Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[2,1]=>1
[[.,.],.]=>[1,2]=>[1,2]=>0
[.,[.,[.,.]]]=>[3,2,1]=>[3,1,2]=>10
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>11
[[.,.],[.,.]]=>[3,1,2]=>[2,3,1]=>01
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>10
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>00
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,1,2,3]=>100
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,1,3,2]=>101
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,3,1,2]=>110
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>111
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>101
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,4,1,3]=>010
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,4,3,1]=>011
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,4,2]=>101
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,3,4,1]=>001
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1,2,4]=>100
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>110
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,3,1,4]=>010
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>100
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>000
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>1000
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,1,2,4,3]=>1001
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,1,4,2,3]=>1010
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,1,4,3,2]=>1011
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,1,3,4,2]=>1001
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,3,1,2,4]=>1100
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,3,1,4,2]=>1101
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,4,2,1,3]=>1110
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,3,4,1,2]=>1010
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,4,2,3,1]=>1101
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>1111
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,3,4,2,1]=>1011
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>1101
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>1001
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,5,1,3,4]=>0100
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,5,1,4,3]=>0101
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>0110
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>0111
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,5,3,4,1]=>0101
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>1010
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,5,4,2]=>1011
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>0010
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>0011
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>1001
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,3,1,5,2]=>1101
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>0101
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>1001
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>0001
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1,2,3,5]=>1000
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1,3,2,5]=>1010
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,3,1,2,5]=>1100
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>1110
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>1010
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[2,4,1,3,5]=>0100
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,4,3,1,5]=>0110
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,4,2,5]=>1010
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,3,4,1,5]=>0010
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,2,4,5]=>1000
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>1100
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,3,1,4,5]=>0100
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>10000
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>10001
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,1,2,5,3,4]=>10010
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>10011
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>10001
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,1,4,2,3,5]=>10100
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,1,4,2,5,3]=>10101
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,1,5,3,2,4]=>10110
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,1,4,5,2,3]=>10010
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>10101
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>10111
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,1,4,5,3,2]=>10011
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>10101
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>10001
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,3,1,2,4,5]=>11000
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,3,1,2,5,4]=>11001
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,3,1,5,2,4]=>11010
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,3,1,5,4,2]=>11011
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,3,1,4,5,2]=>11001
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,2,1,3,5]=>11100
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,2,1,5,3]=>11101
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,3,4,1,2,5]=>10100
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,3,4,1,5,2]=>10101
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,5,2,3,1,4]=>11010
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,5,4,2,1,3]=>11110
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,3,5,2,1,4]=>10110
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,4,2,5,1,3]=>11010
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,3,4,5,1,2]=>10010
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>11001
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>11011
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,5,4,2,3,1]=>11101
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>11111
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>11011
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,3,5,2,4,1]=>10101
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,3,5,4,2,1]=>10111
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,4,2,5,3,1]=>11011
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,3,4,5,2,1]=>10011
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>11001
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>11101
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,3,4,2,5,1]=>10101
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>11001
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>10001
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>01000
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,6,1,3,5,4]=>01001
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,6,1,5,3,4]=>01010
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,6,1,5,4,3]=>01011
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,6,1,4,5,3]=>01001
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>01100
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>01101
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>01110
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,6,4,5,1,3]=>01010
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>01101
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,6,5,4,3,1]=>01111
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,6,4,5,3,1]=>01011
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,6,4,3,5,1]=>01101
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>01001
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>10100
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,6,2,5,4]=>10101
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,6,5,2,4]=>10110
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,6,5,4,2]=>10111
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,6,4,5,2]=>10101
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>00100
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,3,6,1,5,4]=>00101
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>00110
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>00111
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>00101
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>10010
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,6,5,3]=>10011
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,3,1,6,2,5]=>11010
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,3,1,6,5,2]=>11011
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>01010
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,4,1,6,5,3]=>01011
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>10010
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[3,1,4,6,5,2]=>10011
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>00010
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>00011
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>10001
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,4,2,6,3]=>10101
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,3,1,2,6,4]=>11001
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,4,2,1,6,3]=>11101
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,3,4,1,6,2]=>10101
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>01001
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>01101
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>10101
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>00101
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>10001
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,3,1,5,6,2]=>11001
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>01001
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>10001
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>00001
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>10000
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>10010
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,1,4,2,3,6]=>10100
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>10110
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>10010
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,3,1,2,4,6]=>11000
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,3,1,4,2,6]=>11010
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,4,2,1,3,6]=>11100
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,3,4,1,2,6]=>10100
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>11010
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>11110
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,3,4,2,1,6]=>10110
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>11010
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>10010
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>01000
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[2,5,1,4,3,6]=>01010
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>01100
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>01110
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>01010
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>10100
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[3,1,5,4,2,6]=>10110
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>00100
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>00110
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>10010
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,3,1,5,2,6]=>11010
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>01010
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>10010
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>00010
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>10000
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>10100
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,3,1,2,5,6]=>11000
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>11100
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>10100
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>01000
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>01100
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>10100
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>00100
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>10000
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>01000
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>100000
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,6,5]=>100001
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,1,2,3,6,4,5]=>100010
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,1,2,3,6,5,4]=>100011
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,1,2,3,5,6,4]=>100001
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,1,2,5,3,4,6]=>100100
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,1,2,5,3,6,4]=>100101
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,1,2,6,4,3,5]=>100110
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,1,2,5,6,3,4]=>100010
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,1,2,6,4,5,3]=>100101
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,1,2,6,5,4,3]=>100111
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,1,2,5,6,4,3]=>100011
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,1,2,5,4,6,3]=>100101
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,1,2,4,5,6,3]=>100001
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,1,4,2,3,5,6]=>101000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,1,4,2,3,6,5]=>101001
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,1,4,2,6,3,5]=>101010
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,1,4,2,6,5,3]=>101011
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,1,4,2,5,6,3]=>101001
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,1,5,3,2,4,6]=>101100
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,1,5,3,2,6,4]=>101101
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,1,4,5,2,3,6]=>100100
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,1,4,5,2,6,3]=>100101
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,1,6,3,4,2,5]=>101010
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,1,6,5,3,2,4]=>101110
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,1,4,6,3,2,5]=>100110
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,1,5,3,6,2,4]=>101010
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,1,4,5,6,2,3]=>100010
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,1,6,3,4,5,2]=>101001
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,1,6,3,5,4,2]=>101011
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,1,6,5,3,4,2]=>101101
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,1,6,5,4,3,2]=>101111
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,1,6,4,5,3,2]=>101011
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,1,4,6,3,5,2]=>100101
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,1,4,6,5,3,2]=>100111
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,1,5,3,6,4,2]=>101011
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,1,4,5,6,3,2]=>100011
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,1,5,3,4,6,2]=>101001
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,1,5,4,3,6,2]=>101101
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,1,4,5,3,6,2]=>100101
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,1,4,3,5,6,2]=>101001
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,1,3,4,5,6,2]=>100001
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,3,1,2,4,5,6]=>110000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,3,1,2,4,6,5]=>110001
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,3,1,2,6,4,5]=>110010
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,3,1,2,6,5,4]=>110011
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,3,1,2,5,6,4]=>110001
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,3,1,5,2,4,6]=>110100
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,3,1,5,2,6,4]=>110101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,3,1,6,4,2,5]=>110110
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,3,1,5,6,2,4]=>110010
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,3,1,6,4,5,2]=>110101
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,3,1,6,5,4,2]=>110111
