3,5,1,6,8]=>1100100
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,5,1,6,8]=>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
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[7,2,3,4,1,5,6,8]=>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
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[2,4,3,5,6,7,1,8]=>[7,2,3,1,4,5,6,8]=>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
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[6,7,5,4,3,2,1,8]=>0111110
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,6,5,7,4,3,2,8]=>[5,7,6,4,2,1,3,8]=>0111100
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,4,7,6,5,3,2,8]=>[5,7,6,3,4,2,1,8]=>0110110
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,5,4,7,6,3,2,8]=>[5,7,6,3,2,4,1,8]=>0111010
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[4,7,6,2,3,1,5,8]=>0110100
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[3,7,6,1,2,4,5,8]=>0110000
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>[5,7,4,6,3,2,1,8]=>0101110
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[4,7,3,6,5,1,2,8]=>0101100
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[4,7,3,6,2,5,1,8]=>0101010
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[3,7,2,6,1,4,5,8]=>0101000
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[4,7,3,5,2,6,1,8]=>0101010
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[4,7,3,2,5,6,1,8]=>0110010
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[3,7,2,4,5,6,1,8]=>0100010
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[4,7,5,2,1,3,6,8]=>0111000
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>[3,7,5,1,2,4,6,8]=>0110000
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[4,7,3,5,2,1,6,8]=>0101100
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[3,7,2,5,1,4,6,8]=>0101000
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[4,7,3,2,5,1,6,8]=>0110100
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,3,4,6,5,7,2,8]=>[3,7,2,4,5,1,6,8]=>0100100
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[4,7,3,2,1,5,6,8]=>0111000
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[2,7,1,3,4,5,6,8]=>0100000
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>[6,5,7,4,3,2,1,8]=>1011110
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[2,1,6,7,5,4,3,8]=>[5,4,7,6,3,1,2,8]=>1011100
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[4,3,7,2,6,1,5,8]=>1010100
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[4,3,7,2,1,5,6,8]=>1011000
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[5,6,7,4,3,2,1,8]=>0011110
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[3,4,7,6,1,2,5,8]=>0011000
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,2,4,6,5,7,3,8]=>[3,4,7,2,5,1,6,8]=>0010100
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[2,3,7,1,4,5,6,8]=>0010000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[6,5,4,7,3,2,1,8]=>1101110
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[3,2,1,6,7,5,4,8]=>[5,4,3,7,6,1,2,8]=>1101100
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[5,4,3,7,2,6,1,8]=>1101010
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[4,3,2,7,1,5,6,8]=>1101000
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[5,3,4,7,6,1,2,8]=>1001100
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[5,3,4,7,2,1,6,8]=>1001100
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[5,6,4,7,3,2,1,8]=>0101110
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[4,5,3,7,2,6,1,8]=>0101010
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[4,5,3,7,2,1,6,8]=>0101100
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[4,5,6,7,3,2,1,8]=>0001110
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[2,3,4,7,1,5,6,8]=>0001000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[6,5,4,3,7,2,1,8]=>1110110
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[5,4,3,2,7,1,6,8]=>1110100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[5,3,2,4,7,1,6,8]=>1100100
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[5,2,3,4,7,1,6,8]=>1000100
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[5,6,4,3,7,2,1,8]=>0110110
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[4,5,3,2,7,1,6,8]=>0110100
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[3,5,2,4,7,1,6,8]=>0100100
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>[4,3,5,2,7,1,6,8]=>1010100
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[3,4,5,2,7,1,6,8]=>0010100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[5,4,3,6,7,2,1,8]=>1100110
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[3,4,5,6,7,2,1,8]=>0000110
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[2,3,4,5,7,1,6,8]=>0000100
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[6,5,4,3,2,7,1,8]=>1111010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[6,3,4,5,2,7,1,8]=>1001010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[6,4,2,3,5,7,1,8]=>1100010
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[6,2,3,4,5,7,1,8]=>1000010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[5,6,4,3,2,7,1,8]=>0111010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[4,6,3,5,2,7,1,8]=>0101010
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[3,6,2,4,5,7,1,8]=>0100010
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]=>[5,4,6,3,2,7,1,8]=>1011010
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,2,4,5,3,7,6,8]=>[3,4,6,2,5,7,1,8]=>0010010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[5,4,3,6,2,7,1,8]=>1101010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[5,3,4,6,2,7,1,8]=>1001010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[4,5,3,6,2,7,1,8]=>0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[3,4,5,6,2,7,1,8]=>0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[5,4,3,2,6,7,1,8]=>1110010
