Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[1,2]=>0
[[.,.],.]=>[1,2]=>[2,1]=>1
[.,[.,[.,.]]]=>[3,2,1]=>[1,3,2]=>01
[.,[[.,.],.]]=>[2,3,1]=>[1,2,3]=>00
[[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>10
[[.,[.,.]],.]=>[2,1,3]=>[3,2,1]=>11
[[[.,.],.],.]=>[1,2,3]=>[2,3,1]=>01
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,4,3,2]=>011
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,4,2,3]=>010
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,4,2]=>001
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,3,2,4]=>010
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,2,3,4]=>000
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[4,1,3,2]=>101
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,2,3]=>100
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[4,3,1,2]=>110
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,4,1,2]=>010
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,3,2,1]=>111
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,2,3,1]=>101
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,4,2,1]=>011
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[3,2,4,1]=>101
[[[[.,.],.],.],.]=>[1,2,3,4]=>[2,3,4,1]=>001
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,5,4,3,2]=>0111
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,5,4,2,3]=>0110
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,5,3,4,2]=>0101
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,5,3,2,4]=>0110
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,5,2,3,4]=>0100
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,4,5,3,2]=>0011
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,4,5,2,3]=>0010
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,3,5,2]=>0101
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,3,4,5,2]=>0001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,4,3,2,5]=>0110
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,4,2,3,5]=>0100
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,3,4,2,5]=>0010
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,3,2,4,5]=>0100
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,2,3,4,5]=>0000
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[5,1,4,3,2]=>1011
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[5,1,4,2,3]=>1010
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[5,1,3,4,2]=>1001
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,3,2,4]=>1010
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,2,3,4]=>1000
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[5,4,1,3,2]=>1101
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[5,4,1,2,3]=>1100
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,5,1,3,2]=>0101
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[4,5,1,2,3]=>0100
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[5,4,3,1,2]=>1110
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[5,3,4,1,2]=>1010
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,5,3,1,2]=>0110
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,5,1,2]=>1010
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[3,4,5,1,2]=>0010
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,4,3,2,1]=>1111
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,4,2,3,1]=>1101
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,3,4,2,1]=>1011
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,3,2,4,1]=>1101
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,2,3,4,1]=>1001
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[4,5,3,2,1]=>0111
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,5,2,3,1]=>0101
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[4,3,5,2,1]=>1011
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[3,4,5,2,1]=>0011
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[4,3,2,5,1]=>1101
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[4,2,3,5,1]=>1001
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,4,2,5,1]=>0101
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[3,2,4,5,1]=>1001
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[2,3,4,5,1]=>0001
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,6,5,4,3,2]=>01111
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,6,5,4,2,3]=>01110
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,6,5,3,4,2]=>01101
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,6,5,3,2,4]=>01110
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,6,5,2,3,4]=>01100
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,6,4,5,3,2]=>01011
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,6,4,5,2,3]=>01010
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,6,4,3,5,2]=>01101
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,6,3,4,5,2]=>01001
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,6,4,3,2,5]=>01110
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,6,4,2,3,5]=>01100
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,6,3,4,2,5]=>01010
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,6,3,2,4,5]=>01100
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,6,2,3,4,5]=>01000
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,5,6,4,3,2]=>00111
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,5,6,4,2,3]=>00110
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,5,6,3,4,2]=>00101
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,5,6,3,2,4]=>00110
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,5,6,2,3,4]=>00100
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,5,4,6,3,2]=>01011
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,5,4,6,2,3]=>01010
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,5,6,3,2]=>00011
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,5,6,2,3]=>00010
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,4,3,6,2]=>01101
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,3,4,6,2]=>01001
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,4,5,3,6,2]=>00101
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,4,3,5,6,2]=>01001
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,3,4,5,6,2]=>00001
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,5,4,3,2,6]=>01110
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,5,4,2,3,6]=>01100
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,5,3,4,2,6]=>01010
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,5,3,2,4,6]=>01100
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,5,2,3,4,6]=>01000
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,4,5,3,2,6]=>00110
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,4,5,2,3,6]=>00100
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,4,3,5,2,6]=>01010
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,3,4,5,2,6]=>00010
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,4,3,2,5,6]=>01100
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,4,2,3,5,6]=>01000
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,3,4,2,5,6]=>00100
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,3,2,4,5,6]=>01000
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>00000
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[6,1,5,4,3,2]=>10111
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[6,1,5,4,2,3]=>10110
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[6,1,5,3,4,2]=>10101
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[6,1,5,3,2,4]=>10110
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[6,1,5,2,3,4]=>10100
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[6,1,4,5,3,2]=>10011
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[6,1,4,5,2,3]=>10010
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[6,1,4,3,5,2]=>10101
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[6,1,3,4,5,2]=>10001
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,3,2,5]=>10110
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,4,2,3,5]=>10100
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,3,4,2,5]=>10010
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,3,2,4,5]=>10100
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,2,3,4,5]=>10000
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[6,5,1,4,3,2]=>11011
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[6,5,1,4,2,3]=>11010
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[6,5,1,3,4,2]=>11001
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[6,5,1,3,2,4]=>11010
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[6,5,1,2,3,4]=>11000
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[5,6,1,4,3,2]=>01011
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[5,6,1,4,2,3]=>01010
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,6,1,3,4,2]=>01001
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[5,6,1,3,2,4]=>01010
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[5,6,1,2,3,4]=>01000
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[6,5,4,1,3,2]=>11101
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[6,5,4,1,2,3]=>11100
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[6,4,5,1,3,2]=>10101
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[6,4,5,1,2,3]=>10100
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[5,6,4,1,3,2]=>01101
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[5,6,4,1,2,3]=>01100
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[5,4,6,1,3,2]=>10101
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[5,4,6,1,2,3]=>10100
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,5,6,1,3,2]=>00101
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,5,6,1,2,3]=>00100
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[6,5,4,3,1,2]=>11110
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[6,5,3,4,1,2]=>11010
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[6,4,5,3,1,2]=>10110
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[6,4,3,5,1,2]=>11010
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[6,3,4,5,1,2]=>10010
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,6,4,3,1,2]=>01110
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,6,3,4,1,2]=>01010
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,4,6,3,1,2]=>10110
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,5,6,3,1,2]=>00110
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,3,6,1,2]=>11010
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,3,4,6,1,2]=>10010
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[4,5,3,6,1,2]=>01010
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[4,3,5,6,1,2]=>10010
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[3,4,5,6,1,2]=>00010
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,5,4,3,2,1]=>11111
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,5,4,2,3,1]=>11101
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,5,3,4,2,1]=>11011
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,5,3,2,4,1]=>11101
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,5,2,3,4,1]=>11001
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,4,5,3,2,1]=>10111
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,4,5,2,3,1]=>10101
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,4,3,5,2,1]=>11011
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,3,4,5,2,1]=>10011
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,4,3,2,5,1]=>11101
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,4,2,3,5,1]=>11001
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,3,4,2,5,1]=>10101
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,3,2,4,5,1]=>11001
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,2,3,4,5,1]=>10001
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[5,6,4,3,2,1]=>01111
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[5,6,4,2,3,1]=>01101
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[5,6,3,4,2,1]=>01011
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,6,3,2,4,1]=>01101
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,6,2,3,4,1]=>01001
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[5,4,6,3,2,1]=>10111
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[5,4,6,2,3,1]=>10101
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,5,6,3,2,1]=>00111
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[4,5,6,2,3,1]=>00101
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[5,4,3,6,2,1]=>11011
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[5,3,4,6,2,1]=>10011
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[4,5,3,6,2,1]=>01011
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[4,3,5,6,2,1]=>10011
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[3,4,5,6,2,1]=>00011
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[5,4,3,2,6,1]=>11101
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[5,4,2,3,6,1]=>11001
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[5,3,4,2,6,1]=>10101
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[5,3,2,4,6,1]=>11001
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[5,2,3,4,6,1]=>10001
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[4,5,3,2,6,1]=>01101
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,5,2,3,6,1]=>01001
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[4,3,5,2,6,1]=>10101
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[3,4,5,2,6,1]=>00101
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[4,3,2,5,6,1]=>11001
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[4,2,3,5,6,1]=>10001
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,4,2,5,6,1]=>01001
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[3,2,4,5,6,1]=>10001
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>00001
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>011111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,7,6,5,4,2,3]=>011110
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,7,6,5,3,4,2]=>011101
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,7,6,5,3,2,4]=>011110
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,7,6,5,2,3,4]=>011100
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,7,6,4,5,3,2]=>011011
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,7,6,4,5,2,3]=>011010
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,7,6,4,3,5,2]=>011101
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,7,6,3,4,5,2]=>011001
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,7,6,4,3,2,5]=>011110
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,7,6,4,2,3,5]=>011100
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,7,6,3,4,2,5]=>011010
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,7,6,3,2,4,5]=>011100
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,7,6,2,3,4,5]=>011000
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,7,5,6,4,3,2]=>010111
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,7,5,6,4,2,3]=>010110
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,7,5,6,3,4,2]=>010101
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,7,5,6,3,2,4]=>010110
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,7,5,6,2,3,4]=>010100
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,7,5,4,6,3,2]=>011011
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,7,5,4,6,2,3]=>011010
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,7,4,5,6,3,2]=>010011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,7,4,5,6,2,3]=>010010
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,7,5,4,3,6,2]=>011101
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,7,5,3,4,6,2]=>011001
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,7,4,5,3,6,2]=>010101
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,7,4,3,5,6,2]=>011001
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,7,3,4,5,6,2]=>010001
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,7,5,4,3,2,6]=>011110
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,7,5,4,2,3,6]=>011100
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,7,5,3,4,2,6]=>011010
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,7,5,3,2,4,6]=>011100
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,7,5,2,3,4,6]=>011000
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,7,4,5,3,2,6]=>010110
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,7,4,5,2,3,6]=>010100
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,7,4,3,5,2,6]=>011010
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,7,3,4,5,2,6]=>010010
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,7,4,3,2,5,6]=>011100
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,7,4,2,3,5,6]=>011000
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,7,3,4,2,5,6]=>010100
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,7,3,2,4,5,6]=>011000
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,7,2,3,4,5,6]=>010000
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,6,7,5,4,3,2]=>001111
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,6,7,5,4,2,3]=>001110
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,6,7,5,3,4,2]=>001101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,6,7,5,3,2,4]=>001110
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,6,7,5,2,3,4]=>001100
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,6,7,4,5,3,2]=>001011
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,6,7,4,5,2,3]=>001010
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,6,7,4,3,5,2]=>001101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,6,7,3,4,5,2]=>001001
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,6,7,4,3,2,5]=>001110
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,6,7,4,2,3,5]=>001100