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,3,1,5,6,4,2]=>110011
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,3,1,5,4,6,2]=>110101
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,3,1,4,5,6,2]=>110001
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,4,2,1,3,5,6]=>111000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,4,2,1,3,6,5]=>111001
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,4,2,1,6,3,5]=>111010
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,4,2,1,6,5,3]=>111011
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,4,2,1,5,6,3]=>111001
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,3,4,1,2,5,6]=>101000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,3,4,1,2,6,5]=>101001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,3,4,1,6,2,5]=>101010
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,3,4,1,6,5,2]=>101011
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,3,4,1,5,6,2]=>101001
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,2,3,1,4,6]=>110100
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,2,3,1,6,4]=>110101
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,4,2,1,3,6]=>111100
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,4,2,1,6,3]=>111101
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,3,5,2,1,4,6]=>101100
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,3,5,2,1,6,4]=>101101
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,2,5,1,3,6]=>110100
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,2,5,1,6,3]=>110101
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,3,4,5,1,2,6]=>100100
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,3,4,5,1,6,2]=>100101
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,6,2,3,4,1,5]=>110010
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,6,2,5,3,1,4]=>110110
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,6,4,2,3,1,5]=>111010
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,6,5,3,2,1,4]=>111110
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,6,4,5,2,1,3]=>110110
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,3,6,2,4,1,5]=>101010
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,3,6,5,2,1,4]=>101110
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,2,6,3,1,5]=>110110
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,3,4,6,2,1,5]=>100110
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,5,2,3,6,1,4]=>110010
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,5,4,2,6,1,3]=>111010
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,3,5,2,6,1,4]=>101010
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,4,2,5,6,1,3]=>110010
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,3,4,5,6,1,2]=>100010
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,6,2,3,4,5,1]=>110001
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,6,2,3,5,4,1]=>110011
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,6,2,5,3,4,1]=>110101
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,6,2,5,4,3,1]=>110111
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,6,2,4,5,3,1]=>110011
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,6,4,2,3,5,1]=>111001
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,6,4,2,5,3,1]=>111011
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,6,5,3,2,4,1]=>111101
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,6,4,5,2,3,1]=>110101
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,5,3,4,2,1]=>111011
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>111111
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,4,5,3,2,1]=>110111
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>111011
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>110011
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,3,6,2,4,5,1]=>101001
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,3,6,2,5,4,1]=>101011
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,3,6,5,2,4,1]=>101101
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,3,6,5,4,2,1]=>101111
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,3,6,4,5,2,1]=>101011
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,2,6,3,5,1]=>110101
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,2,6,5,3,1]=>110111
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,3,4,6,2,5,1]=>100101
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,3,4,6,5,2,1]=>100111
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,5,2,3,6,4,1]=>110011
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,5,4,2,6,3,1]=>111011
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,3,5,2,6,4,1]=>101011
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,4,2,5,6,3,1]=>110011
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,3,4,5,6,2,1]=>100011
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,5,2,3,4,6,1]=>110001
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,5,2,4,3,6,1]=>110101
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,5,4,2,3,6,1]=>111001
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>111101
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>110101
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,3,5,2,4,6,1]=>101001
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,3,5,4,2,6,1]=>101101
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,4,2,5,3,6,1]=>110101
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,3,4,5,2,6,1]=>100101
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,4,2,3,5,6,1]=>110001
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>111001
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,3,4,2,5,6,1]=>101001
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>110001
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>100001
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,7,1,3,4,5,6]=>010000
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,7,1,3,4,6,5]=>010001
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,7,1,3,6,4,5]=>010010
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,7,1,3,6,5,4]=>010011
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,7,1,3,5,6,4]=>010001
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,7,1,5,3,4,6]=>010100
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,7,1,5,3,6,4]=>010101
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,7,1,6,4,3,5]=>010110
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,7,1,5,6,3,4]=>010010
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,7,1,6,4,5,3]=>010101
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,7,1,6,5,4,3]=>010111
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,7,1,5,6,4,3]=>010011
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,7,1,5,4,6,3]=>010101
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,7,1,4,5,6,3]=>010001
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,7,4,1,3,5,6]=>011000
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,7,4,1,3,6,5]=>011001
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,7,4,1,6,3,5]=>011010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,7,4,1,6,5,3]=>011011
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,7,4,1,5,6,3]=>011001
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,7,5,3,1,4,6]=>011100
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,7,5,3,1,6,4]=>011101
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,7,4,5,1,3,6]=>010100
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,7,4,5,1,6,3]=>010101
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,7,6,3,4,1,5]=>011010
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,7,6,5,3,1,4]=>011110
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,7,4,6,3,1,5]=>010110
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,7,5,3,6,1,4]=>011010
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,7,4,5,6,1,3]=>010010
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,7,6,3,4,5,1]=>011001
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,7,6,3,5,4,1]=>011011
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,7,6,5,3,4,1]=>011101
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,7,6,5,4,3,1]=>011111
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,7,6,4,5,3,1]=>011011
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,7,4,6,3,5,1]=>010101
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,7,4,6,5,3,1]=>010111
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,7,5,3,6,4,1]=>011011
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,7,4,5,6,3,1]=>010011
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,7,5,3,4,6,1]=>011001
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,7,5,4,3,6,1]=>011101
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,7,4,5,3,6,1]=>010101
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,7,4,3,5,6,1]=>011001
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>010001
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,7,2,4,5,6]=>101000
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,7,2,4,6,5]=>101001
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,7,2,6,4,5]=>101010
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,7,2,6,5,4]=>101011
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,7,2,5,6,4]=>101001
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,7,5,2,4,6]=>101100
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,7,5,2,6,4]=>101101
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,7,6,4,2,5]=>101110
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,7,5,6,2,4]=>101010
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,7,6,4,5,2]=>101101
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,7,6,5,4,2]=>101111
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,7,5,6,4,2]=>101011
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,7,5,4,6,2]=>101101
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,7,4,5,6,2]=>101001
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[2,3,7,1,4,5,6]=>001000
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,3,7,1,4,6,5]=>001001
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[2,3,7,1,6,4,5]=>001010
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[2,3,7,1,6,5,4]=>001011
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[2,3,7,1,5,6,4]=>001001
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>001100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>001101
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>001110
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>001010
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>001101
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,3,7,6,5,4,1]=>001111
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>001011
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>001101
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>001001
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>100100
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,7,3,6,5]=>100101
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,7,6,3,5]=>100110
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,7,6,5,3]=>100111
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,7,5,6,3]=>100101
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,3,1,7,2,5,6]=>110100
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,3,1,7,2,6,5]=>110101
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,3,1,7,6,2,5]=>110110
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,3,1,7,6,5,2]=>110111
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,3,1,7,5,6,2]=>110101
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[2,4,1,7,3,5,6]=>010100
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,4,1,7,3,6,5]=>010101
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[2,4,1,7,6,3,5]=>010110
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[2,4,1,7,6,5,3]=>010111
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[2,4,1,7,5,6,3]=>010101
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>100100
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[3,1,4,7,2,6,5]=>100101
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[3,1,4,7,6,2,5]=>100110
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[3,1,4,7,6,5,2]=>100111
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,4,7,5,6,2]=>100101
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>000100
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,3,4,7,1,6,5]=>000101
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>000110
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>000111
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>000101
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>100010
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,7,6,4]=>100011
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,4,2,7,3,6]=>101010
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,4,2,7,6,3]=>101011
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,3,1,2,7,4,6]=>110010
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,3,1,2,7,6,4]=>110011
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,4,2,1,7,3,6]=>111010
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,4,2,1,7,6,3]=>111011
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,3,4,1,7,2,6]=>101010
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,3,4,1,7,6,2]=>101011
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>010010
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,5,1,3,7,6,4]=>010011
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>011010
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>011011
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>101010
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[3,1,5,2,7,6,4]=>101011
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[2,3,5,1,7,4,6]=>001010
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,3,5,1,7,6,4]=>001011
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>100010
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[4,1,2,5,7,6,3]=>100011
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[4,3,1,5,7,2,6]=>110010
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[4,3,1,5,7,6,2]=>110011
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>010010
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,4,1,5,7,6,3]=>010011
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>100010
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[3,1,4,5,7,6,2]=>100011
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>000010
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>000011
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>100001
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,5,3,7,4]=>100101
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,4,2,3,7,5]=>101001
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,5,3,2,7,4]=>101101
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,4,5,2,7,3]=>100101
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,3,1,2,4,7,5]=>110001
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,3,1,5,2,7,4]=>110101
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,2,1,3,7,5]=>111001
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,3,4,1,2,7,5]=>101001
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,5,2,3,1,7,4]=>110101
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,5,4,2,1,7,3]=>111101
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,3,5,2,1,7,4]=>101101
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,4,2,5,1,7,3]=>110101
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,3,4,5,1,7,2]=>100101
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>010001
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[2,6,1,5,3,7,4]=>010101
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>011001
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[2,6,5,3,1,7,4]=>011101
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[2,6,4,5,1,7,3]=>010101
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[3,1,6,2,4,7,5]=>101001
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[3,1,6,5,2,7,4]=>101101
