Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[1,2]=>0
[[.,.],.]=>[1,2]=>[2,1]=>1
[.,[.,[.,.]]]=>[3,2,1]=>[1,3,2]=>01
[.,[[.,.],.]]=>[2,3,1]=>[1,2,3]=>00
[[.,.],[.,.]]=>[1,3,2]=>[2,1,3]=>10
[[.,[.,.]],.]=>[2,1,3]=>[3,2,1]=>11
[[[.,.],.],.]=>[1,2,3]=>[2,3,1]=>01
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,4,3,2]=>011
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,4,2,3]=>010
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[1,2,4,3]=>001
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,3,2,4]=>010
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,2,3,4]=>000
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,1,4,3]=>101
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,1,3,4]=>100
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,2,1,4]=>110
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[2,3,1,4]=>010
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,3,2,1]=>111
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,2,3,1]=>101
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,4,3,1]=>011
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[3,2,4,1]=>101
[[[[.,.],.],.],.]=>[1,2,3,4]=>[2,3,4,1]=>001
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,5,4,3,2]=>0111
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,5,4,2,3]=>0110
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[1,5,2,4,3]=>0101
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,5,3,2,4]=>0110
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,5,2,3,4]=>0100
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[1,2,5,4,3]=>0011
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[1,2,5,3,4]=>0010
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[1,3,2,5,4]=>0101
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[1,2,3,5,4]=>0001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,4,3,2,5]=>0110
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,4,2,3,5]=>0100
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[1,2,4,3,5]=>0010
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,3,2,4,5]=>0100
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,2,3,4,5]=>0000
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,1,5,4,3]=>1011
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[2,1,5,3,4]=>1010
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[2,1,3,5,4]=>1001
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[2,1,4,3,5]=>1010
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,1,3,4,5]=>1000
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[3,2,1,5,4]=>1101
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2,1,4,5]=>1100
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[2,3,1,5,4]=>0101
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[2,3,1,4,5]=>0100
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,3,2,1,5]=>1110
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,2,3,1,5]=>1010
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[2,4,3,1,5]=>0110
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[3,2,4,1,5]=>1010
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[2,3,4,1,5]=>0010
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,4,3,2,1]=>1111
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,4,2,3,1]=>1101
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[5,2,4,3,1]=>1011
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,3,2,4,1]=>1101
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,2,3,4,1]=>1001
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[2,5,4,3,1]=>0111
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[2,5,3,4,1]=>0101
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[3,2,5,4,1]=>1011
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[2,3,5,4,1]=>0011
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[4,3,2,5,1]=>1101
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[4,2,3,5,1]=>1001
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,4,3,5,1]=>0101
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[3,2,4,5,1]=>1001
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[2,3,4,5,1]=>0001
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,6,5,4,3,2]=>01111
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,6,5,4,2,3]=>01110
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[1,6,5,2,4,3]=>01101
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,6,5,3,2,4]=>01110
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,6,5,2,3,4]=>01100
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[1,6,2,5,4,3]=>01011
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[1,6,2,5,3,4]=>01010
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[1,6,3,2,5,4]=>01101
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[1,6,2,3,5,4]=>01001
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,6,4,3,2,5]=>01110
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,6,4,2,3,5]=>01100
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[1,6,2,4,3,5]=>01010
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,6,3,2,4,5]=>01100
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,6,2,3,4,5]=>01000
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[1,2,6,5,4,3]=>00111
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[1,2,6,5,3,4]=>00110
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[1,2,6,3,5,4]=>00101
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[1,2,6,4,3,5]=>00110
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[1,2,6,3,4,5]=>00100
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[1,3,2,6,5,4]=>01011
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[1,3,2,6,4,5]=>01010
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[1,2,3,6,5,4]=>00011
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[1,2,3,6,4,5]=>00010
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[1,4,3,2,6,5]=>01101
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[1,4,2,3,6,5]=>01001
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[1,2,4,3,6,5]=>00101
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[1,3,2,4,6,5]=>01001
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>00001
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,5,4,3,2,6]=>01110
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,5,4,2,3,6]=>01100
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[1,5,2,4,3,6]=>01010
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,5,3,2,4,6]=>01100
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,5,2,3,4,6]=>01000
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[1,2,5,4,3,6]=>00110
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[1,2,5,3,4,6]=>00100
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,3,2,5,4,6]=>01010
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>00010
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,4,3,2,5,6]=>01100
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,4,2,3,5,6]=>01000
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>00100
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,3,2,4,5,6]=>01000
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>00000
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,1,6,5,4,3]=>10111
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[2,1,6,5,3,4]=>10110
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[2,1,6,3,5,4]=>10101
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[2,1,6,4,3,5]=>10110
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[2,1,6,3,4,5]=>10100
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[2,1,3,6,5,4]=>10011
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[2,1,3,6,4,5]=>10010
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[2,1,4,3,6,5]=>10101
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[2,1,3,4,6,5]=>10001
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[2,1,5,4,3,6]=>10110
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[2,1,5,3,4,6]=>10100
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[2,1,3,5,4,6]=>10010
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[2,1,4,3,5,6]=>10100
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,1,3,4,5,6]=>10000
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[3,2,1,6,5,4]=>11011
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[3,2,1,6,4,5]=>11010
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[3,2,1,4,6,5]=>11001
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[3,2,1,5,4,6]=>11010
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,2,1,4,5,6]=>11000
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[2,3,1,6,5,4]=>01011
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[2,3,1,6,4,5]=>01010
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[2,3,1,4,6,5]=>01001
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[2,3,1,5,4,6]=>01010
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[2,3,1,4,5,6]=>01000
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[4,3,2,1,6,5]=>11101
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,3,2,1,5,6]=>11100