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,6,7,3,4,2,5]=>001010
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,6,7,3,2,4,5]=>001100
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,6,7,2,3,4,5]=>001000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,6,5,7,4,3,2]=>010111
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,6,5,7,4,2,3]=>010110
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,6,5,7,3,4,2]=>010101
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,6,5,7,3,2,4]=>010110
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,6,5,7,2,3,4]=>010100
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,5,6,7,4,3,2]=>000111
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,5,6,7,4,2,3]=>000110
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,5,6,7,3,4,2]=>000101
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,5,6,7,3,2,4]=>000110
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,5,6,7,2,3,4]=>000100
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,6,5,4,7,3,2]=>011011
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,6,5,4,7,2,3]=>011010
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,6,4,5,7,3,2]=>010011
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,6,4,5,7,2,3]=>010010
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,6,4,7,3,2]=>001011
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,6,4,7,2,3]=>001010
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,6,7,3,2]=>010011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,6,7,2,3]=>010010
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,4,5,6,7,3,2]=>000011
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,4,5,6,7,2,3]=>000010
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,5,4,3,7,2]=>011101
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,5,3,4,7,2]=>011001
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,4,5,3,7,2]=>010101
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,4,3,5,7,2]=>011001
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,3,4,5,7,2]=>010001
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,5,6,4,3,7,2]=>001101
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,5,6,3,4,7,2]=>001001
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,5,4,6,3,7,2]=>010101
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,4,5,6,3,7,2]=>000101
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,5,4,3,6,7,2]=>011001
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,5,3,4,6,7,2]=>010001
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,4,5,3,6,7,2]=>001001
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,4,3,5,6,7,2]=>010001
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,3,4,5,6,7,2]=>000001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,6,5,4,3,2,7]=>011110
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,6,5,4,2,3,7]=>011100
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,6,5,3,4,2,7]=>011010
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,6,5,3,2,4,7]=>011100
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,6,5,2,3,4,7]=>011000
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,6,4,5,3,2,7]=>010110
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,6,4,5,2,3,7]=>010100
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,6,4,3,5,2,7]=>011010
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,6,3,4,5,2,7]=>010010
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,6,4,3,2,5,7]=>011100
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,6,4,2,3,5,7]=>011000
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,6,3,4,2,5,7]=>010100
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,6,3,2,4,5,7]=>011000
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,6,2,3,4,5,7]=>010000
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,5,6,4,3,2,7]=>001110
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,5,6,4,2,3,7]=>001100
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,5,6,3,4,2,7]=>001010
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,5,6,3,2,4,7]=>001100
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,5,6,2,3,4,7]=>001000
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,5,4,6,3,2,7]=>010110
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,5,4,6,2,3,7]=>010100
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,4,5,6,3,2,7]=>000110
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,4,5,6,2,3,7]=>000100
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,5,4,3,6,2,7]=>011010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,5,3,4,6,2,7]=>010010
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,4,5,3,6,2,7]=>001010
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,4,3,5,6,2,7]=>010010
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,3,4,5,6,2,7]=>000010
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,5,4,3,2,6,7]=>011100
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,5,4,2,3,6,7]=>011000
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,5,3,4,2,6,7]=>010100
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,5,3,2,4,6,7]=>011000
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,5,2,3,4,6,7]=>010000
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,4,5,3,2,6,7]=>001100
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,4,5,2,3,6,7]=>001000
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,4,3,5,2,6,7]=>010100
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,3,4,5,2,6,7]=>000100
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,4,3,2,5,6,7]=>011000
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,4,2,3,5,6,7]=>010000
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,3,4,2,5,6,7]=>001000
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,3,2,4,5,6,7]=>010000
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>000000
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[7,1,6,5,4,3,2]=>101111
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[7,1,6,5,4,2,3]=>101110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[7,1,6,5,3,4,2]=>101101
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[7,1,6,5,3,2,4]=>101110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[7,1,6,5,2,3,4]=>101100
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[7,1,6,4,5,3,2]=>101011
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[7,1,6,4,5,2,3]=>101010
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[7,1,6,4,3,5,2]=>101101
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[7,1,6,3,4,5,2]=>101001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[7,1,6,4,3,2,5]=>101110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[7,1,6,4,2,3,5]=>101100
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[7,1,6,3,4,2,5]=>101010
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[7,1,6,3,2,4,5]=>101100
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[7,1,6,2,3,4,5]=>101000
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[7,1,5,6,4,3,2]=>100111
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[7,1,5,6,4,2,3]=>100110
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[7,1,5,6,3,4,2]=>100101
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[7,1,5,6,3,2,4]=>100110
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[7,1,5,6,2,3,4]=>100100
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[7,1,5,4,6,3,2]=>101011
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[7,1,5,4,6,2,3]=>101010
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[7,1,4,5,6,3,2]=>100011
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[7,1,4,5,6,2,3]=>100010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[7,1,5,4,3,6,2]=>101101
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[7,1,5,3,4,6,2]=>101001
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[7,1,4,5,3,6,2]=>100101
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[7,1,4,3,5,6,2]=>101001
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[7,1,3,4,5,6,2]=>100001
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,1,5,4,3,2,6]=>101110
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,1,5,4,2,3,6]=>101100
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,1,5,3,4,2,6]=>101010
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,1,5,3,2,4,6]=>101100
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,1,5,2,3,4,6]=>101000
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,1,4,5,3,2,6]=>100110
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,1,4,5,2,3,6]=>100100
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,1,4,3,5,2,6]=>101010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,1,3,4,5,2,6]=>100010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,1,4,3,2,5,6]=>101100
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,1,4,2,3,5,6]=>101000
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,1,3,4,2,5,6]=>100100
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,1,3,2,4,5,6]=>101000
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,1,2,3,4,5,6]=>100000
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[7,6,1,5,4,3,2]=>110111
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[7,6,1,5,4,2,3]=>110110
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[7,6,1,5,3,4,2]=>110101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[7,6,1,5,3,2,4]=>110110
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[7,6,1,5,2,3,4]=>110100
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[7,6,1,4,5,3,2]=>110011
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[7,6,1,4,5,2,3]=>110010
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[7,6,1,4,3,5,2]=>110101
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[7,6,1,3,4,5,2]=>110001
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[7,6,1,4,3,2,5]=>110110
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[7,6,1,4,2,3,5]=>110100
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[7,6,1,3,4,2,5]=>110010
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[7,6,1,3,2,4,5]=>110100
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[7,6,1,2,3,4,5]=>110000
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[6,7,1,5,4,3,2]=>010111
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[6,7,1,5,4,2,3]=>010110
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[6,7,1,5,3,4,2]=>010101
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[6,7,1,5,3,2,4]=>010110
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[6,7,1,5,2,3,4]=>010100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[6,7,1,4,5,3,2]=>010011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[6,7,1,4,5,2,3]=>010010
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,7,1,4,3,5,2]=>010101
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,7,1,3,4,5,2]=>010001
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[6,7,1,4,3,2,5]=>010110
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[6,7,1,4,2,3,5]=>010100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[6,7,1,3,4,2,5]=>010010
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[6,7,1,3,2,4,5]=>010100
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[6,7,1,2,3,4,5]=>010000
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[7,6,5,1,4,3,2]=>111011
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[7,6,5,1,4,2,3]=>111010
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[7,6,5,1,3,4,2]=>111001
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[7,6,5,1,3,2,4]=>111010
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[7,6,5,1,2,3,4]=>111000
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[7,5,6,1,4,3,2]=>101011
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[7,5,6,1,4,2,3]=>101010
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[7,5,6,1,3,4,2]=>101001
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[7,5,6,1,3,2,4]=>101010
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[7,5,6,1,2,3,4]=>101000
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[6,7,5,1,4,3,2]=>011011
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[6,7,5,1,4,2,3]=>011010
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[6,7,5,1,3,4,2]=>011001
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[6,7,5,1,3,2,4]=>011010
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[6,7,5,1,2,3,4]=>011000
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[6,5,7,1,4,3,2]=>101011
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[6,5,7,1,4,2,3]=>101010
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[6,5,7,1,3,4,2]=>101001
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[6,5,7,1,3,2,4]=>101010
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[6,5,7,1,2,3,4]=>101000
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,6,7,1,4,3,2]=>001011
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,6,7,1,4,2,3]=>001010
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[5,6,7,1,3,4,2]=>001001
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[5,6,7,1,3,2,4]=>001010
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[5,6,7,1,2,3,4]=>001000
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[7,6,5,4,1,3,2]=>111101
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[7,6,5,4,1,2,3]=>111100
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[7,6,4,5,1,3,2]=>110101
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[7,6,4,5,1,2,3]=>110100
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[7,5,6,4,1,3,2]=>101101
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[7,5,6,4,1,2,3]=>101100
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[7,5,4,6,1,3,2]=>110101
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[7,5,4,6,1,2,3]=>110100
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[7,4,5,6,1,3,2]=>100101
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[7,4,5,6,1,2,3]=>100100
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[6,7,5,4,1,3,2]=>011101
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[6,7,5,4,1,2,3]=>011100
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[6,7,4,5,1,3,2]=>010101
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[6,7,4,5,1,2,3]=>010100
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[6,5,7,4,1,3,2]=>101101
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[6,5,7,4,1,2,3]=>101100
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,6,7,4,1,3,2]=>001101
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,6,7,4,1,2,3]=>001100
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[6,5,4,7,1,3,2]=>110101
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[6,5,4,7,1,2,3]=>110100
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[6,4,5,7,1,3,2]=>100101
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[6,4,5,7,1,2,3]=>100100
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,6,4,7,1,3,2]=>010101
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,6,4,7,1,2,3]=>010100
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,6,7,1,3,2]=>100101
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,6,7,1,2,3]=>100100
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[4,5,6,7,1,3,2]=>000101
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[4,5,6,7,1,2,3]=>000100
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[7,6,5,4,3,1,2]=>111110
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[7,6,5,3,4,1,2]=>111010
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[7,6,4,5,3,1,2]=>110110
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[7,6,4,3,5,1,2]=>111010
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[7,6,3,4,5,1,2]=>110010
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[7,5,6,4,3,1,2]=>101110
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[7,5,6,3,4,1,2]=>101010
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[7,5,4,6,3,1,2]=>110110
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[7,4,5,6,3,1,2]=>100110
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[7,5,4,3,6,1,2]=>111010
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[7,5,3,4,6,1,2]=>110010
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[7,4,5,3,6,1,2]=>101010
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[7,4,3,5,6,1,2]=>110010
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[7,3,4,5,6,1,2]=>100010
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,7,5,4,3,1,2]=>011110
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,7,5,3,4,1,2]=>011010
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,7,4,5,3,1,2]=>010110
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,7,4,3,5,1,2]=>011010
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,7,3,4,5,1,2]=>010010
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,5,7,4,3,1,2]=>101110
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,5,7,3,4,1,2]=>101010
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[5,6,7,4,3,1,2]=>001110
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,6,7,3,4,1,2]=>001010
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,5,4,7,3,1,2]=>110110
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,5,7,3,1,2]=>100110
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[5,6,4,7,3,1,2]=>010110
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[5,4,6,7,3,1,2]=>100110
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[4,5,6,7,3,1,2]=>000110
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,4,3,7,1,2]=>111010
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,3,4,7,1,2]=>110010