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[2,3,6,1,4,7,5]=>001001
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[2,3,6,5,1,7,4]=>001101
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[4,1,2,6,3,7,5]=>100101
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[4,3,1,6,2,7,5]=>110101
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[2,4,1,6,3,7,5]=>010101
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[3,1,4,6,2,7,5]=>100101
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[2,3,4,6,1,7,5]=>000101
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,1,2,3,6,7,4]=>100001
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,1,4,2,6,7,3]=>101001
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,3,1,2,6,7,4]=>110001
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,4,2,1,6,7,3]=>111001
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,3,4,1,6,7,2]=>101001
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[2,5,1,3,6,7,4]=>010001
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[2,5,4,1,6,7,3]=>011001
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[3,1,5,2,6,7,4]=>101001
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[2,3,5,1,6,7,4]=>001001
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,1,2,5,6,7,3]=>100001
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,3,1,5,6,7,2]=>110001
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[2,4,1,5,6,7,3]=>010001
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>100001
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>100000
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,1,2,3,5,4,7]=>100010
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,1,2,5,3,4,7]=>100100
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,1,2,5,4,3,7]=>100110
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,1,2,4,5,3,7]=>100010
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,1,4,2,3,5,7]=>101000
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,1,4,2,5,3,7]=>101010
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,1,5,3,2,4,7]=>101100
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,1,4,5,2,3,7]=>100100
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,1,5,3,4,2,7]=>101010
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,1,5,4,3,2,7]=>101110
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,1,4,5,3,2,7]=>100110
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,1,4,3,5,2,7]=>101010
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,1,3,4,5,2,7]=>100010
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,3,1,2,4,5,7]=>110000
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,3,1,2,5,4,7]=>110010
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,3,1,5,2,4,7]=>110100
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,3,1,5,4,2,7]=>110110
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,3,1,4,5,2,7]=>110010
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,2,1,3,5,7]=>111000
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,2,1,5,3,7]=>111010
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,3,4,1,2,5,7]=>101000
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,3,4,1,5,2,7]=>101010
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,5,2,3,1,4,7]=>110100
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,5,4,2,1,3,7]=>111100
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,3,5,2,1,4,7]=>101100
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,4,2,5,1,3,7]=>110100
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,3,4,5,1,2,7]=>100100
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,5,2,3,4,1,7]=>110010
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,5,2,4,3,1,7]=>110110
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,5,4,2,3,1,7]=>111010
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>111110
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>110110
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,3,5,2,4,1,7]=>101010
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,3,5,4,2,1,7]=>101110
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,4,2,5,3,1,7]=>110110
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,3,4,5,2,1,7]=>100110
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,4,2,3,5,1,7]=>110010
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>111010
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,3,4,2,5,1,7]=>101010
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>110010
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>100010
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[2,6,1,3,4,5,7]=>010000
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[2,6,1,3,5,4,7]=>010010
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[2,6,1,5,3,4,7]=>010100
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[2,6,1,5,4,3,7]=>010110
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[2,6,1,4,5,3,7]=>010010
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[2,6,4,1,3,5,7]=>011000
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,6,4,1,5,3,7]=>011010
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[2,6,5,3,1,4,7]=>011100
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[2,6,4,5,1,3,7]=>010100
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[2,6,5,3,4,1,7]=>011010
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[2,6,5,4,3,1,7]=>011110
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[2,6,4,5,3,1,7]=>010110
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[2,6,4,3,5,1,7]=>011010
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>010010
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[3,1,6,2,4,5,7]=>101000
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[3,1,6,2,5,4,7]=>101010
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[3,1,6,5,2,4,7]=>101100
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[3,1,6,5,4,2,7]=>101110
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[3,1,6,4,5,2,7]=>101010
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[2,3,6,1,4,5,7]=>001000
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,3,6,1,5,4,7]=>001010
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[2,3,6,5,1,4,7]=>001100
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[2,3,6,5,4,1,7]=>001110
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>001010
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[4,1,2,6,3,5,7]=>100100
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[4,1,2,6,5,3,7]=>100110
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[4,3,1,6,2,5,7]=>110100
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[4,3,1,6,5,2,7]=>110110
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[2,4,1,6,3,5,7]=>010100
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[2,4,1,6,5,3,7]=>010110
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[3,1,4,6,2,5,7]=>100100
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[3,1,4,6,5,2,7]=>100110
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[2,3,4,6,1,5,7]=>000100
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>000110
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,1,2,3,6,4,7]=>100010
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,1,4,2,6,3,7]=>101010
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,3,1,2,6,4,7]=>110010
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,4,2,1,6,3,7]=>111010
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,3,4,1,6,2,7]=>101010
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[2,5,1,3,6,4,7]=>010010
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[2,5,4,1,6,3,7]=>011010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[3,1,5,2,6,4,7]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[2,3,5,1,6,4,7]=>001010
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,1,2,5,6,3,7]=>100010
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,3,1,5,6,2,7]=>110010
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[2,4,1,5,6,3,7]=>010010
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>100010
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>000010
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>100000
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,1,2,4,3,6,7]=>100100
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,1,4,2,3,6,7]=>101000
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,1,4,3,2,6,7]=>101100
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,1,3,4,2,6,7]=>100100
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,3,1,2,4,6,7]=>110000
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,3,1,4,2,6,7]=>110100
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,4,2,1,3,6,7]=>111000
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,3,4,1,2,6,7]=>101000
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>110100
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,3,4,2,1,6,7]=>101100
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>110100
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>100100
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[2,5,1,3,4,6,7]=>010000
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[2,5,1,4,3,6,7]=>010100
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>011000
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[2,5,4,3,1,6,7]=>011100
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>010100
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[3,1,5,2,4,6,7]=>101000
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[3,1,5,4,2,6,7]=>101100
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[2,3,5,1,4,6,7]=>001000
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>001100
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,1,2,5,3,6,7]=>100100
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,3,1,5,2,6,7]=>110100
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[2,4,1,5,3,6,7]=>010100
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>100100
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>000100
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>100000
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>110000
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>101000
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>010000
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>011000
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>101000
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>001000
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>010000
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7]=>1000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,1,2,3,4,5,7,6]=>1000001
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[8,1,2,3,4,7,5,6]=>1000010
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,1,2,3,4,7,6,5]=>1000011
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,1,2,3,4,6,7,5]=>1000001
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[8,1,2,3,6,4,5,7]=>1000100
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[8,1,2,3,6,4,7,5]=>1000101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,1,2,3,7,5,4,6]=>1000110
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[8,1,2,3,6,7,4,5]=>1000010
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,1,2,3,7,5,6,4]=>1000101
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,1,2,3,7,6,5,4]=>1000111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,1,2,3,6,7,5,4]=>1000011
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,1,2,3,6,5,7,4]=>1000101
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,1,2,3,5,6,7,4]=>1000001
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,1,2,5,3,4,6,7]=>1001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[8,1,2,5,3,4,7,6]=>1001001
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[8,1,2,5,3,7,4,6]=>1001010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[8,1,2,5,3,7,6,4]=>1001011
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[8,1,2,5,3,6,7,4]=>1001001
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[8,1,2,6,4,3,7,5]=>1001101
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[8,1,2,5,6,3,4,7]=>1000100
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[8,1,2,5,6,3,7,4]=>1000101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[8,1,2,7,4,5,3,6]=>1001010
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[8,1,2,5,6,7,3,4]=>1000010
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,1,2,7,4,5,6,3]=>1001001
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,1,2,7,4,6,5,3]=>1001011
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,1,2,7,6,4,5,3]=>1001101
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,1,2,7,6,5,4,3]=>1001111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[8,1,2,5,7,4,6,3]=>1000101
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[8,1,2,6,4,7,5,3]=>1001011
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,1,2,5,6,7,4,3]=>1000011
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,1,2,6,4,5,7,3]=>1001001
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,1,2,4,5,6,7,3]=>1000001
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,1,4,2,3,5,6,7]=>1010000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[8,1,4,2,3,5,7,6]=>1010001
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[8,1,4,2,3,7,5,6]=>1010010
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,1,4,2,3,7,6,5]=>1010011
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[8,1,4,2,3,6,7,5]=>1010001
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,1,4,2,6,3,5,7]=>1010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,1,4,2,6,3,7,5]=>1010101
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[8,1,4,2,7,5,3,6]=>1010110
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,1,4,2,6,7,3,5]=>1010010
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,1,4,2,7,5,6,3]=>1010101
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[8,1,4,2,6,7,5,3]=>1010011
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[8,1,4,2,6,5,7,3]=>1010101
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,1,4,2,5,6,7,3]=>1010001
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[8,1,5,3,2,4,6,7]=>1011000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[8,1,5,3,2,4,7,6]=>1011001
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[8,1,5,3,2,7,4,6]=>1011010
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,1,5,3,2,6,7,4]=>1011001
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[8,1,4,5,2,3,6,7]=>1001000
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[8,1,4,5,2,3,7,6]=>1001001
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[8,1,4,5,2,7,3,6]=>1001010
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[8,1,4,5,2,6,7,3]=>1001001
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[8,1,6,3,4,2,5,7]=>1010100
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[8,1,6,3,4,2,7,5]=>1010101
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,1,5,3,6,2,4,7]=>1010100
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[8,1,5,3,6,2,7,4]=>1010101
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[8,1,4,5,6,2,3,7]=>1000100
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[8,1,4,5,6,2,7,3]=>1000101
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[8,1,7,3,4,5,2,6]=>1010010
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[8,1,7,3,6,4,2,5]=>1010110
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[8,1,7,6,4,3,2,5]=>1011110
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[8,5,6,3,4,7,2,1]=>[8,1,4,7,6,3,2,5]=>1001110
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[8,1,6,3,4,7,2,5]=>1010010
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[8,1,4,6,3,7,2,5]=>1001010
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[8,1,5,3,6,7,2,4]=>1010010
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[8,1,4,5,6,7,2,3]=>1000010
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,1,7,3,4,5,6,2]=>1010001
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[8,1,7,3,6,4,5,2]=>1010101
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[8,1,7,3,6,5,4,2]=>1010111