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[5,2,3,4,6,7,1,8]=>1000010
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]=>[3,4,5,2,6,7,1,8]=>0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[4,3,2,5,6,7,1,8]=>1100010
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>[4,2,3,5,6,7,1,8]=>1000010
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[3,4,2,5,6,7,1,8]=>0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>[3,2,4,5,6,7,1,8]=>1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[2,3,4,5,6,7,1,8]=>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
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>1101100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>1111000
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[6,3,5,2,4,1,7,8]=>1010100
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>1110100
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>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
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[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
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[5,6,4,3,2,1,7,8]=>0111100
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>[4,6,5,3,1,2,7,8]=>0111000
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[4,6,5,2,1,3,7,8]=>0111000
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>0101000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[4,6,3,2,5,1,7,8]=>0110100
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,4,5,3,6,2,7,8]=>[3,6,4,1,2,5,7,8]=>0110000
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>[3,6,2,4,1,5,7,8]=>0101000
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,3,4,5,6,2,7,8]=>[2,6,1,3,4,5,7,8]=>0100000
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[4,3,6,5,1,2,7,8]=>1011000
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[4,3,6,2,5,1,7,8]=>1010100
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[4,5,6,3,2,1,7,8]=>0011100
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[3,4,6,5,1,2,7,8]=>0011000
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[3,4,6,2,5,1,7,8]=>0010100
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[2,3,6,1,4,5,7,8]=>0010000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[5,4,3,6,2,1,7,8]=>1101100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[4,3,2,6,1,5,7,8]=>1101000
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[3,4,5,6,2,1,7,8]=>0001100
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[2,3,4,6,1,5,7,8]=>0001000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[5,4,3,2,6,1,7,8]=>1110100
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[5,3,2,4,6,1,7,8]=>1100100
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[5,2,3,4,6,1,7,8]=>1000100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[4,3,5,2,6,1,7,8]=>1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[3,4,5,2,6,1,7,8]=>0010100
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[3,4,2,5,6,1,7,8]=>0100100
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[3,2,4,5,6,1,7,8]=>1000100
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[2,3,4,5,6,1,7,8]=>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
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>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
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>1011000
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[5,2,4,1,3,6,7,8]=>1010000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>1101000
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>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
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>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
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>0111000
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[3,5,2,4,1,6,7,8]=>0101000
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,4,3,5,2,6,7,8]=>[3,5,2,1,4,6,7,8]=>0110000
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[2,5,1,3,4,6,7,8]=>0100000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>1011000
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[3,2,5,1,4,6,7,8]=>1010000
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>0011000
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[2,3,5,1,4,6,7,8]=>0010000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>1101000
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>1001000
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>0101000
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>1001000
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>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
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>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
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>0110000
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>0100000
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>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
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>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
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,3,1]=>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
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>111000000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>110000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[2,9,1,3,4,5,6,7,8]=>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
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[6,8,7,9,5,4,3,2,1]=>[9,8,7,6,5,2,3,1,4]=>11111010