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,4,5,3,7,1,2]=>101010
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,4,3,5,7,1,2]=>110010
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,3,4,5,7,1,2]=>100010
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[5,6,4,3,7,1,2]=>011010
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[5,6,3,4,7,1,2]=>010010
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[5,4,6,3,7,1,2]=>101010
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,5,6,3,7,1,2]=>001010
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[5,4,3,6,7,1,2]=>110010
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[5,3,4,6,7,1,2]=>100010
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[4,5,3,6,7,1,2]=>010010
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[4,3,5,6,7,1,2]=>100010
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>000010
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,6,5,4,3,2,1]=>111111
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,6,5,4,2,3,1]=>111101
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,6,5,3,4,2,1]=>111011
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,6,5,3,2,4,1]=>111101
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,6,5,2,3,4,1]=>111001
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,6,4,5,3,2,1]=>110111
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,6,4,5,2,3,1]=>110101
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,6,4,3,5,2,1]=>111011
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,6,3,4,5,2,1]=>110011
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,6,4,3,2,5,1]=>111101
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,6,4,2,3,5,1]=>111001
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,6,3,4,2,5,1]=>110101
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,6,3,2,4,5,1]=>111001
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,6,2,3,4,5,1]=>110001
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,5,6,4,3,2,1]=>101111
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,5,6,4,2,3,1]=>101101
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,5,6,3,4,2,1]=>101011
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,5,6,3,2,4,1]=>101101
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,5,6,2,3,4,1]=>101001
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,5,4,6,3,2,1]=>110111
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,5,4,6,2,3,1]=>110101
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,4,5,6,3,2,1]=>100111
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,4,5,6,2,3,1]=>100101
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,5,4,3,6,2,1]=>111011
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,5,3,4,6,2,1]=>110011
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,4,5,3,6,2,1]=>101011
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,4,3,5,6,2,1]=>110011
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,3,4,5,6,2,1]=>100011
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,5,4,3,2,6,1]=>111101
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,5,4,2,3,6,1]=>111001
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,5,3,4,2,6,1]=>110101
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,5,3,2,4,6,1]=>111001
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,5,2,3,4,6,1]=>110001
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,4,5,3,2,6,1]=>101101
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,4,5,2,3,6,1]=>101001
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,4,3,5,2,6,1]=>110101
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,3,4,5,2,6,1]=>100101
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,4,3,2,5,6,1]=>111001
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,4,2,3,5,6,1]=>110001
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,3,4,2,5,6,1]=>101001
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,3,2,4,5,6,1]=>110001
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,2,3,4,5,6,1]=>100001
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[6,7,5,4,3,2,1]=>011111
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[6,7,5,4,2,3,1]=>011101
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[6,7,5,3,4,2,1]=>011011
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[6,7,5,3,2,4,1]=>011101
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[6,7,5,2,3,4,1]=>011001
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[6,7,4,5,3,2,1]=>010111
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[6,7,4,5,2,3,1]=>010101
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[6,7,4,3,5,2,1]=>011011
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[6,7,3,4,5,2,1]=>010011
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,7,4,3,2,5,1]=>011101
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,7,4,2,3,5,1]=>011001
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,7,3,4,2,5,1]=>010101
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,7,3,2,4,5,1]=>011001
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,7,2,3,4,5,1]=>010001
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[6,5,7,4,3,2,1]=>101111
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[6,5,7,4,2,3,1]=>101101
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[6,5,7,3,4,2,1]=>101011
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[6,5,7,3,2,4,1]=>101101
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[6,5,7,2,3,4,1]=>101001
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[5,6,7,4,3,2,1]=>001111
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[5,6,7,4,2,3,1]=>001101
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[5,6,7,3,4,2,1]=>001011
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[5,6,7,3,2,4,1]=>001101
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[5,6,7,2,3,4,1]=>001001
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[6,5,4,7,3,2,1]=>110111
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[6,5,4,7,2,3,1]=>110101
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[6,4,5,7,3,2,1]=>100111
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[6,4,5,7,2,3,1]=>100101
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[5,6,4,7,3,2,1]=>010111
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[5,6,4,7,2,3,1]=>010101
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[5,4,6,7,3,2,1]=>100111
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[5,4,6,7,2,3,1]=>100101
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[4,5,6,7,3,2,1]=>000111
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[4,5,6,7,2,3,1]=>000101
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[6,5,4,3,7,2,1]=>111011
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[6,5,3,4,7,2,1]=>110011
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[6,4,5,3,7,2,1]=>101011
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[6,4,3,5,7,2,1]=>110011
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[6,3,4,5,7,2,1]=>100011
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[5,6,4,3,7,2,1]=>011011
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[5,6,3,4,7,2,1]=>010011
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[5,4,6,3,7,2,1]=>101011
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[4,5,6,3,7,2,1]=>001011
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[5,4,3,6,7,2,1]=>110011
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[5,3,4,6,7,2,1]=>100011
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[4,5,3,6,7,2,1]=>010011
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[4,3,5,6,7,2,1]=>100011
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[3,4,5,6,7,2,1]=>000011
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[6,5,4,3,2,7,1]=>111101
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[6,5,4,2,3,7,1]=>111001
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[6,5,3,4,2,7,1]=>110101
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[6,5,3,2,4,7,1]=>111001
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[6,5,2,3,4,7,1]=>110001
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[6,4,5,3,2,7,1]=>101101
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[6,4,5,2,3,7,1]=>101001
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[6,4,3,5,2,7,1]=>110101
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[6,3,4,5,2,7,1]=>100101
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[6,4,3,2,5,7,1]=>111001
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[6,4,2,3,5,7,1]=>110001
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[6,3,4,2,5,7,1]=>101001
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[6,3,2,4,5,7,1]=>110001
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[6,2,3,4,5,7,1]=>100001
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[5,6,4,3,2,7,1]=>011101
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[5,6,4,2,3,7,1]=>011001
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[5,6,3,4,2,7,1]=>010101
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,6,3,2,4,7,1]=>011001
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,6,2,3,4,7,1]=>010001
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[5,4,6,3,2,7,1]=>101101
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[5,4,6,2,3,7,1]=>101001
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[4,5,6,3,2,7,1]=>001101
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[4,5,6,2,3,7,1]=>001001
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[5,4,3,6,2,7,1]=>110101
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[5,3,4,6,2,7,1]=>100101
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[4,5,3,6,2,7,1]=>010101
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[4,3,5,6,2,7,1]=>100101
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[3,4,5,6,2,7,1]=>000101
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[5,4,3,2,6,7,1]=>111001
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[5,4,2,3,6,7,1]=>110001
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[5,3,4,2,6,7,1]=>101001
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[5,3,2,4,6,7,1]=>110001
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[5,2,3,4,6,7,1]=>100001
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[4,5,3,2,6,7,1]=>011001
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,5,2,3,6,7,1]=>010001
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[4,3,5,2,6,7,1]=>101001
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[3,4,5,2,6,7,1]=>001001
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[4,3,2,5,6,7,1]=>110001
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[4,2,3,5,6,7,1]=>100001
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,4,2,5,6,7,1]=>010001
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[3,2,4,5,6,7,1]=>100001
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>000001
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,8,7,6,5,4,3,2]=>0111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,8,7,6,5,4,2,3]=>0111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,8,7,6,5,3,4,2]=>0111101
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,8,7,6,5,3,2,4]=>0111110
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,8,7,6,5,2,3,4]=>0111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,8,7,6,4,5,3,2]=>0111011
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,8,7,6,4,5,2,3]=>0111010
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,8,7,6,4,3,5,2]=>0111101
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,8,7,6,3,4,5,2]=>0111001
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,8,7,6,4,3,2,5]=>0111110
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,8,7,6,4,2,3,5]=>0111100
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,8,7,6,3,4,2,5]=>0111010
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,8,7,6,3,2,4,5]=>0111100
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,8,7,6,2,3,4,5]=>0111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,8,7,5,6,4,3,2]=>0110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[1,8,7,5,6,4,2,3]=>0110110
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,8,7,5,6,3,4,2]=>0110101
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[1,8,7,5,6,2,3,4]=>0110100
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,8,7,5,4,6,3,2]=>0111011
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,8,7,5,4,6,2,3]=>0111010
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[1,8,7,4,5,6,3,2]=>0110011
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[1,8,7,4,5,6,2,3]=>0110010
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,8,7,5,4,3,6,2]=>0111101
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,8,7,5,3,4,6,2]=>0111001
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,8,7,4,5,3,6,2]=>0110101
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,8,7,4,3,5,6,2]=>0111001
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,8,7,3,4,5,6,2]=>0110001
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,8,7,5,4,3,2,6]=>0111110
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,8,7,5,3,4,2,6]=>0111010
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,8,7,5,3,2,4,6]=>0111100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,8,7,5,2,3,4,6]=>0111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,8,7,4,5,3,2,6]=>0110110
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,8,7,4,5,2,3,6]=>0110100
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,8,7,4,3,5,2,6]=>0111010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,8,7,3,4,5,2,6]=>0110010
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,8,7,4,3,2,5,6]=>0111100
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,8,7,4,2,3,5,6]=>0111000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,8,7,3,4,2,5,6]=>0110100
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,8,7,3,2,4,5,6]=>0111000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,8,7,2,3,4,5,6]=>0110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,8,6,7,5,4,3,2]=>0101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,8,6,7,5,4,2,3]=>0101110
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,8,6,7,5,3,4,2]=>0101101
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,8,6,7,5,3,2,4]=>0101110
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[1,8,6,7,5,2,3,4]=>0101100
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,8,6,7,4,5,3,2]=>0101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,8,6,7,4,5,2,3]=>0101010
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[1,8,6,7,3,4,5,2]=>0101001
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[1,8,6,7,4,2,3,5]=>0101100
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,8,6,7,3,4,2,5]=>0101010
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[1,8,6,7,3,2,4,5]=>0101100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[1,8,6,7,2,3,4,5]=>0101000
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,8,6,5,7,3,4,2]=>0110101
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,8,6,5,7,3,2,4]=>0110110
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,8,6,5,7,2,3,4]=>0110100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,8,5,6,7,4,3,2]=>0100111
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[1,8,5,6,7,4,2,3]=>0100110
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[1,8,5,6,7,3,4,2]=>0100101
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,8,5,6,7,3,2,4]=>0100110
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[1,8,5,6,7,2,3,4]=>0100100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,8,6,5,4,7,3,2]=>0111011
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[1,8,6,4,5,7,3,2]=>0110011
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[1,8,5,6,4,7,3,2]=>0101011
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[1,8,5,6,4,7,2,3]=>0101010
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,8,5,4,6,7,3,2]=>0110011
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[1,8,5,4,6,7,2,3]=>0110010
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,8,4,5,6,7,3,2]=>0100011
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[1,8,4,5,6,7,2,3]=>0100010
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,8,6,5,4,3,7,2]=>0111101
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[1,8,6,4,5,3,7,2]=>0110101
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,8,6,4,3,5,7,2]=>0111001
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[1,8,5,4,6,3,7,2]=>0110101
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[8,6,3,4,5,7,2,1]=>[1,8,4,5,6,3,7,2]=>0100101
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,8,5,4,3,6,7,2]=>0111001
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[1,8,4,5,3,6,7,2]=>0101001
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[1,8,4,3,5,6,7,2]=>0110001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[1,8,3,4,5,6,7,2]=>0100001
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,8,6,5,4,3,2,7]=>0111110
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,8,6,5,4,2,3,7]=>0111100
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[1,8,6,5,3,2,4,7]=>0111100
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[1,8,6,4,5,2,3,7]=>0110100
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[1,8,6,3,4,5,2,7]=>0110010
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[1,8,6,4,2,3,5,7]=>0111000
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[1,8,6,3,4,2,5,7]=>0110100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,8,6,3,2,4,5,7]=>0111000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,8,6,2,3,4,5,7]=>0110000