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,1,7,3,5,6,4,2]=>1010011
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[8,1,7,6,4,3,5,2]=>1011101
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,1,7,6,4,5,3,2]=>1011011
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[8,1,7,6,5,4,3,2]=>1011111
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[8,1,7,5,6,4,3,2]=>1010111
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[8,1,4,7,3,5,6,2]=>1001001
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[8,1,4,7,3,6,5,2]=>1001011
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[8,1,4,7,6,5,3,2]=>1001111
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[8,1,5,3,7,4,6,2]=>1010101
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[8,1,4,5,7,3,6,2]=>1000101
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[8,1,4,6,3,7,5,2]=>1001011
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[8,1,4,5,6,7,3,2]=>1000011
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,1,6,3,4,5,7,2]=>1010001
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[8,1,6,3,5,4,7,2]=>1010101
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[8,1,4,6,3,5,7,2]=>1001001
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[6,4,3,5,7,8,2,1]=>[8,1,5,3,6,4,7,2]=>1010101
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[8,1,4,5,6,3,7,2]=>1000101
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[8,1,5,4,3,6,7,2]=>1011001
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[8,1,4,5,3,6,7,2]=>1001001
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,1,4,3,5,6,7,2]=>1010001
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,1,3,4,5,6,7,2]=>1000001
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,3,1,2,4,5,6,7]=>1100000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[8,3,1,2,4,5,7,6]=>1100001
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[8,3,1,2,4,7,5,6]=>1100010
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[8,3,1,2,4,7,6,5]=>1100011
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[8,3,1,2,6,4,5,7]=>1100100
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[8,3,1,2,6,4,7,5]=>1100101
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[8,3,1,2,6,7,4,5]=>1100010
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[8,3,1,2,7,6,5,4]=>1100111
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,3,1,2,5,6,7,4]=>1100001
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,3,1,5,2,4,6,7]=>1101000
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,3,1,5,2,7,4,6]=>1101010
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[8,3,1,5,2,7,6,4]=>1101011
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,3,1,5,2,6,7,4]=>1101001
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[8,3,1,6,4,2,5,7]=>1101100
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[8,3,1,5,6,2,7,4]=>1100101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,3,1,7,4,5,2,6]=>1101010
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[8,3,1,7,6,4,2,5]=>1101110
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[8,3,1,7,6,4,5,2]=>1101101
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,3,1,7,6,5,4,2]=>1101111
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,2,3,1]=>[8,3,1,7,5,6,4,2]=>1101011
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[8,3,1,5,4,6,7,2]=>1101001
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[8,3,1,4,5,6,7,2]=>1100001
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,4,2,1,3,5,6,7]=>1110000
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[8,4,2,1,3,5,7,6]=>1110001
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[8,4,2,1,3,7,5,6]=>1110010
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[8,4,2,1,3,7,6,5]=>1110011
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[8,4,2,1,3,6,7,5]=>1110001
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[8,4,2,1,6,3,5,7]=>1110100
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[8,4,2,1,7,5,3,6]=>1110110
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,4,2,1,7,5,6,3]=>1110101
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[8,4,2,1,7,6,5,3]=>1110111
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[8,4,2,1,6,7,5,3]=>1110011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,4,2,1,5,6,7,3]=>1110001
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,3,4,1,2,5,6,7]=>1010000
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[8,3,4,1,2,7,5,6]=>1010010
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,3,4,1,2,6,7,5]=>1010001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[8,3,4,1,6,2,5,7]=>1010100
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[8,3,4,1,6,7,2,5]=>1010010
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,3,4,1,7,5,6,2]=>1010101
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[8,3,4,1,6,5,7,2]=>1010101
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,3,4,1,5,6,7,2]=>1010001
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[8,5,2,3,1,7,6,4]=>1101011
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[8,5,2,3,1,6,7,4]=>1101001
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,5,4,2,1,3,6,7]=>1111000
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[8,5,4,2,1,3,7,6]=>1111001
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,5,4,2,1,7,3,6]=>1111010
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[8,5,4,2,1,7,6,3]=>1111011
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[8,5,4,2,1,6,7,3]=>1111001
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[8,3,5,2,1,4,6,7]=>1011000
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[8,3,5,2,1,4,7,6]=>1011001
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[8,3,5,2,1,7,4,6]=>1011010
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,3,5,2,1,6,7,4]=>1011001
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[8,4,2,5,1,3,6,7]=>1101000
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[8,4,2,5,1,3,7,6]=>1101001
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[8,4,2,5,1,7,3,6]=>1101010
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[8,4,2,5,1,6,7,3]=>1101001
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[8,3,4,5,1,2,6,7]=>1001000
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[8,3,4,5,1,7,2,6]=>1001010
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[8,3,4,5,1,6,7,2]=>1001001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[8,6,2,3,4,1,5,7]=>1100100
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[8,6,2,3,4,1,7,5]=>1100101
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[8,6,4,2,3,1,5,7]=>1110100
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[8,6,4,2,3,1,7,5]=>1110101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[8,6,5,3,2,1,4,7]=>1111100
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[8,6,5,3,2,1,7,4]=>1111101
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[7,8,3,4,5,2,6,1]=>[8,6,4,5,2,1,7,3]=>1101101
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[8,3,6,2,4,1,5,7]=>1010100
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,2,3,6,1]=>[8,3,6,2,4,1,7,5]=>1010101
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,2,3,6,1]=>[8,3,6,5,2,1,7,4]=>1011101
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[8,5,2,3,6,1,4,7]=>1100100
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[8,5,2,3,6,1,7,4]=>1100101
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[8,5,4,2,6,1,3,7]=>1110100
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,5,4,2,6,1,7,3]=>1110101
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[8,3,5,2,6,1,7,4]=>1010101
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,4,2,5,6,1,7,3]=>1100101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[8,3,4,5,6,1,2,7]=>1000100
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[8,3,4,5,6,1,7,2]=>1000101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[8,7,2,3,4,5,1,6]=>1100010
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[8,7,4,2,6,3,1,5]=>1110110
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,7,5,3,2,4,1,6]=>1111010
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,7,4,5,2,3,1,6]=>1101010
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[8,7,6,3,4,2,1,5]=>1110110
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,7,6,5,3,2,1,4]=>1111110
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[8,5,3,4,6,2,7,1]=>[8,7,4,6,3,2,1,5]=>1101110
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[8,7,4,5,6,2,1,3]=>1100110
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,3,7,2,6,4,1,5]=>1010110
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,2,3,7,1]=>[8,3,7,6,4,2,1,5]=>1011110
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[8,5,2,3,7,4,1,6]=>1100110
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[8,3,5,2,7,4,1,6]=>1010110
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[8,3,4,5,7,2,1,6]=>1000110
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[8,6,2,3,4,7,1,5]=>1100010
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[8,6,4,2,3,7,1,5]=>1110010
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[8,4,3,5,2,6,7,1]=>[8,6,5,3,2,7,1,4]=>1111010
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[8,6,4,5,2,7,1,3]=>1101010
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[8,3,6,5,2,7,1,4]=>1011010
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[8,5,4,2,6,7,1,3]=>1110010
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[8,4,2,5,6,7,1,3]=>1100010
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[8,3,4,5,6,7,1,2]=>1000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,7,2,3,4,5,6,1]=>1100001
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,7,2,3,6,5,4,1]=>1100111
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,7,2,6,4,5,3,1]=>1101011
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[8,7,2,6,5,4,3,1]=>1101111
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,7,2,5,6,4,3,1]=>1100111
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,7,2,4,5,6,3,1]=>1100011
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,7,4,2,6,3,5,1]=>1110101
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,7,4,2,6,5,3,1]=>1110111
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[8,7,5,3,2,4,6,1]=>1111001
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[6,7,4,3,5,2,8,1]=>[8,7,5,3,2,6,4,1]=>1111011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,7,6,3,4,2,5,1]=>1110101
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,7,6,5,3,2,4,1]=>1111101
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[8,7,4,6,3,2,5,1]=>1101101
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[8,7,4,5,6,2,3,1]=>1100101
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>1110011
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>1110111
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,7,6,5,3,4,2,1]=>1111011
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>1110111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>1101011
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,7,4,6,5,3,2,1]=>1101111
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>1110111
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[8,7,4,5,6,3,2,1]=>1100111
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,7,5,3,4,6,2,1]=>1110011
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>1111011
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[8,7,4,5,3,6,2,1]=>1101011
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[8,7,4,3,5,6,2,1]=>1110011
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>1100011
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,3,7,2,4,5,6,1]=>1010001
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,3,7,2,6,4,5,1]=>1010101
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[8,3,7,2,6,5,4,1]=>1010111
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[8,3,7,5,2,4,6,1]=>1011001
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,3,7,5,2,6,4,1]=>1011011
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[8,3,7,6,5,4,2,1]=>1011111
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,3,7,5,6,4,2,1]=>1010111
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[8,3,7,5,4,6,2,1]=>1011011
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,3,7,4,5,6,2,1]=>1010011
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[8,4,2,7,3,5,6,1]=>1101001
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,4,2,7,6,5,3,1]=>1101111
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,3,4,7,2,5,6,1]=>1001001
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[8,3,4,7,6,2,5,1]=>1001101
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[7,6,4,3,2,5,8,1]=>[8,5,2,3,7,4,6,1]=>1100101
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[7,6,3,4,2,5,8,1]=>[8,5,4,2,7,3,6,1]=>1110101
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,3,5,2,7,4,6,1]=>1010101
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[8,4,2,5,7,3,6,1]=>1100101
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,4,2,5,7,6,3,1]=>1100111
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[8,3,4,5,7,6,2,1]=>1000111
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[7,5,3,4,2,6,8,1]=>[8,6,4,2,3,7,5,1]=>1110011
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,6,4,5,2,7,3,1]=>1101011
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[8,3,6,2,4,7,5,1]=>1010011
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,4,2,6,3,7,5,1]=>1101011
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[8,5,2,3,6,7,4,1]=>1100011
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[8,3,5,2,6,7,4,1]=>1010011
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[8,4,2,5,6,7,3,1]=>1100011
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[8,3,4,5,6,7,2,1]=>1000011
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,6,2,3,4,5,7,1]=>1100001
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[6,4,5,3,2,7,8,1]=>[8,6,2,5,3,4,7,1]=>1101001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,6,2,5,4,3,7,1]=>1101101
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,6,2,4,5,3,7,1]=>1100101
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[8,6,4,2,3,5,7,1]=>1110001
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[8,6,4,2,5,3,7,1]=>1110101
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[8,6,5,3,2,4,7,1]=>1111001
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[8,6,4,5,2,3,7,1]=>1101001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,6,5,3,4,2,7,1]=>1110101
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>1111101
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[5,3,4,6,2,7,8,1]=>[8,6,4,5,3,2,7,1]=>1101101
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>1110101
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>1100101
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,3,6,2,4,5,7,1]=>1010001
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[8,3,6,5,4,2,7,1]=>1011101
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,3,6,4,5,2,7,1]=>1010101
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[6,3,2,4,5,7,8,1]=>[8,4,2,5,6,3,7,1]=>1100101
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[8,3,4,5,6,2,7,1]=>1000101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,5,2,3,4,6,7,1]=>1100001
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[8,5,4,2,3,6,7,1]=>1110001
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>1111001
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>1101001
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>1011001
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[8,4,2,5,3,6,7,1]=>1101001
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>1001001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,4,2,3,5,6,7,1]=>1100001
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>1110001
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>1010001
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>1100001
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>1000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,8,1,3,4,5,6,7]=>0100000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,8,1,3,4,5,7,6]=>0100001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,8,1,3,4,7,5,6]=>0100010