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>111111110
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[5,8,7,6,9,4,3,2,1]=>[9,8,7,6,3,4,2,1,5]=>11110110
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>111111110
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[4,8,7,6,5,9,3,2,1]=>[9,8,7,4,5,3,2,1,6]=>11101110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>111111110
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[3,8,7,6,5,4,9,2,1]=>[9,8,5,6,4,3,2,1,7]=>11011110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>111111110
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[2,8,7,6,5,4,3,9,1]=>[9,6,7,5,4,3,2,1,8]=>10111110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>111111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>[7,8,6,5,4,3,2,1,9]=>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
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[1,3,5,7,9,10,8,6,4,2]=>[5,10,4,9,3,8,2,7,1,6]=>010101010
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>111100000
[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,1,4,6,5,3,8,10,9,7]=>[6,5,8,4,7,3,10,2,9,1]=>101010101
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[6,5,7,4,8,3,9,2,10,1]=>101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[2,3,4,5,6,7,8,9,1]=>00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>[3,2,4,5,6,7,8,9,1]=>10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>11000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]=>[3,2,4,5,6,7,8,9,10,1]=>100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]=>[3,4,2,5,6,7,8,9,1]=>01000001
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[2,3,1,4,5,6,7,9,8]=>[4,2,3,5,6,7,8,9,1]=>10000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[2,4,3,5,6,7,8,9,1]=>[9,2,3,1,4,5,6,7,8]=>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
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[2,3,4,5,6,7,9,1,8]=>00000010
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[2,3,4,5,6,9,1,7,8]=>00000100
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[2,3,4,5,9,1,6,7,8]=>00001000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[2,3,4,9,1,5,6,7,8]=>00010000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[2,3,9,1,4,5,6,7,8]=>00100000
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[3,4,5,6,7,8,9,2,1]=>00000011
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[2,3,4,5,6,7,8,10,1,9]=>000000010
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[2,3,4,5,6,7,10,1,8,9]=>000000100
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[2,3,4,5,6,10,1,7,8,9]=>000001000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[2,3,4,5,10,1,6,7,8,9]=>000010000
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[2,3,4,10,1,5,6,7,8,9]=>000100000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>[3,9,2,1,4,5,6,7,8]=>01100000
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[2,3,10,1,4,5,6,7,8,9]=>001000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[2,10,1,3,4,5,6,7,8,9]=>010000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[8,9,7,6,5,4,3,2,1]=>01111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>11111100
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[9,10,8,7,6,5,4,3,2,1]=>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
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[10,11,9,8,7,6,5,4,3,2,1]=>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
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[8,7,9,6,5,4,3,2,1]=>10111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>[8,7,6,9,5,4,3,2,1]=>11011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>[8,7,6,5,9,4,3,2,1]=>11101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>[8,7,6,5,4,9,3,2,1]=>11110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>[8,7,6,5,4,3,9,2,1]=>11111011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[8,7,6,5,4,3,2,9,1]=>11111101
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>[7,8,9,6,5,4,3,2,1]=>00111111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[9,8,10,7,6,5,4,3,2,1]=>101111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>[8,6,7,9,5,4,3,2,1]=>10011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>[9,8,7,10,6,5,4,3,2,1]=>110111111
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[3,4,2,1,9,8,7,6,5]=>[8,7,5,6,9,4,3,2,1]=>11001111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[9,8,7,6,10,5,4,3,2,1]=>111011111
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[4,5,3,2,1,9,8,7,6]=>[8,7,6,4,5,9,3,2,1]=>11100111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]=>[9,8,7,6,5,10,4,3,2,1]=>111101111
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[5,6,4,3,2,1,9,8,7]=>[8,7,6,5,3,4,9,2,1]=>11110011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[9,8,7,6,5,4,10,3,2,1]=>111110111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[6,7,5,4,3,2,1,9,8]=>[8,7,6,5,4,2,3,9,1]=>11111001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>[9,8,7,6,5,4,3,10,2,1]=>111111011
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[9,8,7,6,5,4,3,2,10,1]=>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
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>01100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,5,6,4,3,2,1]=>11101111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[9,7,8,6,5,4,3,2,1]=>10111111
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,5,8,10,9,7]=>[6,5,7,4,8,3,10,2,9,1]=>101010101
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>[9,2,3,4,5,6,7,8,1]=>10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]=>[3,2,4,5,6,7,8,1,9]=>10000010