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,8,5,6,4,3,2,7]=>0101110
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[1,8,5,6,4,2,3,7]=>0101100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,8,5,6,2,3,4,7]=>0101000
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[1,8,5,4,6,3,2,7]=>0110110
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,8,4,5,6,3,2,7]=>0100110
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[1,8,5,4,3,6,2,7]=>0111010
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[7,4,5,3,6,8,2,1]=>[1,8,5,3,4,6,2,7]=>0110010
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,8,4,5,3,6,2,7]=>0101010
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[1,8,3,4,5,6,2,7]=>0100010
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,8,5,4,3,2,6,7]=>0111100
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[1,8,5,4,2,3,6,7]=>0111000
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[5,4,6,3,7,8,2,1]=>[1,8,5,3,2,4,6,7]=>0111000
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[1,8,4,5,3,2,6,7]=>0101100
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,8,3,4,5,2,6,7]=>0100100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[1,8,4,3,2,5,6,7]=>0111000
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[1,8,4,2,3,5,6,7]=>0110000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[1,8,3,4,2,5,6,7]=>0101000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,8,3,2,4,5,6,7]=>0110000
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,8,2,3,4,5,6,7]=>0100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,7,8,6,5,4,3,2]=>0011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[1,7,8,6,5,4,2,3]=>0011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,7,8,6,5,3,4,2]=>0011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,7,8,6,5,3,2,4]=>0011110
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,7,8,6,4,5,3,2]=>0011011
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,7,8,6,3,4,5,2]=>0011001
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,7,8,6,4,3,2,5]=>0011110
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[1,7,8,6,4,2,3,5]=>0011100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,7,8,6,3,4,2,5]=>0011010
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,2,3,1]=>[1,7,8,6,3,2,4,5]=>0011100
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[1,7,8,6,2,3,4,5]=>0011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,7,8,5,6,4,3,2]=>0010111
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,2,3,1]=>[1,7,8,5,6,4,2,3]=>0010110
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,7,8,5,6,3,4,2]=>0010101
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,7,8,5,6,3,2,4]=>0010110
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,7,8,5,4,6,3,2]=>0011011
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[1,7,8,4,5,6,2,3]=>0010010
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,7,8,5,4,3,6,2]=>0011101
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,7,8,5,3,4,6,2]=>0011001
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,7,8,4,5,3,6,2]=>0010101
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[1,7,8,3,4,5,6,2]=>0010001
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,7,8,5,4,3,2,6]=>0011110
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,2,3,1]=>[1,7,8,5,4,2,3,6]=>0011100
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,7,8,5,3,4,2,6]=>0011010
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,7,8,4,5,3,2,6]=>0010110
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[1,7,8,4,5,2,3,6]=>0010100
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[1,7,8,4,3,5,2,6]=>0011010
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,7,8,3,4,5,2,6]=>0010010
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,2,3,1]=>[1,7,8,4,2,3,5,6]=>0011000
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[1,7,8,3,4,2,5,6]=>0010100
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[1,7,8,2,3,4,5,6]=>0010000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,7,6,8,5,4,3,2]=>0101111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,7,6,8,5,4,2,3]=>0101110
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,7,6,8,4,5,3,2]=>0101011
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,7,6,8,4,5,2,3]=>0101010
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,7,6,8,4,3,5,2]=>0101101
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[1,7,6,8,3,4,5,2]=>0101001
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,7,6,8,4,3,2,5]=>0101110
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[1,7,6,8,4,2,3,5]=>0101100
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,7,6,8,3,4,2,5]=>0101010
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,7,6,8,3,2,4,5]=>0101100
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[1,7,6,8,2,3,4,5]=>0101000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,6,7,8,5,4,3,2]=>0001111
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,6,7,8,5,3,4,2]=>0001101
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[1,6,7,8,5,2,3,4]=>0001100
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[1,6,7,8,4,5,3,2]=>0001011
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[1,6,7,8,4,3,5,2]=>0001101
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,6,7,8,3,4,5,2]=>0001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,6,7,8,4,3,2,5]=>0001110
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[1,6,7,8,4,2,3,5]=>0001100
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[1,6,7,8,3,2,4,5]=>0001100
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,6,7,8,2,3,4,5]=>0001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,7,6,5,8,4,3,2]=>0110111
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,7,6,5,8,4,2,3]=>0110110
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,7,6,5,8,3,4,2]=>0110101
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[1,7,6,5,8,2,3,4]=>0110100
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,7,5,6,8,4,3,2]=>0100111
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,7,5,6,8,3,4,2]=>0100101
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,6,7,5,8,4,3,2]=>0010111
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[1,6,7,5,8,4,2,3]=>0010110
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,6,7,5,8,3,4,2]=>0010101
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,6,7,5,8,3,2,4]=>0010110
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,6,7,5,8,2,3,4]=>0010100
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,6,5,7,8,4,3,2]=>0100111
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[1,6,5,7,8,4,2,3]=>0100110
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,6,5,7,8,3,4,2]=>0100101
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[1,6,5,7,8,2,3,4]=>0100100
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,5,6,7,8,4,3,2]=>0000111
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[1,5,6,7,8,4,2,3]=>0000110
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,5,6,7,8,3,4,2]=>0000101
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[1,5,6,7,8,3,2,4]=>0000110
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[1,5,6,7,8,2,3,4]=>0000100
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,7,6,5,4,8,3,2]=>0111011
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,7,6,5,4,8,2,3]=>0111010
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[1,7,5,6,4,8,3,2]=>0101011
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[1,7,5,6,4,8,2,3]=>0101010
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[1,7,5,4,6,8,2,3]=>0110010
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[7,8,3,4,5,2,6,1]=>[1,7,4,5,6,8,2,3]=>0100010
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,2,3,6,1]=>[1,6,7,5,4,8,2,3]=>0011010
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[1,5,6,7,4,8,2,3]=>0001010
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[1,6,5,4,7,8,3,2]=>0110011
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[1,6,4,5,7,8,3,2]=>0100011
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[1,5,4,6,7,8,2,3]=>0100010
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[1,4,5,6,7,8,3,2]=>0000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[1,4,5,6,7,8,2,3]=>0000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,6,5,4,3,8,2]=>0111101
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[1,7,6,4,3,5,8,2]=>0111001
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,7,5,6,3,4,8,2]=>0101001
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,7,4,5,6,3,8,2]=>0100101
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,7,5,4,3,6,8,2]=>0111001
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,7,5,3,4,6,8,2]=>0110001
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[8,5,3,4,6,2,7,1]=>[1,7,4,5,3,6,8,2]=>0101001
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[1,7,3,4,5,6,8,2]=>0100001
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,6,7,5,4,3,8,2]=>0011101
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,6,7,5,3,4,8,2]=>0011001
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,6,7,4,5,3,8,2]=>0010101
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,2,3,7,1]=>[1,6,7,4,3,5,8,2]=>0011001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[1,6,5,7,4,3,8,2]=>0101101
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[8,6,3,4,2,5,7,1]=>[1,6,4,5,7,3,8,2]=>0100101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,5,6,4,7,3,8,2]=>0010101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[1,4,5,6,7,3,8,2]=>0000101
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,6,5,4,3,7,8,2]=>0111001
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[1,6,5,3,4,7,8,2]=>0110001
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[1,5,6,3,4,7,8,2]=>0010001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[1,5,4,3,6,7,8,2]=>0110001
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[1,5,3,4,6,7,8,2]=>0100001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[1,4,5,3,6,7,8,2]=>0010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[1,4,3,5,6,7,8,2]=>0100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[1,3,4,5,6,7,8,2]=>0000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,7,6,5,4,3,2,8]=>0111110
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[1,7,6,5,4,2,3,8]=>0111100
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,7,6,5,3,2,4,8]=>0111100
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,7,6,4,5,3,2,8]=>0110110
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,7,6,3,4,5,2,8]=>0110010
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[1,7,6,4,2,3,5,8]=>0111000
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,7,6,3,4,2,5,8]=>0110100
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,7,6,3,2,4,5,8]=>0111000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,7,6,2,3,4,5,8]=>0110000
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,7,5,6,4,3,2,8]=>0101110
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,7,5,6,3,4,2,8]=>0101010
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,7,5,6,3,2,4,8]=>0101100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[1,7,5,6,2,3,4,8]=>0101000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[6,7,4,3,5,2,8,1]=>[1,7,5,4,6,2,3,8]=>0110100
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>[1,7,4,5,6,3,2,8]=>0100110
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,7,5,4,3,6,2,8]=>0111010
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[1,7,3,4,5,6,2,8]=>0100010
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,7,5,4,3,2,6,8]=>0111100
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,7,5,3,2,4,6,8]=>0111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,7,5,2,3,4,6,8]=>0110000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,7,4,5,3,2,6,8]=>0101100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[1,7,4,5,2,3,6,8]=>0101000
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,7,4,3,2,5,6,8]=>0111000
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,7,4,2,3,5,6,8]=>0110000
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,7,3,4,2,5,6,8]=>0101000
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[1,7,3,2,4,5,6,8]=>0110000
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,7,2,3,4,5,6,8]=>0100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,6,7,5,4,3,2,8]=>0011110
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,6,7,5,3,2,4,8]=>0011100
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,6,7,4,5,3,2,8]=>0010110
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,6,7,4,5,2,3,8]=>0010100
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,6,7,4,3,5,2,8]=>0011010
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[1,6,7,4,3,2,5,8]=>0011100
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[1,6,7,3,4,2,5,8]=>0010100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,6,7,3,2,4,5,8]=>0011000
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,6,7,2,3,4,5,8]=>0010000
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[1,6,5,7,4,3,2,8]=>0101110
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,6,5,7,4,2,3,8]=>0101100
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,5,6,7,4,3,2,8]=>0001110
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[1,5,6,7,3,4,2,8]=>0001010
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[1,5,6,7,2,3,4,8]=>0001000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[1,6,5,4,7,2,3,8]=>0110100
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[7,6,3,4,2,5,8,1]=>[1,6,4,5,7,3,2,8]=>0100110
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,5,6,4,7,3,2,8]=>0010110
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,5,6,4,7,2,3,8]=>0010100
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[1,5,4,6,7,3,2,8]=>0100110
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,5,4,6,7,2,3,8]=>0100100
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,4,5,6,7,3,2,8]=>0000110
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,4,5,6,7,2,3,8]=>0000100
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[1,5,6,3,4,7,2,8]=>0010010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,5,4,6,3,7,2,8]=>0101010
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[1,4,5,6,3,7,2,8]=>0001010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[1,5,4,3,6,7,2,8]=>0110010
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[7,3,4,2,5,6,8,1]=>[1,5,3,4,6,7,2,8]=>0100010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[1,4,5,3,6,7,2,8]=>0010010
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[1,3,4,5,6,7,2,8]=>0000010
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,6,5,4,3,2,7,8]=>0111100
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,6,5,3,2,4,7,8]=>0111000
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[1,6,4,5,3,2,7,8]=>0101100
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[1,6,4,5,2,3,7,8]=>0101000
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[1,6,4,3,5,2,7,8]=>0110100
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[1,6,3,4,5,2,7,8]=>0100100
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,6,4,3,2,5,7,8]=>0111000
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,6,4,2,3,5,7,8]=>0110000
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[5,3,4,6,2,7,8,1]=>[1,6,3,4,2,5,7,8]=>0101000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[1,6,3,2,4,5,7,8]=>0110000
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,6,2,3,4,5,7,8]=>0100000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,5,6,4,3,2,7,8]=>0011100
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[1,5,6,4,2,3,7,8]=>0011000
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,5,6,3,4,2,7,8]=>0010100
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,5,6,3,2,4,7,8]=>0011000
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[1,5,6,2,3,4,7,8]=>0010000
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[1,5,4,6,3,2,7,8]=>0101100
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,4,5,6,3,2,7,8]=>0001100
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[1,4,5,6,2,3,7,8]=>0001000
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,4,5,3,6,2,7,8]=>0010100
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[6,3,2,4,5,7,8,1]=>[1,4,3,5,6,2,7,8]=>0100100
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,3,4,5,6,2,7,8]=>0000100
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,5,4,3,2,6,7,8]=>0111000
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[1,5,4,2,3,6,7,8]=>0110000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,5,3,4,2,6,7,8]=>0101000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[1,5,3,2,4,6,7,8]=>0110000
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,5,2,3,4,6,7,8]=>0100000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,4,5,3,2,6,7,8]=>0011000
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[1,4,5,2,3,6,7,8]=>0010000
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,3,4,5,2,6,7,8]=>0001000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,4,3,2,5,6,7,8]=>0110000
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,4,2,3,5,6,7,8]=>0100000
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[1,3,4,2,5,6,7,8]=>0010000
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,3,2,4,5,6,7,8]=>0100000
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>0000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[8,1,7,6,5,4,3,2]=>1011111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[8,1,7,6,5,4,2,3]=>1011110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[8,1,7,6,5,3,4,2]=>1011101