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[2,8,1,3,4,6,7,5]=>0100001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,8,1,3,6,4,5,7]=>0100100
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,8,1,3,6,4,7,5]=>0100101
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,8,1,3,7,5,4,6]=>0100110
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,3,1,2]=>[2,8,1,3,6,7,4,5]=>0100010
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,8,1,3,7,5,6,4]=>0100101
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,8,1,3,7,6,5,4]=>0100111
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,8,1,3,6,7,5,4]=>0100011
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,8,1,3,6,5,7,4]=>0100101
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,8,1,3,5,6,7,4]=>0100001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,8,1,5,3,4,6,7]=>0101000
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,8,1,5,3,4,7,6]=>0101001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[2,8,1,5,3,7,4,6]=>0101010
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,3,1,2]=>[2,8,1,5,3,7,6,4]=>0101011
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,8,1,6,4,3,5,7]=>0101100
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[2,8,1,5,6,3,4,7]=>0100100
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,8,1,5,6,3,7,4]=>0100101
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[2,8,1,7,4,6,5,3]=>0101011
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[2,8,1,7,6,5,4,3]=>0101111
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,8,1,6,4,7,5,3]=>0101011
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,8,1,5,4,6,7,3]=>0101001
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,8,1,4,5,6,7,3]=>0100001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,8,4,1,3,5,6,7]=>0110000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,8,4,1,3,5,7,6]=>0110001
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,4,1,2]=>[2,8,4,1,3,7,5,6]=>0110010
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,8,4,1,3,7,6,5]=>0110011
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[2,8,4,1,3,6,7,5]=>0110001
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,8,4,1,6,3,5,7]=>0110100
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,8,4,1,6,3,7,5]=>0110101
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[2,8,4,1,7,5,3,6]=>0110110
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[2,8,4,1,6,7,3,5]=>0110010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,8,4,1,7,5,6,3]=>0110101
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,8,4,1,6,7,5,3]=>0110011
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,8,4,1,6,5,7,3]=>0110101
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,8,4,1,5,6,7,3]=>0110001
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,8,5,3,1,4,6,7]=>0111000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,8,5,3,1,4,7,6]=>0111001
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2]=>[2,8,5,3,1,7,4,6]=>0111010
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[2,8,5,3,1,7,6,4]=>0111011
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,8,4,5,1,3,6,7]=>0101000
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,8,4,5,1,7,3,6]=>0101010
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[2,8,4,5,1,7,6,3]=>0101011
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,8,4,5,1,6,7,3]=>0101001
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,8,6,3,4,1,7,5]=>0110101
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[2,8,6,5,3,1,4,7]=>0111100
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,8,4,6,3,1,5,7]=>0101100
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,8,5,3,6,1,7,4]=>0110101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[2,8,4,5,6,1,3,7]=>0100100
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,8,4,5,6,1,7,3]=>0100101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,8,7,3,4,5,1,6]=>0110010
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[2,8,7,6,4,3,1,5]=>0111110
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[8,5,6,3,4,7,1,2]=>[2,8,4,7,6,3,1,5]=>0101110
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,8,6,3,4,7,1,5]=>0110010
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[2,8,4,6,3,7,1,5]=>0101010
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,8,5,3,6,7,1,4]=>0110010
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,8,4,5,6,7,1,3]=>0100010
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,8,7,3,4,5,6,1]=>0110001
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[2,8,7,3,4,6,5,1]=>0110011
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,8,7,5,3,6,4,1]=>0111011
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,8,7,6,4,3,5,1]=>0111101
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[2,8,7,5,6,3,4,1]=>0110101
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[2,8,7,6,4,5,3,1]=>0111011
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,8,7,6,5,4,3,1]=>0111111
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[2,8,7,5,6,4,3,1]=>0110111
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,8,7,5,4,6,3,1]=>0111011
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[2,8,7,4,5,6,3,1]=>0110011
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[2,8,4,7,3,5,6,1]=>0101001
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,8,4,7,3,6,5,1]=>0101011
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,8,4,7,6,3,5,1]=>0101101
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,8,4,7,6,5,3,1]=>0101111
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,8,4,5,7,3,6,1]=>0100101
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[2,8,6,3,4,7,5,1]=>0110011
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,8,4,6,3,7,5,1]=>0101011
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,8,4,5,6,7,3,1]=>0100011
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,8,6,3,4,5,7,1]=>0110001
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[2,8,6,3,5,4,7,1]=>0110101
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,8,4,6,5,3,7,1]=>0101101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,8,5,3,6,4,7,1]=>0110101
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,8,4,5,6,3,7,1]=>0100101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,8,5,3,4,6,7,1]=>0110001
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,8,5,4,3,6,7,1]=>0111001
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,8,4,5,3,6,7,1]=>0101001
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,8,4,3,5,6,7,1]=>0110001
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,8,3,4,5,6,7,1]=>0100001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,8,2,4,5,6,7]=>1010000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,8,2,4,5,7,6]=>1010001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,8,2,4,7,5,6]=>1010010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,8,2,4,7,6,5]=>1010011
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[3,1,8,2,6,4,5,7]=>1010100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,8,2,6,4,7,5]=>1010101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,8,2,7,5,4,6]=>1010110
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[3,1,8,2,6,7,4,5]=>1010010
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,8,2,7,5,6,4]=>1010101
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,1,8,2,7,6,5,4]=>1010111
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,8,2,6,7,5,4]=>1010011
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,8,2,6,5,7,4]=>1010101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,8,2,5,6,7,4]=>1010001
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[3,1,8,5,2,4,6,7]=>1011000
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,8,5,2,7,4,6]=>1011010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[3,1,8,5,2,7,6,4]=>1011011
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,8,6,4,2,7,5]=>1011101
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[3,1,8,5,6,2,4,7]=>1010100
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[3,1,8,5,6,2,7,4]=>1010101
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,8,5,7,4,2,6]=>1010110
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,8,6,4,7,2,5]=>1011010
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[3,1,8,5,6,7,2,4]=>1010010
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[3,1,8,7,6,4,5,2]=>1011101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,8,7,6,5,4,2]=>1011111
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[3,1,8,7,5,6,4,2]=>1011011
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[3,1,8,5,7,4,6,2]=>1010101
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,8,5,7,6,4,2]=>1010111
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,8,6,4,7,5,2]=>1011011
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,8,5,4,6,7,2]=>1011001
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,8,4,5,6,7,2]=>1010001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[2,3,8,1,4,5,6,7]=>0010000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[2,3,8,1,4,5,7,6]=>0010001
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[2,3,8,1,4,6,7,5]=>0010001
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[2,3,8,1,6,4,7,5]=>0010101
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[2,3,8,1,6,7,4,5]=>0010010
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[2,3,8,1,7,6,5,4]=>0010111
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[2,3,8,1,6,7,5,4]=>0010011
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[2,3,8,1,6,5,7,4]=>0010101
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[2,3,8,1,5,6,7,4]=>0010001
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[2,3,8,5,1,4,6,7]=>0011000
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[2,3,8,5,1,4,7,6]=>0011001
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[2,3,8,5,1,7,4,6]=>0011010
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[2,3,8,5,1,6,7,4]=>0011001
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[2,3,8,6,4,1,5,7]=>0011100
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[2,3,8,6,4,1,7,5]=>0011101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[2,3,8,5,6,1,4,7]=>0010100
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[2,3,8,5,6,1,7,4]=>0010101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[2,3,8,7,4,5,1,6]=>0011010
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[2,3,8,7,6,4,1,5]=>0011110
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[2,3,8,5,6,7,1,4]=>0010010
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[2,3,8,7,4,5,6,1]=>0011001
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[2,3,8,7,6,5,4,1]=>0011111
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[2,3,8,5,7,4,6,1]=>0010101
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[2,3,8,5,7,6,4,1]=>0010111
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[2,3,8,6,4,7,5,1]=>0011011
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[2,3,8,5,6,7,4,1]=>0010011
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[2,3,8,6,4,5,7,1]=>0011001
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[2,3,8,6,5,4,7,1]=>0011101
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[2,3,8,5,6,4,7,1]=>0010101
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[2,3,8,5,4,6,7,1]=>0011001
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[2,3,8,4,5,6,7,1]=>0010001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,8,3,5,6,7]=>1001000
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,8,3,7,5,6]=>1001010
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,8,3,6,7,5]=>1001001
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,8,6,3,5,7]=>1001100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,8,6,3,7,5]=>1001101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,8,7,5,3,6]=>1001110
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,8,6,7,3,5]=>1001010
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,8,7,5,6,3]=>1001101
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,8,7,6,5,3]=>1001111
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,8,5,6,7,3]=>1001001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,3,1,8,2,5,6,7]=>1101000
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[4,3,1,8,2,5,7,6]=>1101001
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,3,1,8,2,7,5,6]=>1101010
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[4,3,1,8,2,6,7,5]=>1101001
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[4,3,1,8,6,2,5,7]=>1101100
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,3,1,8,6,2,7,5]=>1101101
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[4,3,1,8,7,5,2,6]=>1101110
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[4,3,1,8,6,7,2,5]=>1101010
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,3,1,8,7,5,6,2]=>1101101
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,3,1,8,7,6,5,2]=>1101111
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,3,1,8,6,7,5,2]=>1101011
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,3,1,8,6,5,7,2]=>1101101
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,3,1,8,5,6,7,2]=>1101001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[2,4,1,8,3,5,6,7]=>0101000
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[2,4,1,8,3,5,7,6]=>0101001
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[2,4,1,8,3,7,5,6]=>0101010
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[2,4,1,8,3,6,7,5]=>0101001
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[2,4,1,8,6,3,5,7]=>0101100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[2,4,1,8,6,3,7,5]=>0101101
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[2,4,1,8,6,7,3,5]=>0101010
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[2,4,1,8,7,6,5,3]=>0101111
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[2,4,1,8,6,7,5,3]=>0101011
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[2,4,1,8,5,6,7,3]=>0101001
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[3,1,4,8,2,5,6,7]=>1001000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[3,1,4,8,2,5,7,6]=>1001001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[3,1,4,8,2,7,5,6]=>1001010
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,1,4,8,2,6,7,5]=>1001001
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[3,1,4,8,6,2,5,7]=>1001100
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[3,1,4,8,6,2,7,5]=>1001101
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[3,1,4,8,6,7,2,5]=>1001010
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[3,1,4,8,7,6,5,2]=>1001111
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[3,1,4,8,6,5,7,2]=>1001101
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[3,1,4,8,5,6,7,2]=>1001001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[2,3,4,8,1,5,6,7]=>0001000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,3,4,8,1,5,7,6]=>0001001
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[2,3,4,8,1,7,5,6]=>0001010
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[2,3,4,8,1,7,6,5]=>0001011
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[2,3,4,8,1,6,7,5]=>0001001
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[2,3,4,8,6,1,5,7]=>0001100
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,3,4,8,6,1,7,5]=>0001101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[2,3,4,8,7,5,1,6]=>0001110
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[2,3,4,8,6,7,1,5]=>0001010
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[2,3,4,8,7,5,6,1]=>0001101
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[2,3,4,8,7,6,5,1]=>0001111
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[2,3,4,8,6,7,5,1]=>0001011
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[2,3,4,8,6,5,7,1]=>0001101
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[2,3,4,8,5,6,7,1]=>0001001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,8,4,6,7]=>1000100
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,8,4,7,6]=>1000101
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[5,1,2,3,8,7,4,6]=>1000110