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[2,1,3,4,5,6,8,9,7]=>[3,2,4,5,6,7,9,1,8]=>10000010
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>[10,2,3,4,5,6,7,8,9,1]=>100000001
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>10100000
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[3,2,1,5,4,6,7,8,9]=>[4,3,2,5,1,6,7,8,9]=>11010000
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]=>[7,6,5,4,3,2,8,1,9]=>11111010
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[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
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>100000000
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[2,4,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>10100000
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[2,3,5,4,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>10010000
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[2,3,4,6,5,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>10001000
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[2,3,4,5,7,6,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>10000100
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[2,3,4,5,6,8,7,1,9]=>[8,2,3,4,5,6,7,1,9]=>10000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>[2,3,4,5,6,7,8,1,9]=>00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>000000010
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,3,4,5,6,7,9,8,2]=>[3,9,2,4,5,6,7,8,1]=>01000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>[9,7,6,5,4,3,2,8,1]=>11111101
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>11111000
[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1]=>[9,6,5,4,3,2,1,7,8]=>11111100
[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[8,7,6,5,4,3,2,9,10,1]=>[10,7,6,5,4,3,2,1,8,9]=>111111100
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>[7,8,6,5,4,3,2,9,1]=>01111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7]=>[7,6,5,4,3,2,9,1,8]=>11111010
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]=>[8,9,10,7,6,5,4,3,2,1]=>001111111
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>[7,6,8,5,4,3,2,1,9]=>10111110
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>011111110
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[1,2,4,5,3,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>00100000
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[2,1,4,5,3,6,7,8,9]=>[3,2,5,1,4,6,7,8,9]=>10100000
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>01010000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[8,7,6,5,4,3,2,10,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>111111101
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>[3,2,9,1,4,5,6,7,8]=>10100000
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[1,3,4,5,6,7,8,2,9]=>[2,8,1,3,4,5,6,7,9]=>01000000
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>[3,4,5,6,7,8,9,10,2,1]=>000000011
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>11111000
[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]=>[5,4,3,2,1,7,8,9,6]=>[6,5,4,3,2,9,1,7,8]=>11110100
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>[4,5,6,7,8,9,3,2,1]=>00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>[5,6,7,8,9,4,3,2,1]=>00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]=>[6,7,8,9,5,4,3,2,1]=>00011111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>[3,4,5,6,7,8,2,9,1]=>00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]=>[4,5,6,7,8,9,10,3,2,1]=>000000111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]=>[5,6,7,8,9,10,4,3,2,1]=>000001111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]=>[6,7,8,9,10,5,4,3,2,1]=>000011111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]=>[7,8,9,10,6,5,4,3,2,1]=>000111111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]=>[3,4,5,6,7,8,9,2,10,1]=>000000101
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[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
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>11000000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>11111100
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[8,7,6,5,3,2,1,4,9]=>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
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]=>[7,6,5,4,3,8,2,1,9]=>11110110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>111111010
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[9,6,7,8,5,4,3,2,1]=>10011111
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[8,6,7,5,4,3,2,1,9]=>10111110
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[8,2,3,4,5,6,7,9,1]=>10000001
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>01000000
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>111111100
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>0000000010
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>11110000
[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>[6,5,4,3,1,2,7,8,9,10]=>111100000
[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[6,7,5,4,3,2,1,8,9,10,11]=>[7,6,5,4,3,1,2,8,9,10,11]=>1111100000
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[6,7,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,1,2,8,9,10]=>111110000
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[5,6,4,3,2,7,1,8,9]=>[7,5,4,3,1,2,6,8,9]=>11110000
[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[5,4,3,2,1,8,9,7,6]=>[7,6,5,4,3,9,8,1,2]=>11110110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[7,6,5,4,3,2,1,9,10,8]=>[8,7,6,5,4,3,2,10,1,9]=>111111010
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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.
searching the database
Sorry, this map was not found in the database.