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[8,1,7,6,5,3,2,4]=>1011110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[8,1,7,6,5,2,3,4]=>1011100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[8,1,7,6,4,5,3,2]=>1011011
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[8,1,7,6,4,5,2,3]=>1011010
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[8,1,7,6,4,3,5,2]=>1011101
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[8,1,7,6,4,3,2,5]=>1011110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[8,1,7,6,4,2,3,5]=>1011100
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[8,1,7,6,3,2,4,5]=>1011100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[8,1,7,6,2,3,4,5]=>1011000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[8,1,7,5,6,4,3,2]=>1010111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[8,1,7,5,6,4,2,3]=>1010110
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[8,1,7,5,6,2,3,4]=>1010100
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[8,1,7,4,5,6,2,3]=>1010010
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[8,1,7,4,3,5,6,2]=>1011001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[8,1,7,5,4,3,2,6]=>1011110
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[8,1,7,5,4,2,3,6]=>1011100
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[8,1,7,5,3,2,4,6]=>1011100
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[8,1,7,4,5,3,2,6]=>1010110
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[8,1,7,4,5,2,3,6]=>1010100
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[8,1,7,3,4,5,2,6]=>1010010
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[8,1,7,4,2,3,5,6]=>1011000
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[8,1,7,3,2,4,5,6]=>1011000
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[8,1,7,2,3,4,5,6]=>1010000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[8,1,6,7,5,4,3,2]=>1001111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[8,1,6,7,5,4,2,3]=>1001110
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,4,1,2]=>[8,1,6,7,5,3,4,2]=>1001101
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[8,1,6,7,5,3,2,4]=>1001110
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[8,1,6,7,5,2,3,4]=>1001100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[8,1,6,7,4,5,3,2]=>1001011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[8,1,6,7,4,5,2,3]=>1001010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[8,1,6,7,4,3,2,5]=>1001110
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[8,1,6,7,4,2,3,5]=>1001100
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[8,1,6,7,3,4,2,5]=>1001010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[8,1,6,7,3,2,4,5]=>1001100
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[8,1,6,7,2,3,4,5]=>1001000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[8,1,6,5,7,4,3,2]=>1010111
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2]=>[8,1,6,5,7,3,4,2]=>1010101
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[8,1,5,6,7,4,3,2]=>1000111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[8,1,5,6,7,4,2,3]=>1000110
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[8,1,5,6,7,3,4,2]=>1000101
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[8,1,5,6,7,3,2,4]=>1000110
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[8,1,5,6,7,2,3,4]=>1000100
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[8,1,6,5,4,7,2,3]=>1011010
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[8,1,6,4,5,7,2,3]=>1010010
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[8,1,5,6,4,7,3,2]=>1001011
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[8,1,5,6,4,7,2,3]=>1001010
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[8,1,5,4,6,7,2,3]=>1010010
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[8,1,4,5,6,7,3,2]=>1000011
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[8,1,4,5,6,7,2,3]=>1000010
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[8,1,6,4,3,5,7,2]=>1011001
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[8,1,5,4,6,3,7,2]=>1010101
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[8,6,3,4,5,7,1,2]=>[8,1,4,5,6,3,7,2]=>1000101
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[8,1,5,4,3,6,7,2]=>1011001
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[8,1,4,5,3,6,7,2]=>1001001
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[8,1,4,3,5,6,7,2]=>1010001
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[8,1,3,4,5,6,7,2]=>1000001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[8,1,6,5,4,3,2,7]=>1011110
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[8,1,6,5,2,3,4,7]=>1011000
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,3,8,1,2]=>[8,1,6,4,5,3,2,7]=>1010110
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[8,1,6,4,5,2,3,7]=>1010100
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[8,1,6,4,3,5,2,7]=>1011010
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[8,1,6,3,4,5,2,7]=>1010010
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[8,1,6,4,2,3,5,7]=>1011000
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[8,1,6,3,4,2,5,7]=>1010100
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[8,1,6,3,2,4,5,7]=>1011000
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[8,1,6,2,3,4,5,7]=>1010000
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[8,1,5,6,4,3,2,7]=>1001110
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[8,1,5,6,4,2,3,7]=>1001100
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[8,1,5,6,3,2,4,7]=>1001100
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[8,1,4,5,6,3,2,7]=>1000110
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[8,1,4,5,6,2,3,7]=>1000100
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[8,1,5,4,3,6,2,7]=>1011010
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[7,4,5,3,6,8,1,2]=>[8,1,5,3,4,6,2,7]=>1010010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[8,1,4,5,3,6,2,7]=>1001010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[8,1,5,4,3,2,6,7]=>1011100
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[8,1,5,4,2,3,6,7]=>1011000
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[8,1,5,3,4,2,6,7]=>1010100
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[8,1,5,3,2,4,6,7]=>1011000
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[8,1,5,2,3,4,6,7]=>1010000
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[8,1,4,5,3,2,6,7]=>1001100
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[8,1,4,5,2,3,6,7]=>1001000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[8,1,4,3,5,2,6,7]=>1010100
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[8,1,3,4,5,2,6,7]=>1000100
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[8,1,4,3,2,5,6,7]=>1011000
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[8,1,4,2,3,5,6,7]=>1010000
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[8,1,3,2,4,5,6,7]=>1010000
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[8,1,2,3,4,5,6,7]=>1000000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[8,7,1,6,5,4,3,2]=>1101111
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[8,7,1,6,5,3,2,4]=>1101110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[8,7,1,6,5,2,3,4]=>1101100
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[8,7,1,6,4,5,3,2]=>1101011
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[8,7,1,6,4,5,2,3]=>1101010
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[8,7,1,6,4,3,5,2]=>1101101
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[8,7,1,6,4,3,2,5]=>1101110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[8,7,1,6,4,2,3,5]=>1101100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[8,7,1,6,3,4,2,5]=>1101010
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[8,7,1,6,2,3,4,5]=>1101000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[8,7,1,5,6,4,3,2]=>1100111
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[8,7,1,5,6,3,2,4]=>1100110
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,2,1,3]=>[8,7,1,5,6,2,3,4]=>1100100
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[8,7,1,5,4,6,3,2]=>1101011
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[8,7,1,5,4,6,2,3]=>1101010
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[8,7,1,4,5,6,3,2]=>1100011
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[8,7,1,4,5,6,2,3]=>1100010
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[8,7,1,4,5,3,6,2]=>1100101
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[8,7,1,4,3,5,6,2]=>1101001
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[8,7,1,3,4,5,6,2]=>1100001
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[8,7,1,5,4,2,3,6]=>1101100
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[8,7,1,5,2,3,4,6]=>1101000
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[8,7,1,4,5,3,2,6]=>1100110
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[8,7,1,4,5,2,3,6]=>1100100
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[8,7,1,4,3,5,2,6]=>1101010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[8,7,1,3,4,5,2,6]=>1100010
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[8,7,1,4,3,2,5,6]=>1101100
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[8,7,1,4,2,3,5,6]=>1101000
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[8,7,1,3,2,4,5,6]=>1101000
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[8,7,1,2,3,4,5,6]=>1100000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[7,8,1,6,5,4,3,2]=>0101111
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[7,8,1,6,5,3,2,4]=>0101110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[7,8,1,6,5,2,3,4]=>0101100
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[7,8,1,6,4,5,2,3]=>0101010
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[7,8,1,6,3,4,5,2]=>0101001
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[7,8,1,6,4,2,3,5]=>0101100
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[7,8,1,6,3,4,2,5]=>0101010
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[7,8,1,6,2,3,4,5]=>0101000
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[7,8,1,5,6,4,3,2]=>0100111
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[7,8,1,5,6,4,2,3]=>0100110
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[7,8,1,5,6,3,4,2]=>0100101
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[7,8,1,5,6,2,3,4]=>0100100
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[7,8,1,5,4,6,3,2]=>0101011
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[7,8,1,5,4,6,2,3]=>0101010
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[7,8,1,4,5,6,3,2]=>0100011
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[7,8,1,4,5,6,2,3]=>0100010
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[7,8,1,5,4,3,6,2]=>0101101
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[7,8,1,5,3,4,6,2]=>0101001
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[7,8,1,4,5,3,6,2]=>0100101
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[7,8,1,4,3,5,6,2]=>0101001
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[7,8,1,3,4,5,6,2]=>0100001
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[7,8,1,5,4,2,3,6]=>0101100
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[7,8,1,5,3,2,4,6]=>0101100
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[7,8,1,4,5,3,2,6]=>0100110
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[7,8,1,4,5,2,3,6]=>0100100
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[7,8,1,4,3,5,2,6]=>0101010
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[7,8,1,3,4,5,2,6]=>0100010
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[7,8,1,4,3,2,5,6]=>0101100
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[7,8,1,4,2,3,5,6]=>0101000
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[7,8,1,3,2,4,5,6]=>0101000
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[7,8,1,2,3,4,5,6]=>0100000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[8,7,6,1,5,4,3,2]=>1110111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[8,7,6,1,5,4,2,3]=>1110110
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[8,7,6,1,5,3,4,2]=>1110101
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[8,7,6,1,5,3,2,4]=>1110110
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[8,7,6,1,5,2,3,4]=>1110100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[8,7,6,1,4,5,3,2]=>1110011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[8,7,6,1,4,5,2,3]=>1110010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[8,7,6,1,4,3,5,2]=>1110101
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[8,7,6,1,3,4,5,2]=>1110001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[8,7,6,1,4,3,2,5]=>1110110
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[8,7,6,1,4,2,3,5]=>1110100
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[8,7,6,1,3,4,2,5]=>1110010
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[8,7,6,1,3,2,4,5]=>1110100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[8,7,6,1,2,3,4,5]=>1110000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[8,6,7,1,5,4,3,2]=>1010111
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[8,6,7,1,5,3,4,2]=>1010101
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[8,6,7,1,5,3,2,4]=>1010110
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[8,6,7,1,5,2,3,4]=>1010100
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[8,6,7,1,4,5,3,2]=>1010011
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[8,6,7,1,4,5,2,3]=>1010010
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[8,6,7,1,4,3,5,2]=>1010101
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[8,6,7,1,3,4,5,2]=>1010001
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[8,6,7,1,4,3,2,5]=>1010110
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[8,6,7,1,4,2,3,5]=>1010100
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[8,6,7,1,3,4,2,5]=>1010010
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[8,6,7,1,2,3,4,5]=>1010000
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[7,8,6,1,5,4,3,2]=>0110111
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[7,8,6,1,5,3,4,2]=>0110101
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[7,8,6,1,5,3,2,4]=>0110110
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[7,8,6,1,5,2,3,4]=>0110100
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[7,8,6,1,4,5,3,2]=>0110011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[7,8,6,1,4,5,2,3]=>0110010
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[7,8,6,1,4,3,5,2]=>0110101
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[7,8,6,1,3,4,5,2]=>0110001
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[7,8,6,1,4,3,2,5]=>0110110
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[7,8,6,1,4,2,3,5]=>0110100
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[7,8,6,1,3,2,4,5]=>0110100
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[7,8,6,1,2,3,4,5]=>0110000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[7,6,8,1,5,4,3,2]=>1010111
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[7,6,8,1,5,3,4,2]=>1010101
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[7,6,8,1,4,5,3,2]=>1010011
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[7,6,8,1,4,5,2,3]=>1010010
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[7,6,8,1,4,3,5,2]=>1010101
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[7,6,8,1,3,4,5,2]=>1010001
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[7,6,8,1,4,3,2,5]=>1010110
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[7,6,8,1,4,2,3,5]=>1010100
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[7,6,8,1,3,2,4,5]=>1010100
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[7,6,8,1,2,3,4,5]=>1010000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[6,7,8,1,5,4,3,2]=>0010111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[6,7,8,1,5,4,2,3]=>0010110
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[6,7,8,1,5,3,4,2]=>0010101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[6,7,8,1,5,3,2,4]=>0010110
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[6,7,8,1,5,2,3,4]=>0010100
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,7,8,1,4,5,3,2]=>0010011
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,7,8,1,4,5,2,3]=>0010010
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[6,7,8,1,4,3,5,2]=>0010101
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[6,7,8,1,3,4,5,2]=>0010001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[6,7,8,1,4,3,2,5]=>0010110
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[6,7,8,1,4,2,3,5]=>0010100
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[6,7,8,1,3,4,2,5]=>0010010
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[6,7,8,1,3,2,4,5]=>0010100
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[6,7,8,1,2,3,4,5]=>0010000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,1,4,3,2]=>1111011
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[8,7,6,5,1,4,2,3]=>1111010
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[8,7,6,5,1,3,4,2]=>1111001
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[8,7,6,5,1,3,2,4]=>1111010
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[8,7,6,5,1,2,3,4]=>1111000
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[8,7,5,6,1,4,3,2]=>1101011
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[8,7,5,6,1,4,2,3]=>1101010
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[8,7,5,6,1,3,4,2]=>1101001
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[8,7,5,6,1,2,3,4]=>1101000