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,8,7,6,4]=>1000111
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,8,6,7,4]=>1000101
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,4,2,8,3,6,7]=>1010100
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,4,2,8,3,7,6]=>1010101
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,4,2,8,6,7,3]=>1010101
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,3,1,2,8,4,6,7]=>1100100
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,3,1,2,8,4,7,6]=>1100101
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,3,1,2,8,7,4,6]=>1100110
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,3,1,2,8,6,7,4]=>1100101
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,4,2,1,8,3,6,7]=>1110100
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[5,4,2,1,8,7,3,6]=>1110110
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,4,2,1,8,7,6,3]=>1110111
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,3,4,1,8,2,6,7]=>1010100
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[5,3,4,1,8,2,7,6]=>1010101
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,3,4,1,8,6,7,2]=>1010101
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[2,5,1,3,8,4,6,7]=>0100100
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[2,5,1,3,8,4,7,6]=>0100101
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,3,1,2,5]=>[2,5,1,3,8,7,4,6]=>0100110
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[2,5,1,3,8,6,7,4]=>0100101
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[2,5,4,1,8,3,6,7]=>0110100
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[2,5,4,1,8,3,7,6]=>0110101
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[2,5,4,1,8,7,3,6]=>0110110
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[2,5,4,1,8,7,6,3]=>0110111
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[2,5,4,1,8,6,7,3]=>0110101
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[3,1,5,2,8,4,6,7]=>1010100
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[3,1,5,2,8,4,7,6]=>1010101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[3,1,5,2,8,7,4,6]=>1010110
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[3,1,5,2,8,7,6,4]=>1010111
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[3,1,5,2,8,6,7,4]=>1010101
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[2,3,5,1,8,4,6,7]=>0010100
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[2,3,5,1,8,4,7,6]=>0010101
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[2,3,5,1,8,7,4,6]=>0010110
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[2,3,5,1,8,7,6,4]=>0010111
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[4,1,2,5,8,3,6,7]=>1000100
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[4,1,2,5,8,3,7,6]=>1000101
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[4,1,2,5,8,7,3,6]=>1000110
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[4,1,2,5,8,7,6,3]=>1000111
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[4,1,2,5,8,6,7,3]=>1000101
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[4,3,1,5,8,2,6,7]=>1100100
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[4,3,1,5,8,2,7,6]=>1100101
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[4,3,1,5,8,7,6,2]=>1100111
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[4,3,1,5,8,6,7,2]=>1100101
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[2,4,1,5,8,3,6,7]=>0100100
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[2,4,1,5,8,3,7,6]=>0100101
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[2,4,1,5,8,7,3,6]=>0100110
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[2,4,1,5,8,7,6,3]=>0100111
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[3,1,4,5,8,2,6,7]=>1000100
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[3,1,4,5,8,7,2,6]=>1000110
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[3,1,4,5,8,6,7,2]=>1000101
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[2,3,4,5,8,1,6,7]=>0000100
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[2,3,4,5,8,1,7,6]=>0000101
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[2,3,4,5,8,7,1,6]=>0000110
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[2,3,4,5,8,7,6,1]=>0000111
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[2,3,4,5,8,6,7,1]=>0000101
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,8,5,7]=>1000010
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,8,7,5]=>1000011
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,5,3,8,4,7]=>1001010
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,4,2,3,8,5,7]=>1010010
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[6,1,5,3,2,8,4,7]=>1011010
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[6,1,4,5,2,8,3,7]=>1001010
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[6,1,4,5,2,8,7,3]=>1001011
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[6,3,1,2,4,8,5,7]=>1100010
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[6,3,1,5,2,8,4,7]=>1101010
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,4,2,1,3,8,5,7]=>1110010
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,4,2,1,3,8,7,5]=>1110011
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[6,3,4,1,2,8,5,7]=>1010010
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[6,3,4,1,2,8,7,5]=>1010011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,5,2,3,1,8,7,4]=>1101011
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[6,3,5,2,1,8,4,7]=>1011010
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[6,3,5,2,1,8,7,4]=>1011011
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[8,7,3,2,4,5,1,6]=>[6,4,2,5,1,8,3,7]=>1101010
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,4,2,5,1,8,7,3]=>1101011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[6,3,4,5,1,8,2,7]=>1001010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[2,6,1,3,4,8,5,7]=>0100010
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[2,6,4,1,3,8,5,7]=>0110010
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[2,6,4,1,3,8,7,5]=>0110011
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[2,6,5,3,1,8,7,4]=>0111011
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[2,6,4,5,1,8,7,3]=>0101011
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[3,1,6,2,4,8,5,7]=>1010010
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[3,1,6,2,4,8,7,5]=>1010011
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[3,1,6,5,2,8,7,4]=>1011011
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[2,3,6,1,4,8,5,7]=>0010010
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[2,3,6,1,4,8,7,5]=>0010011
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[2,3,6,5,1,8,4,7]=>0011010
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,3,6,5,1,8,7,4]=>0011011
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[4,1,2,6,3,8,5,7]=>1001010
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[4,1,2,6,3,8,7,5]=>1001011
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[4,3,1,6,2,8,5,7]=>1101010
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[2,4,1,6,3,8,5,7]=>0101010
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[2,4,1,6,3,8,7,5]=>0101011
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[3,1,4,6,2,8,5,7]=>1001010
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[3,1,4,6,2,8,7,5]=>1001011
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[2,3,4,6,1,8,5,7]=>0001010
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[2,3,4,6,1,8,7,5]=>0001011
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[5,1,2,3,6,8,4,7]=>1000010
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[5,1,2,3,6,8,7,4]=>1000011
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[5,1,4,2,6,8,3,7]=>1010010
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[5,1,4,2,6,8,7,3]=>1010011
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[5,4,2,1,6,8,3,7]=>1110010
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[5,4,2,1,6,8,7,3]=>1110011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[5,3,4,1,6,8,2,7]=>1010010
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[2,5,1,3,6,8,4,7]=>0100010
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[2,5,1,3,6,8,7,4]=>0100011
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[2,5,4,1,6,8,3,7]=>0110010
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[3,1,5,2,6,8,4,7]=>1010010
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[2,3,5,1,6,8,4,7]=>0010010
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[4,1,2,5,6,8,3,7]=>1000010
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[4,1,2,5,6,8,7,3]=>1000011
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[4,3,1,5,6,8,7,2]=>1100011
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[3,1,4,5,6,8,2,7]=>1000010
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[3,1,4,5,6,8,7,2]=>1000011
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[2,3,4,5,6,8,1,7]=>0000010
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,3,4,5,6,8,7,1]=>0000011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,8,6]=>1000001
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,1,2,3,6,4,8,5]=>1000101
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,1,2,5,3,4,8,6]=>1001001
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[7,1,2,6,4,3,8,5]=>1001101
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,5,6,3,8,4]=>1000101
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,1,4,2,3,5,8,6]=>1010001
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[7,1,4,2,6,3,8,5]=>1010101
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,1,5,3,2,4,8,6]=>1011001
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,6,3,4,2,8,5]=>1010101
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,5,3,6,2,8,4]=>1010101
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,1,4,5,6,2,8,3]=>1000101
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,3,1,2,4,5,8,6]=>1100001
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,3,1,2,6,4,8,5]=>1100101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,3,1,5,2,4,8,6]=>1101001
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[7,3,1,5,6,2,8,4]=>1100101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,3,4,1,2,5,8,6]=>1010001
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[7,3,4,1,6,2,8,5]=>1010101
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[7,5,2,3,1,4,8,6]=>1101001
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,4,2,5,1,3,8,6]=>1101001
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,6,2,3,4,1,8,5]=>1100101
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[7,6,2,5,3,1,8,4]=>1101101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,6,5,3,2,1,8,4]=>1111101
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[7,6,4,5,2,1,8,3]=>1101101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,3,6,5,2,1,8,4]=>1011101
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,5,4,2,6,1,8,3]=>1110101
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[7,3,5,2,6,1,8,4]=>1010101
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,3,4,5,6,1,8,2]=>1000101
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[2,7,1,3,4,5,8,6]=>0100001
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[2,7,1,5,3,4,8,6]=>0101001
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[2,7,4,1,3,5,8,6]=>0110001
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[2,7,4,1,6,3,8,5]=>0110101
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[8,6,4,3,5,1,2,7]=>[2,7,5,3,1,4,8,6]=>0111001
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[2,7,4,5,1,3,8,6]=>0101001
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[2,7,6,3,4,1,8,5]=>0110101
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[2,7,6,5,3,1,8,4]=>0111101
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[2,7,4,6,3,1,8,5]=>0101101
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[2,7,4,5,6,1,8,3]=>0100101
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[3,1,7,2,4,5,8,6]=>1010001
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[3,1,7,2,6,4,8,5]=>1010101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[3,1,7,5,2,4,8,6]=>1011001
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[3,1,7,6,4,2,8,5]=>1011101
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[2,3,7,1,4,5,8,6]=>0010001
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[2,3,7,1,6,4,8,5]=>0010101
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[2,3,7,5,1,4,8,6]=>0011001
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[2,3,7,5,6,1,8,4]=>0010101
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[4,1,2,7,3,5,8,6]=>1001001
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[4,1,2,7,6,3,8,5]=>1001101
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[4,3,1,7,2,5,8,6]=>1101001
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[4,3,1,7,6,2,8,5]=>1101101
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[2,4,1,7,3,5,8,6]=>0101001
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[2,4,1,7,6,3,8,5]=>0101101
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[3,1,4,7,2,5,8,6]=>1001001
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[3,1,4,7,6,2,8,5]=>1001101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[2,3,4,7,1,5,8,6]=>0001001
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[2,3,4,7,6,1,8,5]=>0001101
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[5,1,2,3,7,4,8,6]=>1000101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[5,1,4,2,7,3,8,6]=>1010101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[5,3,1,2,7,4,8,6]=>1100101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[5,3,4,1,7,2,8,6]=>1010101
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[2,5,1,3,7,4,8,6]=>0100101
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[2,5,4,1,7,3,8,6]=>0110101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[3,1,5,2,7,4,8,6]=>1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[2,3,5,1,7,4,8,6]=>0010101
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[4,1,2,5,7,3,8,6]=>1000101
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[4,3,1,5,7,2,8,6]=>1100101
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[2,3,4,5,7,1,8,6]=>0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,1,2,3,4,7,8,5]=>1000001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[6,1,2,5,3,7,8,4]=>1001001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[6,1,4,5,2,7,8,3]=>1001001
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[8,5,4,2,3,1,6,7]=>[6,3,1,2,4,7,8,5]=>1100001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[6,3,1,5,2,7,8,4]=>1101001
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[6,4,2,1,3,7,8,5]=>1110001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[6,3,4,1,2,7,8,5]=>1010001
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[8,3,2,4,5,1,6,7]=>[6,4,2,5,1,7,8,3]=>1101001
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[6,3,4,5,1,7,8,2]=>1001001
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[8,5,4,3,1,2,6,7]=>[2,6,1,3,4,7,8,5]=>0100001
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[2,6,4,1,3,7,8,5]=>0110001
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[8,4,3,5,1,2,6,7]=>[2,6,5,3,1,7,8,4]=>0111001
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[2,6,4,5,1,7,8,3]=>0101001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[3,1,6,2,4,7,8,5]=>1010001
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[3,1,6,5,2,7,8,4]=>1011001
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[2,3,6,1,4,7,8,5]=>0010001
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[2,3,6,5,1,7,8,4]=>0011001
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[4,1,2,6,3,7,8,5]=>1001001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[2,4,1,6,3,7,8,5]=>0101001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[3,1,4,6,2,7,8,5]=>1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[2,3,4,6,1,7,8,5]=>0001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[5,1,2,3,6,7,8,4]=>1000001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[5,1,4,2,6,7,8,3]=>1010001
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[5,3,1,2,6,7,8,4]=>1100001
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[5,4,2,1,6,7,8,3]=>1110001
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[5,3,4,1,6,7,8,2]=>1010001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[2,5,1,3,6,7,8,4]=>0100001
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[2,5,4,1,6,7,8,3]=>0110001
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[3,1,5,2,6,7,8,4]=>1010001
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[2,3,5,1,6,7,8,4]=>0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,1,2,5,6,7,8,3]=>1000001
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[4,3,1,5,6,7,8,2]=>1100001
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[2,4,1,5,6,7,8,3]=>0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[3,1,4,5,6,7,8,2]=>1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,1,2,3,4,5,6,8]=>1000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,1,2,3,4,6,5,8]=>1000010
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[7,1,2,3,6,4,5,8]=>1000100
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,1,2,3,6,5,4,8]=>1000110
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,1,2,3,5,6,4,8]=>1000010
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,1,2,5,3,4,6,8]=>1001000
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[7,1,2,6,4,3,5,8]=>1001100
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,1,2,6,4,5,3,8]=>1001010
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[7,1,2,6,5,4,3,8]=>1001110
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,1,2,5,4,6,3,8]=>1001010
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,1,2,4,5,6,3,8]=>1000010
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[7,1,4,2,3,5,6,8]=>1010000
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,1,4,2,6,3,5,8]=>1010100
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[7,1,4,2,6,5,3,8]=>1010110
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[7,1,4,2,5,6,3,8]=>1010010
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[7,1,5,3,2,4,6,8]=>1011000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,1,4,5,2,3,6,8]=>1001000
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[7,1,6,3,4,2,5,8]=>1010100
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,1,6,5,3,2,4,8]=>1011100
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[7,1,5,3,6,2,4,8]=>1010100
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[7,1,6,3,5,4,2,8]=>1010110
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,1,6,5,4,3,2,8]=>1011110
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[7,1,4,6,5,3,2,8]=>1001110
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[7,1,5,3,6,4,2,8]=>1010110
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[7,1,3,4,5,6,2,8]=>1000010
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[7,3,1,2,4,5,6,8]=>1100000
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[7,3,1,2,4,6,5,8]=>1100010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,3,1,2,6,4,5,8]=>1100100
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[7,3,1,2,5,6,4,8]=>1100010
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,3,1,5,2,4,6,8]=>1101000
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,3,1,5,2,6,4,8]=>1101010
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,3,1,5,6,2,4,8]=>1100100
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[7,3,1,6,4,5,2,8]=>1101010
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,3,1,6,5,4,2,8]=>1101110
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[7,3,1,5,6,4,2,8]=>1100110
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[7,3,1,5,4,6,2,8]=>1101010
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[7,3,1,4,5,6,2,8]=>1100010
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[7,4,2,1,6,5,3,8]=>1110110
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[7,4,2,1,5,6,3,8]=>1110010
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,3,4,1,2,5,6,8]=>1010000
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[7,3,4,1,2,6,5,8]=>1010010
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,3,4,1,6,2,5,8]=>1010100
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[7,3,4,1,6,5,2,8]=>1010110
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,3,4,1,5,6,2,8]=>1010010
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[7,5,2,3,1,4,6,8]=>1101000
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[7,5,2,3,1,6,4,8]=>1101010
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[7,5,4,2,1,6,3,8]=>1111010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,3,5,2,1,4,6,8]=>1011000
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[7,3,5,2,1,6,4,8]=>1011010
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[7,4,2,5,1,3,6,8]=>1101000
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[7,4,2,5,1,6,3,8]=>1101010
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[7,6,2,3,4,1,5,8]=>1100100
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[7,6,2,5,3,1,4,8]=>1101100
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[7,6,5,3,2,1,4,8]=>1111100
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[7,3,4,5,2,6,1,8]=>[7,6,4,5,2,1,3,8]=>1101100
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,3,6,5,2,1,4,8]=>1011100
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[7,5,2,3,4,6,1,8]=>[7,3,4,6,2,1,5,8]=>1001100
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[7,3,5,2,6,1,4,8]=>1010100
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[7,3,2,4,5,6,1,8]=>[7,4,2,5,6,1,3,8]=>1100100
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,6,2,3,4,5,1,8]=>1100010
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[7,6,2,3,5,4,1,8]=>1100110
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,6,2,5,4,3,1,8]=>1101110
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,6,4,2,5,3,1,8]=>1110110
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[7,6,5,3,2,4,1,8]=>1111010
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,6,4,5,2,3,1,8]=>1101010
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>1110110
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>1101110
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>1110110
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>1100110
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[7,3,6,4,5,2,1,8]=>1010110
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,4,2,6,3,5,1,8]=>1101010
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[7,3,4,6,5,2,1,8]=>1001110
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,3,5,2,6,4,1,8]=>1010110
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[7,4,2,5,6,3,1,8]=>1100110
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,3,4,5,6,2,1,8]=>1000110
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[7,5,4,2,3,6,1,8]=>1110010
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>1111010
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>1101010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[7,3,5,2,4,6,1,8]=>1010010
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[7,3,5,4,2,6,1,8]=>1011010
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[7,4,2,5,3,6,1,8]=>1101010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>1100010
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>1000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[2,7,1,3,4,5,6,8]=>0100000
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[2,7,1,3,6,4,5,8]=>0100100
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[2,7,1,3,6,5,4,8]=>0100110
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[2,7,1,3,5,6,4,8]=>0100010
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[2,7,1,5,6,3,4,8]=>0100100
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[6,7,5,3,4,1,2,8]=>[2,7,4,1,3,6,5,8]=>0110010
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[2,7,4,1,6,3,5,8]=>0110100
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[2,7,4,1,6,5,3,8]=>0110110
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[2,7,6,5,3,1,4,8]=>0111100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[2,7,6,3,4,5,1,8]=>0110010
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[2,7,6,3,5,4,1,8]=>0110110
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[5,4,6,3,7,1,2,8]=>[2,7,6,5,4,3,1,8]=>0111110
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[2,7,4,6,5,3,1,8]=>0101110
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[2,7,5,3,6,4,1,8]=>0110110
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[2,7,4,5,6,3,1,8]=>0100110
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[2,7,3,4,5,6,1,8]=>0100010
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[3,1,7,2,4,5,6,8]=>1010000
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[3,1,7,2,5,6,4,8]=>1010010
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[3,1,7,5,2,4,6,8]=>1011000
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[3,1,7,5,6,2,4,8]=>1010100
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[3,1,7,6,4,5,2,8]=>1011010
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,2,1,3,8]=>[3,1,7,6,5,4,2,8]=>1011110
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[3,1,7,4,5,6,2,8]=>1010010
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[2,3,7,1,4,5,6,8]=>0010000
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[2,3,7,1,6,5,4,8]=>0010110
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[2,3,7,1,5,6,4,8]=>0010010
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[2,3,7,6,5,4,1,8]=>0011110
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[2,3,7,5,6,4,1,8]=>0010110
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[2,3,7,5,4,6,1,8]=>0011010
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[4,1,2,7,3,5,6,8]=>1001000
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[4,1,2,7,5,6,3,8]=>1001010
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[4,3,1,7,6,2,5,8]=>1101100
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[2,4,1,7,5,6,3,8]=>0101010
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[3,1,4,7,6,2,5,8]=>1001100
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[3,1,4,7,5,6,2,8]=>1001010
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[2,3,4,7,1,5,6,8]=>0001000
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[2,3,4,7,1,6,5,8]=>0001010
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[2,3,4,7,6,1,5,8]=>0001100
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[2,3,4,7,6,5,1,8]=>0001110
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[2,3,4,7,5,6,1,8]=>0001010
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[5,1,2,3,7,6,4,8]=>1000110
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[5,1,4,2,7,3,6,8]=>1010100
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[5,3,1,2,7,4,6,8]=>1100100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[5,4,2,1,7,6,3,8]=>1110110
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[5,3,4,1,7,2,6,8]=>1010100
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[2,5,1,3,7,4,6,8]=>0100100
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[6,7,4,3,1,2,5,8]=>[2,5,1,3,7,6,4,8]=>0100110
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[3,1,5,2,7,4,6,8]=>1010100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[4,1,2,5,7,3,6,8]=>1000100
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[4,1,2,5,7,6,3,8]=>1000110
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[4,3,1,5,7,2,6,8]=>1100100
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[6,7,2,1,3,4,5,8]=>[3,1,4,5,7,6,2,8]=>1000110
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[2,3,4,5,7,1,6,8]=>0000100
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[2,3,4,5,7,6,1,8]=>0000110
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[6,1,2,3,4,7,5,8]=>1000010
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[6,1,4,5,2,7,3,8]=>1001010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[6,3,1,2,4,7,5,8]=>1100010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[6,4,2,1,3,7,5,8]=>1110010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[6,3,5,2,1,7,4,8]=>1011010
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[7,3,2,4,5,1,6,8]=>[6,4,2,5,1,7,3,8]=>1101010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[7,5,4,3,1,2,6,8]=>[2,6,1,3,4,7,5,8]=>0100010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[7,4,5,3,1,2,6,8]=>[2,6,1,5,3,7,4,8]=>0101010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[2,6,4,1,3,7,5,8]=>0110010
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[3,1,6,5,2,7,4,8]=>1011010
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[2,3,6,1,4,7,5,8]=>0010010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[4,1,2,6,3,7,5,8]=>1001010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[4,3,1,6,2,7,5,8]=>1101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[2,4,1,6,3,7,5,8]=>0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[2,3,4,6,1,7,5,8]=>0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[5,1,2,3,6,7,4,8]=>1000010
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[2,5,4,1,6,7,3,8]=>0110010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[4,1,2,5,6,7,3,8]=>1000010
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[2,4,1,5,6,7,3,8]=>0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[3,1,4,5,6,7,2,8]=>1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,1,2,3,4,5,7,8]=>1000000
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,1,2,3,5,4,7,8]=>1000100
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[6,4,5,3,2,1,7,8]=>[6,1,2,5,3,4,7,8]=>1001000
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[6,1,2,4,5,3,7,8]=>1000100
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[6,1,4,2,3,5,7,8]=>1010000
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[6,1,4,2,5,3,7,8]=>1010100
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[5,3,4,6,2,1,7,8]=>[6,1,4,5,3,2,7,8]=>1001100
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[6,1,3,4,5,2,7,8]=>1000100
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[6,5,4,2,3,1,7,8]=>[6,3,1,2,4,5,7,8]=>1100000
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[6,3,1,5,4,2,7,8]=>1101100
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[6,5,3,2,4,1,7,8]=>[6,4,2,1,3,5,7,8]=>1110000
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[6,4,2,1,5,3,7,8]=>1110100
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[6,3,4,1,5,2,7,8]=>1010100
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[6,3,4,2,5,1,7,8]=>[6,5,4,2,1,3,7,8]=>1111000
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[6,4,2,3,5,1,7,8]=>[6,3,5,2,1,4,7,8]=>1011000
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[6,4,2,5,1,3,7,8]=>1101000
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>1100100
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>1101100
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[6,3,5,2,4,1,7,8]=>1010100
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[6,4,2,5,3,1,7,8]=>1101100
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>1110100
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>1000100
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[2,6,1,3,4,5,7,8]=>0100000
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[2,6,1,3,5,4,7,8]=>0100100
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[2,6,1,5,3,4,7,8]=>0101000
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[2,6,1,5,4,3,7,8]=>0101100
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[4,5,6,3,1,2,7,8]=>[2,6,1,4,5,3,7,8]=>0100100
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[2,6,4,1,3,5,7,8]=>0110000
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[2,6,4,1,5,3,7,8]=>0110100
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[2,6,4,5,1,3,7,8]=>0101000
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[2,6,5,3,4,1,7,8]=>0110100
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[5,3,4,6,1,2,7,8]=>[2,6,4,5,3,1,7,8]=>0101100
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[2,6,3,4,5,1,7,8]=>0100100
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[3,1,6,2,4,5,7,8]=>1010000
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[3,1,6,2,5,4,7,8]=>1010100
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[3,1,6,5,2,4,7,8]=>1011000