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[8,6,7,5,1,4,3,2]=>1011011
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[8,6,7,5,1,4,2,3]=>1011010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[8,6,7,5,1,3,2,4]=>1011010
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[8,6,7,5,1,2,3,4]=>1011000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[8,6,5,7,1,4,3,2]=>1101011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[8,6,5,7,1,3,2,4]=>1101010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[8,6,5,7,1,2,3,4]=>1101000
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[8,5,6,7,1,4,3,2]=>1001011
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[8,5,6,7,1,4,2,3]=>1001010
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[8,5,6,7,1,2,3,4]=>1001000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[7,8,6,5,1,4,3,2]=>0111011
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[7,8,6,5,1,4,2,3]=>0111010
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[7,8,6,5,1,2,3,4]=>0111000
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[7,8,5,6,1,4,3,2]=>0101011
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[7,8,5,6,1,3,4,2]=>0101001
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[7,8,5,6,1,3,2,4]=>0101010
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[7,8,5,6,1,2,3,4]=>0101000
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[7,6,8,5,1,4,3,2]=>1011011
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[7,6,8,5,1,4,2,3]=>1011010
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[7,6,8,5,1,3,2,4]=>1011010
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[7,6,8,5,1,2,3,4]=>1011000
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[6,7,8,5,1,4,3,2]=>0011011
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[6,7,8,5,1,4,2,3]=>0011010
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[6,7,8,5,1,3,2,4]=>0011010
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[6,7,8,5,1,2,3,4]=>0011000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[7,6,5,8,1,4,3,2]=>1101011
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[7,6,5,8,1,4,2,3]=>1101010
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[7,6,5,8,1,3,4,2]=>1101001
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[7,6,5,8,1,3,2,4]=>1101010
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[7,6,5,8,1,2,3,4]=>1101000
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[7,5,6,8,1,4,3,2]=>1001011
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[7,5,6,8,1,4,2,3]=>1001010
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[7,5,6,8,1,3,4,2]=>1001001
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[7,5,6,8,1,3,2,4]=>1001010
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[7,5,6,8,1,2,3,4]=>1001000
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[6,7,5,8,1,4,3,2]=>0101011
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[6,7,5,8,1,4,2,3]=>0101010
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[6,7,5,8,1,3,4,2]=>0101001
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[6,7,5,8,1,3,2,4]=>0101010
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[6,7,5,8,1,2,3,4]=>0101000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[6,5,7,8,1,4,3,2]=>1001011
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[6,5,7,8,1,4,2,3]=>1001010
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[6,5,7,8,1,3,4,2]=>1001001
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[6,5,7,8,1,2,3,4]=>1001000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,6,7,8,1,4,3,2]=>0001011
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,6,7,8,1,4,2,3]=>0001010
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,6,7,8,1,3,4,2]=>0001001
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,6,7,8,1,3,2,4]=>0001010
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,6,7,8,1,2,3,4]=>0001000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[8,7,6,5,4,1,3,2]=>1111101
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[8,7,6,5,4,1,2,3]=>1111100
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[8,7,6,4,5,1,3,2]=>1110101
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[8,7,5,6,4,1,3,2]=>1101101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[8,7,5,4,6,1,3,2]=>1110101
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[8,7,5,4,6,1,2,3]=>1110100
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[8,7,4,5,6,1,3,2]=>1100101
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[8,7,4,5,6,1,2,3]=>1100100
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[8,6,7,5,4,1,3,2]=>1011101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[8,6,7,4,5,1,3,2]=>1010101
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[8,6,7,4,5,1,2,3]=>1010100
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[8,6,5,7,4,1,3,2]=>1101101
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[8,6,5,7,4,1,2,3]=>1101100
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[8,5,6,7,4,1,3,2]=>1001101
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[8,5,6,7,4,1,2,3]=>1001100
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[8,6,5,4,7,1,3,2]=>1110101
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[8,6,4,5,7,1,2,3]=>1100100
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[8,5,6,4,7,1,2,3]=>1010100
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[8,5,4,6,7,1,2,3]=>1100100
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[8,4,5,6,7,1,2,3]=>1000100
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[7,8,6,5,4,1,3,2]=>0111101
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[7,8,6,5,4,1,2,3]=>0111100
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[7,8,5,6,4,1,3,2]=>0101101
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[7,8,5,6,4,1,2,3]=>0101100
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[7,8,5,4,6,1,2,3]=>0110100
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[7,8,4,5,6,1,3,2]=>0100101
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[7,8,4,5,6,1,2,3]=>0100100
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[7,6,8,5,4,1,3,2]=>1011101
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[7,6,8,5,4,1,2,3]=>1011100
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,7,8,5,4,1,2,3]=>0011100
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,7,8,4,5,1,2,3]=>0010100
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[7,6,5,8,4,1,3,2]=>1101101
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[7,6,5,8,4,1,2,3]=>1101100
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[7,5,6,8,4,1,3,2]=>1001101
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[7,5,6,8,4,1,2,3]=>1001100
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,7,5,8,4,1,3,2]=>0101101
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,7,5,8,4,1,2,3]=>0101100
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,5,7,8,4,1,3,2]=>1001101
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,5,7,8,4,1,2,3]=>1001100
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,6,7,8,4,1,3,2]=>0001101
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,6,7,8,4,1,2,3]=>0001100
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[7,6,5,4,8,1,3,2]=>1110101
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[7,6,5,4,8,1,2,3]=>1110100
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[7,6,4,5,8,1,3,2]=>1100101
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[7,6,4,5,8,1,2,3]=>1100100
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[7,5,6,4,8,1,2,3]=>1010100
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[7,5,4,6,8,1,2,3]=>1100100
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[7,4,5,6,8,1,3,2]=>1000101
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[7,4,5,6,8,1,2,3]=>1000100
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[6,7,5,4,8,1,3,2]=>0110101
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,7,5,4,8,1,2,3]=>0110100
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[6,7,4,5,8,1,3,2]=>0100101
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,7,4,5,8,1,2,3]=>0100100
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[6,5,7,4,8,1,3,2]=>1010101
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,7,4,8,1,2,3]=>1010100
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[5,6,7,4,8,1,3,2]=>0010101
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[5,6,7,4,8,1,2,3]=>0010100
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,7,8,1,3,2]=>1100101
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,7,8,1,2,3]=>1100100
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[6,4,5,7,8,1,3,2]=>1000101
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,4,5,7,8,1,2,3]=>1000100
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[5,6,4,7,8,1,2,3]=>0100100
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[5,4,6,7,8,1,3,2]=>1000101
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[5,4,6,7,8,1,2,3]=>1000100
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>0000101
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[4,5,6,7,8,1,2,3]=>0000100
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,1,2]=>1111110
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[8,7,6,5,3,4,1,2]=>1111010
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[8,7,6,4,5,3,1,2]=>1110110
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[8,7,6,3,4,5,1,2]=>1110010
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[8,7,5,6,4,3,1,2]=>1101110
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[8,7,5,6,3,4,1,2]=>1101010
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[8,7,5,4,6,3,1,2]=>1110110
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[8,7,4,3,5,6,1,2]=>1110010
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[8,7,3,4,5,6,1,2]=>1100010
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[8,6,7,5,4,3,1,2]=>1011110
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[8,6,7,4,5,3,1,2]=>1010110
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[8,6,7,3,4,5,1,2]=>1010010
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[8,6,5,7,4,3,1,2]=>1101110
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[8,5,6,7,3,4,1,2]=>1001010
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[8,6,3,4,2,5,1,7]=>[8,6,4,5,7,3,1,2]=>1100110
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[8,5,6,4,7,3,1,2]=>1010110
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[8,5,4,6,7,3,1,2]=>1100110
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[8,6,5,4,3,7,1,2]=>1111010
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[8,4,3,2,5,6,1,7]=>[8,5,4,3,6,7,1,2]=>1110010
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[8,5,3,4,6,7,1,2]=>1100010
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[8,4,3,5,6,7,1,2]=>1100010
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[8,3,4,5,6,7,1,2]=>1000010
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,8,6,5,4,3,1,2]=>0111110
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,8,5,6,4,3,1,2]=>0101110
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,8,5,6,3,4,1,2]=>0101010
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,8,5,3,4,6,1,2]=>0110010
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[7,8,4,5,3,6,1,2]=>0101010
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[7,8,4,3,5,6,1,2]=>0110010
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[7,8,3,4,5,6,1,2]=>0100010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,6,8,5,4,3,1,2]=>1011110
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,6,8,5,3,4,1,2]=>1011010
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[6,7,8,5,4,3,1,2]=>0011110
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[6,7,8,5,3,4,1,2]=>0011010
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[6,7,8,4,5,3,1,2]=>0010110
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[6,7,8,4,3,5,1,2]=>0011010
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,6,5,8,4,3,1,2]=>1101110
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[7,6,5,8,3,4,1,2]=>1101010
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,5,6,8,4,3,1,2]=>1001110
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,5,6,8,3,4,1,2]=>1001010
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[6,7,5,8,4,3,1,2]=>0101110
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[6,7,5,8,3,4,1,2]=>0101010
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[6,5,7,8,4,3,1,2]=>1001110
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[6,5,7,8,3,4,1,2]=>1001010
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[5,6,7,8,4,3,1,2]=>0001110
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[5,6,7,8,3,4,1,2]=>0001010
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,6,5,4,8,3,1,2]=>1110110
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,6,4,5,8,3,1,2]=>1100110
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,6,4,8,3,1,2]=>1010110
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[6,7,4,5,8,3,1,2]=>0100110
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[6,5,7,4,8,3,1,2]=>1010110
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[6,5,4,7,8,3,1,2]=>1100110
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,1,2]=>0000110
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[7,6,5,4,3,8,1,2]=>1111010
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[7,6,5,3,4,8,1,2]=>1110010
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[7,6,4,3,5,8,1,2]=>1110010
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[7,6,3,4,5,8,1,2]=>1100010
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[8,5,4,2,3,1,6,7]=>[7,5,6,4,3,8,1,2]=>1011010
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[7,5,6,3,4,8,1,2]=>1010010
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[7,3,4,5,6,8,1,2]=>1000010
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[6,7,4,5,3,8,1,2]=>0101010
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[6,5,7,4,3,8,1,2]=>1011010
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[5,6,7,4,3,8,1,2]=>0011010
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[5,6,7,3,4,8,1,2]=>0010010
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[5,6,4,7,3,8,1,2]=>0101010
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[5,4,6,7,3,8,1,2]=>1001010
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[4,5,6,7,3,8,1,2]=>0001010
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[6,5,4,3,7,8,1,2]=>1110010
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[6,5,3,4,7,8,1,2]=>1100010
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[6,4,3,5,7,8,1,2]=>1100010
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[6,3,4,5,7,8,1,2]=>1000010
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[5,6,4,3,7,8,1,2]=>0110010
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[5,6,3,4,7,8,1,2]=>0100010
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[5,4,6,3,7,8,1,2]=>1010010
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,1,2]=>0010010
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[5,4,3,6,7,8,1,2]=>1100010
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[5,3,4,6,7,8,1,2]=>1000010
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[4,5,3,6,7,8,1,2]=>0100010
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[4,3,5,6,7,8,1,2]=>1000010
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>0000010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,1]=>1111111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[8,7,6,5,4,2,3,1]=>1111101
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[8,7,6,5,3,4,2,1]=>1111011
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[8,7,6,5,3,2,4,1]=>1111101
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,7,6,5,2,3,4,1]=>1111001
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,7,6,4,5,3,2,1]=>1110111
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,7,6,4,5,2,3,1]=>1110101
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[8,7,6,4,3,5,2,1]=>1111011
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,7,6,3,4,5,2,1]=>1110011
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,7,6,4,3,2,5,1]=>1111101
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[8,7,6,4,2,3,5,1]=>1111001
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[8,7,6,3,4,2,5,1]=>1110101
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[8,7,6,3,2,4,5,1]=>1111001
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,7,6,2,3,4,5,1]=>1110001
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,7,5,6,4,3,2,1]=>1101111
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[8,7,5,6,4,2,3,1]=>1101101
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,7,5,6,3,4,2,1]=>1101011
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[8,7,5,6,3,2,4,1]=>1101101
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[8,7,5,6,2,3,4,1]=>1101001
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,7,5,4,6,3,2,1]=>1110111
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[8,7,5,4,6,2,3,1]=>1110101
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,7,4,5,6,3,2,1]=>1100111
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[8,7,5,4,3,6,2,1]=>1111011
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[8,7,5,3,4,6,2,1]=>1110011
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[8,7,4,3,5,6,2,1]=>1110011
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,7,3,4,5,6,2,1]=>1100011
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,7,5,4,3,2,6,1]=>1111101
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[8,7,5,3,4,2,6,1]=>1110101
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,7,5,3,2,4,6,1]=>1111001
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[8,7,4,3,5,2,6,1]=>1110101
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,7,4,3,2,5,6,1]=>1111001
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,7,2,3,4,5,6,1]=>1100001
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,6,7,5,4,3,2,1]=>1011111
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[8,6,7,5,4,2,3,1]=>1011101
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,6,7,5,3,4,2,1]=>1011011
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[8,6,7,5,2,3,4,1]=>1011001
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,6,7,4,5,3,2,1]=>1010111
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,6,7,4,5,2,3,1]=>1010101
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,2,3,1,8]=>[8,6,7,4,3,5,2,1]=>1011011
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,6,7,3,4,5,2,1]=>1010011
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[8,6,7,4,3,2,5,1]=>1011101
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,6,7,4,2,3,5,1]=>1011001
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[8,6,7,3,4,2,5,1]=>1010101
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[8,6,7,3,2,4,5,1]=>1011001
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[8,6,7,2,3,4,5,1]=>1010001
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,6,5,7,4,3,2,1]=>1101111
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[8,6,5,7,3,2,4,1]=>1101101
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,6,5,7,2,3,4,1]=>1101001
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,5,6,7,4,3,2,1]=>1001111
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,5,6,7,4,2,3,1]=>1001101
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,5,6,7,3,4,2,1]=>1001011
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,5,6,7,3,2,4,1]=>1001101
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,5,6,7,2,3,4,1]=>1001001
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[8,6,5,4,7,3,2,1]=>1110111
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[8,6,5,4,7,2,3,1]=>1110101
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[8,6,4,5,7,2,3,1]=>1100101
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[8,5,6,4,7,3,2,1]=>1010111
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[8,5,6,4,7,2,3,1]=>1010101
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[8,5,4,6,7,3,2,1]=>1100111
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,4,5,6,7,3,2,1]=>1000111
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[8,4,5,6,7,2,3,1]=>1000101
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,6,5,4,3,7,2,1]=>1111011
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[8,6,4,5,3,7,2,1]=>1101011
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[8,6,4,3,5,7,2,1]=>1110011
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[8,5,4,3,6,7,2,1]=>1110011
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[7,3,2,4,5,6,1,8]=>[8,4,3,5,6,7,2,1]=>1100011
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[8,3,4,5,6,7,2,1]=>1000011
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,6,5,4,3,2,7,1]=>1111101
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[8,6,5,4,2,3,7,1]=>1111001
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,6,5,3,2,4,7,1]=>1111001
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[8,6,4,5,2,3,7,1]=>1101001
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[8,6,4,3,5,2,7,1]=>1110101
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[8,6,3,4,5,2,7,1]=>1100101
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,6,4,3,2,5,7,1]=>1111001
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,6,4,2,3,5,7,1]=>1110001
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,6,2,3,4,5,7,1]=>1100001
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[8,5,6,4,3,2,7,1]=>1011101
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[6,4,5,2,3,7,1,8]=>[8,5,6,3,4,2,7,1]=>1010101
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[8,5,4,6,3,2,7,1]=>1101101
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[6,4,3,2,5,7,1,8]=>[8,5,4,3,6,2,7,1]=>1110101
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[8,4,5,3,6,2,7,1]=>1010101
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[8,4,3,5,6,2,7,1]=>1100101
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[8,3,4,5,6,2,7,1]=>1000101
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,5,4,3,2,6,7,1]=>1111001
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[8,5,4,2,3,6,7,1]=>1110001
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[8,5,3,4,2,6,7,1]=>1101001
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,5,2,3,4,6,7,1]=>1100001
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[8,4,5,3,2,6,7,1]=>1011001
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[8,4,5,2,3,6,7,1]=>1010001
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[8,3,4,5,2,6,7,1]=>1001001
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,4,3,2,5,6,7,1]=>1110001
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[8,4,2,3,5,6,7,1]=>1100001
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[8,3,4,2,5,6,7,1]=>1010001
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[8,3,2,4,5,6,7,1]=>1100001
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,2,3,4,5,6,7,1]=>1000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[7,8,6,5,4,3,2,1]=>0111111
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[7,8,6,5,4,2,3,1]=>0111101
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[7,8,6,5,3,4,2,1]=>0111011
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[7,8,6,5,3,2,4,1]=>0111101
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,3,1,2,8]=>[7,8,6,4,3,5,2,1]=>0111011
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[7,8,6,3,4,5,2,1]=>0110011
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[7,8,6,3,2,4,5,1]=>0111001
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[7,8,6,2,3,4,5,1]=>0110001
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[7,8,5,6,4,3,2,1]=>0101111
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[7,8,5,6,3,4,2,1]=>0101011
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[5,6,7,3,4,1,2,8]=>[7,8,5,6,2,3,4,1]=>0101001
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[7,8,4,5,6,2,3,1]=>0100101
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[7,8,5,4,3,6,2,1]=>0111011
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[7,8,5,3,4,6,2,1]=>0110011
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[7,3,4,5,6,1,2,8]=>[7,8,3,4,5,6,2,1]=>0100011
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[7,8,5,4,3,2,6,1]=>0111101
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[7,8,5,3,4,2,6,1]=>0110101
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[7,8,4,2,3,5,6,1]=>0110001
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[5,3,4,6,7,1,2,8]=>[7,8,3,4,2,5,6,1]=>0101001
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[4,3,5,6,7,1,2,8]=>[7,8,3,2,4,5,6,1]=>0110001
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[7,8,2,3,4,5,6,1]=>0100001
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[7,6,8,5,4,3,2,1]=>1011111
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[7,6,8,5,4,2,3,1]=>1011101
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[7,6,8,5,3,2,4,1]=>1011101
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[7,6,8,5,2,3,4,1]=>1011001
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[7,6,8,4,5,3,2,1]=>1010111
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[7,6,8,4,5,2,3,1]=>1010101
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[7,6,8,4,3,5,2,1]=>1011011
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[7,6,8,3,4,5,2,1]=>1010011
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[7,6,8,4,3,2,5,1]=>1011101
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,2,1,3,8]=>[7,6,8,4,2,3,5,1]=>1011001
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[7,6,8,2,3,4,5,1]=>1010001
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[6,7,8,5,4,3,2,1]=>0011111
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[6,7,8,5,3,2,4,1]=>0011101
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[6,7,8,5,2,3,4,1]=>0011001
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[6,7,8,4,3,5,2,1]=>0011011
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[6,7,8,3,4,5,2,1]=>0010011
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[6,7,8,4,3,2,5,1]=>0011101
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[6,7,8,4,2,3,5,1]=>0011001
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[6,7,8,3,4,2,5,1]=>0010101
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[6,7,8,3,2,4,5,1]=>0011001
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[6,7,8,2,3,4,5,1]=>0010001
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[7,6,5,8,4,3,2,1]=>1101111
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[6,7,5,3,2,1,4,8]=>[7,6,5,8,4,2,3,1]=>1101101
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[7,6,5,8,3,4,2,1]=>1101011
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[7,6,5,8,2,3,4,1]=>1101001
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[7,5,6,8,4,3,2,1]=>1001111
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[7,5,6,8,4,2,3,1]=>1001101
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[6,7,5,8,4,3,2,1]=>0101111
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[6,7,5,3,1,2,4,8]=>[6,7,5,8,4,2,3,1]=>0101101
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[6,7,5,8,3,4,2,1]=>0101011
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[6,7,5,8,2,3,4,1]=>0101001
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[6,5,7,8,4,3,2,1]=>1001111
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[6,5,7,8,3,4,2,1]=>1001011
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[6,5,7,8,2,3,4,1]=>1001001
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[5,6,7,8,4,3,2,1]=>0001111
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[5,6,7,8,4,2,3,1]=>0001101
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0001011
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[5,6,7,8,3,2,4,1]=>0001101
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[5,6,7,8,2,3,4,1]=>0001001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[7,6,5,4,8,3,2,1]=>1110111
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[7,6,5,4,8,2,3,1]=>1110101
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[7,6,4,5,8,3,2,1]=>1100111
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[7,5,6,4,8,3,2,1]=>1010111
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[7,5,6,4,8,2,3,1]=>1010101
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[7,5,4,6,8,3,2,1]=>1100111
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[7,4,5,6,8,3,2,1]=>1000111
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[6,7,5,4,8,3,2,1]=>0110111
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[6,7,4,5,8,3,2,1]=>0100111
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[6,7,4,5,8,2,3,1]=>0100101
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[6,5,7,4,8,3,2,1]=>1010111
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[5,6,7,4,8,3,2,1]=>0010111
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[6,5,4,7,8,3,2,1]=>1100111
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[6,4,5,7,8,3,2,1]=>1000111
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[5,6,4,7,8,3,2,1]=>0100111
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[4,5,6,7,8,3,2,1]=>0000111
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[4,5,6,7,8,2,3,1]=>0000101
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[7,6,5,4,3,8,2,1]=>1111011
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[7,6,4,3,5,8,2,1]=>1110011
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[7,6,3,4,5,8,2,1]=>1100011
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[7,5,6,4,3,8,2,1]=>1011011
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[7,5,4,6,3,8,2,1]=>1101011
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[7,4,5,6,3,8,2,1]=>1001011
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[7,5,4,3,6,8,2,1]=>1110011
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[7,3,4,5,6,8,2,1]=>1000011
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[7,5,4,3,1,2,6,8]=>[6,7,5,4,3,8,2,1]=>0111011
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[6,7,4,5,3,8,2,1]=>0101011
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[5,6,7,4,3,8,2,1]=>0011011
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[6,5,4,7,3,8,2,1]=>1101011
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[6,4,5,7,3,8,2,1]=>1001011
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[5,4,6,7,3,8,2,1]=>1001011
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[4,5,6,7,3,8,2,1]=>0001011
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[6,5,4,3,7,8,2,1]=>1110011
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[6,5,3,4,7,8,2,1]=>1100011
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[6,3,4,5,7,8,2,1]=>1000011
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[4,5,6,3,7,8,2,1]=>0010011
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[5,4,3,6,7,8,2,1]=>1100011
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[5,3,4,6,7,8,2,1]=>1000011
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[4,3,5,6,7,8,2,1]=>1000011
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,2,1]=>0000011
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[7,6,5,4,3,2,8,1]=>1111101
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[7,6,5,4,2,3,8,1]=>1111001
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[6,4,5,3,2,1,7,8]=>[7,6,5,3,4,2,8,1]=>1110101
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[7,6,5,3,2,4,8,1]=>1111001
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[7,6,5,2,3,4,8,1]=>1110001
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[7,6,4,5,3,2,8,1]=>1101101
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[7,6,4,5,2,3,8,1]=>1101001
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[6,4,3,5,2,1,7,8]=>[7,6,4,3,5,2,8,1]=>1110101
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[7,6,3,4,5,2,8,1]=>1100101
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[4,5,3,6,2,1,7,8]=>[7,6,4,2,3,5,8,1]=>1110001
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[7,6,3,2,4,5,8,1]=>1110001
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[7,6,2,3,4,5,8,1]=>1100001
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[6,5,4,2,3,1,7,8]=>[7,5,6,4,3,2,8,1]=>1011101
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[7,5,6,4,2,3,8,1]=>1011001
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[7,5,6,3,4,2,8,1]=>1010101
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[4,5,6,2,3,1,7,8]=>[7,5,6,2,3,4,8,1]=>1010001
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[7,5,4,6,2,3,8,1]=>1101001
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[7,4,5,6,3,2,8,1]=>1001101
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[7,4,5,6,2,3,8,1]=>1001001
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[7,5,4,3,6,2,8,1]=>1110101
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[6,3,4,2,5,1,7,8]=>[7,5,3,4,6,2,8,1]=>1100101
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[6,4,2,3,5,1,7,8]=>[7,4,5,3,6,2,8,1]=>1010101
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[7,3,4,5,6,2,8,1]=>1000101
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[7,5,4,3,2,6,8,1]=>1111001
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[7,5,4,2,3,6,8,1]=>1110001
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[7,5,3,2,4,6,8,1]=>1110001
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[7,5,2,3,4,6,8,1]=>1100001
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[4,5,2,3,6,1,7,8]=>[7,4,5,2,3,6,8,1]=>1010001
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[7,4,3,5,2,6,8,1]=>1101001
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[7,4,3,2,5,6,8,1]=>1110001
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[7,4,2,3,5,6,8,1]=>1100001
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[7,3,2,4,5,6,8,1]=>1100001
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[7,2,3,4,5,6,8,1]=>1000001
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[6,7,5,4,3,2,8,1]=>0111101
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[6,7,5,4,2,3,8,1]=>0111001
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[6,7,5,3,2,4,8,1]=>0111001
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[6,7,4,5,3,2,8,1]=>0101101
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[6,7,4,5,2,3,8,1]=>0101001
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[6,7,4,3,2,5,8,1]=>0111001
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[4,3,5,6,1,2,7,8]=>[6,7,3,2,4,5,8,1]=>0110001
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[6,7,2,3,4,5,8,1]=>0100001
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[6,5,7,4,3,2,8,1]=>1011101
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[6,5,7,4,2,3,8,1]=>1011001
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[6,5,7,3,4,2,8,1]=>1010101
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[6,5,7,3,2,4,8,1]=>1011001
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[5,6,7,4,3,2,8,1]=>0011101
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[5,6,7,4,2,3,8,1]=>0011001
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[6,4,5,1,2,3,7,8]=>[5,6,7,3,4,2,8,1]=>0010101
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[5,6,7,2,3,4,8,1]=>0010001
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[6,5,4,7,3,2,8,1]=>1101101