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[3,1,6,5,4,2,7,8]=>1011100
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[4,5,6,2,1,3,7,8]=>[3,1,6,4,5,2,7,8]=>1010100
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[2,3,6,1,4,5,7,8]=>0010000
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[2,3,6,1,5,4,7,8]=>0010100
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[2,3,6,5,4,1,7,8]=>0011100
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[2,3,6,4,5,1,7,8]=>0010100
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[4,1,2,6,5,3,7,8]=>1001100
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[4,3,1,6,2,5,7,8]=>1101000
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[4,3,1,6,5,2,7,8]=>1101100
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[6,5,3,1,2,4,7,8]=>[2,4,1,6,3,5,7,8]=>0101000
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[2,4,1,6,5,3,7,8]=>0101100
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[5,6,2,1,3,4,7,8]=>[3,1,4,6,5,2,7,8]=>1001100
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[2,3,4,6,1,5,7,8]=>0001000
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[2,3,4,6,5,1,7,8]=>0001100
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[5,1,2,3,6,4,7,8]=>1000100
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[5,4,2,1,6,3,7,8]=>1110100
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[5,3,4,1,6,2,7,8]=>1010100
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[2,5,1,3,6,4,7,8]=>0100100
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[6,3,4,1,2,5,7,8]=>[2,5,4,1,6,3,7,8]=>0110100
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[2,3,5,1,6,4,7,8]=>0010100
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[4,1,2,5,6,3,7,8]=>1000100
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[2,4,1,5,6,3,7,8]=>0100100
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[3,1,4,5,6,2,7,8]=>1000100
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>1010000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,1,3,4,2,6,7,8]=>1001000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>1100000
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>1101000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>1110000
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,3,4,1,2,6,7,8]=>1010000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>1101000
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>1011000
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>1101000
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>1001000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[2,5,1,3,4,6,7,8]=>0100000
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[2,5,4,1,3,6,7,8]=>0110000
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[2,5,4,3,1,6,7,8]=>0111000
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[2,5,3,4,1,6,7,8]=>0101000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[3,1,5,2,4,6,7,8]=>1010000
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[2,3,5,1,4,6,7,8]=>0010000
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[2,3,5,4,1,6,7,8]=>0011000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>1001000
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[2,4,1,5,3,6,7,8]=>0101000
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[3,1,4,5,2,6,7,8]=>1001000
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1100000
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>1010000
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>0100000
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>0110000
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,1,2,3,4,5,6,7,8]=>10000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,1,2,3,4,5,6,8,7]=>10000001
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,1,2,3,4,5,7,8,6]=>10000001
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[9,1,2,3,4,6,7,8,5]=>10000001
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[9,1,3,4,5,6,7,8,2]=>10000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>10000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[9,1,2,3,4,5,8,6,7]=>10000010
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,8,9,7]=>100000001
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[10,1,2,3,4,5,7,8,9,6]=>100000001
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,1,2,3,4,6,7,8,9,5]=>100000001
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,1,3,4,5,6,7,8,9,2]=>100000001
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[2,9,3,4,5,6,7,8,1]=>01000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>100000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,1,2,3,4,5,8,7,6]=>10000011
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,1,2,3,4,8,6,7,5]=>10000101
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,1,2,3,8,5,6,7,4]=>10001001
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,1,2,8,4,5,6,7,3]=>10010001
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,1,8,3,4,5,6,7,2]=>10100001
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,8,2,3,4,5,6,7,1]=>11000001
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,6,7,9]=>10000000
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,9,8,7]=>100000011
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[9,1,2,3,4,7,8,6,5]=>10000011
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,1,2,3,4,5,9,7,8,6]=>100000101
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[9,1,2,3,6,8,5,7,4]=>10000101
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[10,1,2,3,4,9,6,7,8,5]=>100001001
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>[9,1,2,5,8,4,6,7,3]=>10001001
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[10,1,2,3,9,5,6,7,8,4]=>100010001
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>[9,1,4,8,3,5,6,7,2]=>10010001
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[10,1,2,9,4,5,6,7,8,3]=>100100001
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[9,3,8,2,4,5,6,7,1]=>10100001
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,1,9,3,4,5,6,7,8,2]=>101000001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[2,8,1,3,4,5,6,7,9]=>01000000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,9,2,3,4,5,6,7,8,1]=>110000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,10,4,1,6,3,8,5,9,7]=>011010101
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[6,7,5,8,4,9,3,10,1,2]=>[2,10,9,8,7,6,5,4,3,1]=>011111111
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>[8,9,7,10,3,4,2,5,1,6]=>[6,5,4,2,1,10,9,8,7,3]=>111101111
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>11111111110
[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]=>[7,5,4,6,3,8,2,9,1,10]=>[9,8,7,6,4,3,5,2,1,10]=>111110110
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[3,1,5,2,7,4,9,6,10,8]=>101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[3,1,5,2,7,4,9,6,11,8,12,10]=>10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[3,1,4,5,6,7,8,9,2]=>10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>11000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[3,1,4,5,6,7,8,9,10,2]=>100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[2,4,1,5,6,7,8,9,3]=>01000001
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[4,3,1,5,6,7,8,9,2]=>11000001
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[9,3,4,2,5,6,7,8,1]=>10100001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>11100001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>110000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>1000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,9,8,1]=>00000011
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[2,3,4,5,6,9,7,8,1]=>00000101
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[2,3,4,5,9,6,7,8,1]=>00001001
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[2,3,4,9,5,6,7,8,1]=>00010001
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[2,3,9,4,5,6,7,8,1]=>00100001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,9,1,8]=>00000010
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,10,9,1]=>000000011
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[2,3,4,5,6,9,8,7,1]=>00000111
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,10,8,9,1]=>000000101
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[7,6,8,9,1,2,3,4,5]=>[2,3,4,5,9,7,6,8,1]=>00001101
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[2,3,4,5,6,10,7,8,9,1]=>000001001
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[6,5,7,8,9,1,2,3,4]=>[2,3,4,9,6,5,7,8,1]=>00011001
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[2,3,4,5,10,6,7,8,9,1]=>000010001
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[5,4,6,7,8,9,1,2,3]=>[2,3,9,5,4,6,7,8,1]=>00110001
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[2,3,4,10,5,6,7,8,9,1]=>000100001
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>[2,9,4,3,5,6,7,8,1]=>01100001
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[2,3,10,4,5,6,7,8,9,1]=>001000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[2,10,3,4,5,6,7,8,9,1]=>010000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[2,9,1,3,4,5,6,7,8]=>01000000
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[2,10,1,3,4,5,6,7,8,9]=>010000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>1000000000
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,1,2,3,4,5,6,8,7,10]=>100000010
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[8,1,2,3,4,7,6,5,9]=>10000110
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[2,9,1,3,4,5,8,6,7]=>01000010
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[2,11,1,3,4,5,6,7,8,9,10]=>0100000000
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[7,6,8,5,9,4,10,2,1,3]=>[3,1,10,9,8,7,6,5,4,2]=>101111111
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[10,5,4,6,3,7,2,8,1,9]=>[9,8,7,6,4,3,2,1,10,5]=>111111101
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[10,9,11,8,12,4,3,5,2,6,1,7]=>[7,6,5,3,2,1,12,11,10,9,8,4]=>11111011111
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[6,4,5,7,3,8,2,9,1,10]=>[9,8,7,5,6,4,3,2,1,10]=>111011110
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,9,2,4,5,6,7,8]=>10100000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,9,5,7,8]=>10000100
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,9,6,8]=>10000010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,9,7]=>10000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[2,3,9,1,4,5,6,7,8]=>00100000
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[4,3,1,9,2,5,6,7,8]=>11010000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[4,1,2,10,3,5,6,7,8,9]=>100100000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[5,1,2,3,10,4,6,7,8,9]=>100010000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[8,1,2,3,4,7,5,9,6]=>10000101
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,10,8]=>100000001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>10000000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>10000000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>10000000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>100000000
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>100000000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>100000000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>100000000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>100000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>01000000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>100000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[9,1,2,3,6,4,5,7,8]=>10001000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[9,1,2,5,3,4,6,7,8]=>10010000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[9,3,1,2,4,5,6,7,8]=>11000000
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[10,3,1,2,4,5,6,7,8,9]=>110000000
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[10,3,1,5,2,7,4,9,6,8]=>110101010
[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[12,10,11,8,9,6,7,4,5,2,3,1]=>[12,3,1,5,2,7,4,9,6,11,8,10]=>11010101010
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[9,3,4,5,6,7,8,1,2]=>10000010
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[3,1,4,5,6,7,8,2,9]=>10000010
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,3,4,5,6,7,8,2,1]=>10000011
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[10,3,4,5,6,7,8,9,1,2]=>100000010
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[4,2,1,3,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>10100000
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[5,3,2,1,4,6,7,8,9]=>[4,1,2,5,3,6,7,8,9]=>10010000
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]=>[6,4,3,2,1,5,7,8,9]=>[5,1,2,3,6,4,7,8,9]=>10001000
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[6,1,2,3,4,7,5,8,9]=>10000100
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[7,1,2,3,4,5,8,6,9]=>10000010
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>10000010
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>10010000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>10000100
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>100000010
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>000000010
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[2,9,4,5,6,7,8,1,3]=>01000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[9,8,2,3,4,5,6,1,7]=>11000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[2,8,1,3,4,5,6,9,7]=>01000001
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[2,3,10,1,4,5,6,7,8,9]=>001000000
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[7,8,2,3,4,5,6,9,1]=>[9,3,4,5,6,8,7,2,1]=>10000111
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[4,5,1,2,3,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>00110000
[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[9,2,3,4,5,1,6,7,8]=>[6,3,4,5,1,7,8,9,2]=>10010001
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[5,3,1,2,4,6,7,8,9]=>[2,4,1,5,3,6,7,8,9]=>01010000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[10,9,2,3,4,5,6,7,1,8]=>110000010
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[2,8,3,4,5,6,7,1,9]=>01000010
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,10,1,9]=>000000010
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,10,2,3,4,5,6,7,8,9,1]=>1100000001
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[2,3,4,5,6,9,1,7,8]=>00000100
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[2,3,4,5,9,1,6,7,8]=>00001000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[2,3,4,9,1,5,6,7,8]=>00010000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,1,9,7]=>00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,10,1,8,9]=>000000100
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[2,3,4,5,6,10,1,7,8,9]=>000001000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[2,3,4,5,10,1,6,7,8,9]=>000010000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[2,3,4,10,1,5,6,7,8,9]=>000100000
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[5,1,2,3,6,7,8,9,4]=>10000001
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[2,3,4,5,6,8,1,7,9]=>00000100
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>[8,3,1,2,4,5,6,7,9]=>11000000
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[8,3,4,5,6,7,1,9,2]=>10000101
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>01100000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,11,10,1]=>0000000011
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>[9,3,4,5,6,7,1,2,8]=>10000100
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>[10,3,4,5,6,7,8,1,2,9]=>100000100
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[2,4,1,5,6,7,8,9,10,3]=>010000001
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[9,2,3,4,5,6,1,7,8]=>[7,3,4,5,6,1,8,9,2]=>10001001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[2,9,1,3,4,5,6,7,10,8]=>010000001
[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[9,8,2,3,4,5,6,1,7]=>[7,3,4,5,6,1,9,2,8]=>10001010
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[9,3,4,5,6,7,8,2,1]=>[9,1,4,5,6,7,8,2,3]=>10000010
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
searching the database
Sorry, this map was not found in the database.