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[6,5,4,7,2,3,8,1]=>1101001
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[6,4,5,7,3,2,8,1]=>1001101
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[6,4,5,7,2,3,8,1]=>1001001
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[5,6,4,7,2,3,8,1]=>0101001
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[5,6,2,1,3,4,7,8]=>[5,4,6,7,2,3,8,1]=>1001001
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[4,5,6,7,3,2,8,1]=>0001101
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[4,5,6,7,2,3,8,1]=>0001001
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[6,5,4,3,7,2,8,1]=>1110101
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[6,5,3,4,7,2,8,1]=>1100101
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[6,4,2,3,1,5,7,8]=>[6,4,5,3,7,2,8,1]=>1010101
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[6,4,3,5,7,2,8,1]=>1100101
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[6,3,4,5,7,2,8,1]=>1000101
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[6,3,4,1,2,5,7,8]=>[5,6,3,4,7,2,8,1]=>0100101
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[5,4,6,3,7,2,8,1]=>1010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[4,5,6,3,7,2,8,1]=>0010101
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[5,4,3,6,7,2,8,1]=>1100101
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[4,5,3,6,7,2,8,1]=>0100101
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[4,3,5,6,7,2,8,1]=>1000101
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[3,4,5,6,7,2,8,1]=>0000101
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[6,5,4,3,2,7,8,1]=>1111001
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[6,5,4,2,3,7,8,1]=>1110001
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[6,5,3,4,2,7,8,1]=>1101001
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[6,5,3,2,4,7,8,1]=>1110001
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[6,5,2,3,4,7,8,1]=>1100001
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[6,4,5,2,3,7,8,1]=>1010001
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[6,3,4,5,2,7,8,1]=>1001001
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[6,2,3,4,5,7,8,1]=>1000001
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[4,5,3,1,2,6,7,8]=>[5,6,4,2,3,7,8,1]=>0110001
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[5,4,6,3,2,7,8,1]=>1011001
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[4,5,2,1,3,6,7,8]=>[5,4,6,2,3,7,8,1]=>1010001
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[4,5,6,3,2,7,8,1]=>0011001
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[4,5,6,2,3,7,8,1]=>0010001
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[5,4,3,6,2,7,8,1]=>1101001
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[4,3,5,6,2,7,8,1]=>1001001
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0001001
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[5,4,3,2,6,7,8,1]=>1110001
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[5,4,2,3,6,7,8,1]=>1100001
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[5,3,4,2,6,7,8,1]=>1010001
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[5,3,2,4,6,7,8,1]=>1100001
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[5,2,3,4,6,7,8,1]=>1000001
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[4,5,3,2,6,7,8,1]=>0110001
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[4,5,2,3,6,7,8,1]=>0100001
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[4,3,5,2,6,7,8,1]=>1010001
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[3,4,5,2,6,7,8,1]=>0010001
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[4,3,2,5,6,7,8,1]=>1100001
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,1]=>1000001
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,4,2,5,6,7,8,1]=>0100001
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,1]=>1000001
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>0000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,3,2]=>01111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,2,3]=>01111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[1,9,8,7,6,5,2,3,4]=>01111100
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[1,9,2,3,4,5,6,7,8]=>01000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,8,9]=>00000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,1]=>00000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,2,3]=>011111110
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[1,10,9,8,7,2,3,4,5,6]=>011110000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[1,8,9,2,3,4,5,6,7]=>00100000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[9,1,2,3,4,5,6,7,8]=>10000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[1,9,8,7,6,5,3,2,4]=>01111110
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[1,9,8,7,6,4,3,2,5]=>01111110
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[1,9,8,7,5,4,3,2,6]=>01111110
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[1,9,8,6,5,4,3,2,7]=>01111110
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[1,9,7,6,5,4,3,2,8]=>01111110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[1,8,7,6,5,4,3,2,9]=>01111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,3,2,4]=>011111110
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[1,9,8,7,6,3,4,2,5]=>01111010
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[1,10,9,8,7,6,4,3,2,5]=>011111110
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[1,9,8,7,4,5,3,2,6]=>01110110
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[1,10,9,8,7,5,4,3,2,6]=>011111110
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>[1,9,8,5,6,4,3,2,7]=>01101110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[1,10,9,8,6,5,4,3,2,7]=>011111110
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>[1,9,6,7,5,4,3,2,8]=>01011110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[1,10,9,7,6,5,4,3,2,8]=>011111110
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[1,7,8,6,5,4,3,2,9]=>00111110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[1,10,8,7,6,5,4,3,2,9]=>011111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[8,9,7,6,5,4,3,2,1]=>01111111
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[10,1,8,9,6,7,4,5,2,3]=>100101010
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[9,10,6,7,4,5,2,3,1,8]=>[10,8,9,6,7,4,5,1,2,3]=>101010100
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]=>[8,9,6,7,4,5,2,3,1,10]=>[10,8,9,6,7,4,5,2,3,1]=>101010101
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[10,8,6,4,2,3,5,7,9,1]=>[1,6,7,5,8,4,9,3,10,2]=>001010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,1,2]=>00000010
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,10,1,2]=>000000010
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[4,3,5,6,7,8,9,1,2]=>10000010
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[1,3,2,4,5,6,7,8,9]=>01000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[3,4,5,6,7,8,9,10,11,1,2]=>0000000010
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[4,3,5,6,7,8,9,10,1,2]=>100000010
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[4,5,3,6,7,8,9,1,2]=>01000010
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[5,3,4,6,7,8,9,1,2]=>10000010
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[1,3,4,2,5,6,7,8,9]=>00100000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[1,4,2,3,5,6,7,8,9]=>01000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,1,2,3]=>00000100
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[5,6,7,8,9,1,2,3,4]=>00001000
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[6,7,8,9,1,2,3,4,5]=>00010000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[7,8,9,1,2,3,4,5,6]=>00100000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[8,9,1,2,3,4,5,6,7]=>01000000
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,1,3,2]=>00000101
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[4,5,6,7,8,9,10,1,2,3]=>000000100
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[5,6,7,8,9,10,1,2,3,4]=>000001000
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[6,7,8,9,10,1,2,3,4,5]=>000010000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[7,8,9,10,1,2,3,4,5,6]=>000100000
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[8,9,10,1,2,3,4,5,6,7]=>001000000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>[9,1,3,2,4,5,6,7,8]=>10100000
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[9,10,1,2,3,4,5,6,7,8]=>010000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[9,1,8,7,6,5,4,3,2]=>10111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,2,3,1]=>11111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[10,1,9,8,7,6,5,4,3,2]=>101111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,2,3,1]=>111111101
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[9,8,7,6,5,3,2,4,1]=>11111101
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[8,6,7,5,4,3,2,1,9]=>[9,8,7,6,5,3,4,2,1]=>11111011
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[11,1,10,9,8,7,6,5,4,3,2]=>1011111111
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[8,9,6,7,4,5,2,3,10,1]=>[1,8,9,6,7,4,5,2,3,10]=>001010100
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[9,8,1,7,6,5,4,3,2]=>11011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[9,8,7,1,6,5,4,3,2]=>11101111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[9,8,7,6,1,5,4,3,2]=>11110111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,1,4,3,2]=>11111011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,1,3,2]=>11111101
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,1,2]=>11111110
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[8,9,1,7,6,5,4,3,2]=>01011111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[10,9,1,8,7,6,5,4,3,2]=>110111111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[10,9,8,1,7,6,5,4,3,2]=>111011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[10,9,8,7,1,6,5,4,3,2]=>111101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[10,9,8,7,6,1,5,4,3,2]=>111110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[10,9,8,7,6,5,1,4,3,2]=>111111011
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[9,8,7,6,5,3,4,1,2]=>11111010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[10,9,8,7,6,5,4,1,3,2]=>111111101
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,1,2]=>111111110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,2,9,1]=>11111101
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[7,6,5,4,3,2,8,9,1]=>11111001
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[6,5,4,3,2,7,8,9,1]=>11110001
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[5,4,3,2,6,7,8,9,1]=>11100001
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[4,3,2,5,6,7,8,9,1]=>11000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,1]=>10000001
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[9,8,7,6,5,4,3,2,10,1]=>111111101
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[8,7,6,5,4,3,2,9,10,1]=>111111001
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[7,6,5,4,3,1,2,8,9]=>[7,8,6,5,4,3,2,9,1]=>01111101
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[7,6,5,4,3,2,8,9,10,1]=>111110001
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[6,5,4,3,2,7,8,9,10,1]=>111100001
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[5,4,3,2,6,7,8,9,10,1]=>111000001
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[4,3,2,5,6,7,8,9,10,1]=>110000001
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[3,4,2,5,6,7,8,9,1]=>01000001
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[3,2,4,5,6,7,8,9,10,1]=>100000001
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[1,9,8,7,5,6,4,3,2]=>01110111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[1,8,9,7,6,5,4,3,2]=>00111111
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[1,10,9,8,7,5,6,4,3,2]=>011110111
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[1,10,9,8,6,7,5,4,3,2]=>011101111
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[1,9,10,8,7,6,5,4,3,2]=>001111111
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[1,3,4,5,6,7,8,9,2]=>00000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[3,2,4,5,6,7,8,9,10,11,1]=>1000000001
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[8,9,2,1,3,4,5,6,7]=>[5,4,6,7,8,9,1,2,3]=>10000100
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[1,3,4,5,6,7,8,2,9]=>00000010
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[1,4,5,6,7,8,9,2,3]=>00000010
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[1,3,4,5,6,7,8,9,10,2]=>000000001
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[8,7,6,5,4,3,9,2,1]=>11111011
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[1,8,2,3,4,5,6,7,9]=>01000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[9,2,3,4,5,6,7,8,1]=>10000001
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[4,2,3,5,6,7,8,9,1]=>10000001
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[8,2,3,4,5,6,7,9,1]=>10000001
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>[9,3,4,5,6,7,8,2,1]=>10000011
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[10,2,3,4,5,6,7,8,9,1]=>100000001
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[3,4,5,6,7,8,2,9,1]=>00000101
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[3,4,5,6,7,8,9,2,1]=>00000011
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[3,4,5,6,2,7,8,9,10,1]=>000100001
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[3,4,5,6,7,8,9,2,10,1]=>000000101
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[3,4,5,6,7,8,9,10,2,1]=>000000011
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[9,1,3,4,5,6,7,8,2]=>10000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[8,9,7,6,5,4,3,1,2]=>01111110
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,1,2,3]=>11111100
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[9,10,1,8,7,6,5,4,3,2]=>010111111
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>[8,7,9,6,5,4,3,2,1]=>10111111
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[9,10,8,7,6,5,4,3,2,1]=>011111111
[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]=>[7,8,9,2,3,4,5,6,1]=>[1,5,6,7,8,9,2,3,4]=>00000100
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[9,8,1,2,3,4,5,6,7]=>11000000
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[8,9,2,3,4,5,6,7,1]=>01000001
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[4,5,6,7,8,9,10,1,3,2]=>000000101
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[9,8,7,6,5,2,3,4,1]=>11111001
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,1,4,3,2]=>00001011
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[6,7,8,9,1,5,4,3,2]=>00010111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[7,8,9,1,6,5,4,3,2]=>00101111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[4,5,6,7,8,9,3,1,2]=>00000110
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[5,6,7,8,9,10,1,4,3,2]=>000001011
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[6,7,8,9,10,1,5,4,3,2]=>000010111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[7,8,9,10,1,6,5,4,3,2]=>000101111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[8,9,10,1,7,6,5,4,3,2]=>001011111
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[5,4,2,3,6,7,8,9,1]=>11000001
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[9,7,6,5,4,3,2,8,1]=>11111101
[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[6,5,4,3,2,7,1,8,9]=>[8,6,5,4,3,2,7,9,1]=>11111001
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[6,5,4,2,3,7,8,9,1]=>11100001
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[6,5,4,3,7,8,9,1,2]=>11100010
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[4,5,6,7,8,9,3,2,1]=>00000111
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[9,3,2,4,5,6,7,8,1]=>11000001
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>[8,7,6,5,4,9,3,2,1]=>11110111
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[9,7,6,5,4,3,2,1,8,10]=>[9,8,7,6,5,4,3,10,2,1]=>111111011
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>[9,7,8,6,5,4,3,2,1]=>10111111
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[9,3,4,5,6,7,8,1,2]=>10000010
[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,4,5,2,1,3]=>[9,8,1,6,7,5,4,3,2]=>11001111
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[4,5,2,3,6,7,8,9,1]=>01000001
[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]=>[8,6,5,4,3,2,7,1,9]=>[9,7,6,5,4,3,8,2,1]=>11111011
[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,9,2,10,1]=>[1,9,2,3,4,5,6,7,8,10]=>010000000
[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[9,3,4,5,6,7,2,1,8]=>[9,8,3,4,5,6,7,1,2]=>11000010
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[4,5,6,7,8,9,10,2,3,1]=>[1,9,10,2,3,4,5,6,7,8]=>001000000
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,1,2,3,9]=>[7,8,9,6,5,4,3,2,1]=>00111111
[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[8,7,6,5,1,2,3,4,9]=>[6,7,8,9,5,4,3,2,1]=>00011111
[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[8,7,6,1,2,3,4,5,9]=>[5,6,7,8,9,4,3,2,1]=>00001111
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>[1,4,5,6,7,8,9,3,2]=>00000011
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>[1,4,5,6,7,8,9,10,3,2]=>000000011
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[9,8,2,3,4,5,6,7,1]=>11000001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[9,10,8,7,6,5,4,3,1,2]=>011111110
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[9,3,4,5,6,7,8,2,1]=>[1,9,3,4,5,6,7,8,2]=>01000001
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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