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[4,2,3,1,6,5]=>10101
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,2,3,1,5,6]=>10100
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[2,4,3,1,6,5]=>01101
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[2,4,3,1,5,6]=>01100
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[3,2,4,1,6,5]=>10101
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[3,2,4,1,5,6]=>10100
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[2,3,4,1,6,5]=>00101
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[2,3,4,1,5,6]=>00100
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,4,3,2,1,6]=>11110
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,4,2,3,1,6]=>11010
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,2,4,3,1,6]=>10110
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,3,2,4,1,6]=>11010
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,2,3,4,1,6]=>10010
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[2,5,4,3,1,6]=>01110
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[2,5,3,4,1,6]=>01010
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[3,2,5,4,1,6]=>10110
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[2,3,5,4,1,6]=>00110
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[4,3,2,5,1,6]=>11010
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[4,2,3,5,1,6]=>10010
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[2,4,3,5,1,6]=>01010
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[3,2,4,5,1,6]=>10010
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[2,3,4,5,1,6]=>00010
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,5,4,3,2,1]=>11111
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,5,4,2,3,1]=>11101
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[6,5,2,4,3,1]=>11011
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,5,3,2,4,1]=>11101
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,5,2,3,4,1]=>11001
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[6,2,5,4,3,1]=>10111
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[6,2,5,3,4,1]=>10101
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[6,3,2,5,4,1]=>11011
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[6,2,3,5,4,1]=>10011
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,4,3,2,5,1]=>11101
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,4,2,3,5,1]=>11001
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[6,2,4,3,5,1]=>10101
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,3,2,4,5,1]=>11001
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,2,3,4,5,1]=>10001
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[2,6,5,4,3,1]=>01111
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[2,6,5,3,4,1]=>01101
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[2,6,3,5,4,1]=>01011
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[2,6,4,3,5,1]=>01101
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[2,6,3,4,5,1]=>01001
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[3,2,6,5,4,1]=>10111
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[3,2,6,4,5,1]=>10101
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[2,3,6,5,4,1]=>00111
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[2,3,6,4,5,1]=>00101
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[4,3,2,6,5,1]=>11011
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[4,2,3,6,5,1]=>10011
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[2,4,3,6,5,1]=>01011
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[3,2,4,6,5,1]=>10011
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[2,3,4,6,5,1]=>00011
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[5,4,3,2,6,1]=>11101
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[5,4,2,3,6,1]=>11001
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[5,2,4,3,6,1]=>10101
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[5,3,2,4,6,1]=>11001
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[5,2,3,4,6,1]=>10001
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[2,5,4,3,6,1]=>01101
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[2,5,3,4,6,1]=>01001
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[3,2,5,4,6,1]=>10101
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[2,3,5,4,6,1]=>00101
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[4,3,2,5,6,1]=>11001
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[4,2,3,5,6,1]=>10001
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[2,4,3,5,6,1]=>01001
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[3,2,4,5,6,1]=>10001
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>00001
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>011111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,7,6,5,4,2,3]=>011110
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[1,7,6,5,2,4,3]=>011101
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,7,6,5,3,2,4]=>011110
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,7,6,5,2,3,4]=>011100
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[1,7,6,2,5,4,3]=>011011
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[1,7,6,2,5,3,4]=>011010
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[1,7,6,3,2,5,4]=>011101
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[1,7,6,2,3,5,4]=>011001
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,7,6,4,3,2,5]=>011110
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,7,6,4,2,3,5]=>011100
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[1,7,6,2,4,3,5]=>011010
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,7,6,3,2,4,5]=>011100
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,7,6,2,3,4,5]=>011000
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[1,7,2,6,5,4,3]=>010111
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[1,7,2,6,5,3,4]=>010110
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[1,7,2,6,3,5,4]=>010101
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[1,7,2,6,4,3,5]=>010110
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[1,7,2,6,3,4,5]=>010100
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[1,7,3,2,6,5,4]=>011011
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[1,7,3,2,6,4,5]=>011010
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[1,7,2,3,6,5,4]=>010011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[1,7,2,3,6,4,5]=>010010
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[1,7,4,3,2,6,5]=>011101
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[1,7,4,2,3,6,5]=>011001
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[1,7,2,4,3,6,5]=>010101
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[1,7,3,2,4,6,5]=>011001
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[1,7,2,3,4,6,5]=>010001
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,7,5,4,3,2,6]=>011110
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,7,5,4,2,3,6]=>011100
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[1,7,5,2,4,3,6]=>011010
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,7,5,3,2,4,6]=>011100
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,7,5,2,3,4,6]=>011000
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[1,7,2,5,4,3,6]=>010110
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[1,7,2,5,3,4,6]=>010100
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,7,3,2,5,4,6]=>011010
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[1,7,2,3,5,4,6]=>010010
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,7,4,3,2,5,6]=>011100
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,7,4,2,3,5,6]=>011000
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[1,7,2,4,3,5,6]=>010100
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,7,3,2,4,5,6]=>011000
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,7,2,3,4,5,6]=>010000
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[1,2,7,6,5,4,3]=>001111
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[1,2,7,6,5,3,4]=>001110
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[1,2,7,6,3,5,4]=>001101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[1,2,7,6,4,3,5]=>001110
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[1,2,7,6,3,4,5]=>001100
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[1,2,7,3,6,5,4]=>001011
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[1,2,7,3,6,4,5]=>001010
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[1,2,7,4,3,6,5]=>001101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[1,2,7,3,4,6,5]=>001001
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[1,2,7,5,4,3,6]=>001110
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[1,2,7,5,3,4,6]=>001100
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[1,2,7,3,5,4,6]=>001010
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[1,2,7,4,3,5,6]=>001100
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[1,2,7,3,4,5,6]=>001000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[1,3,2,7,6,5,4]=>010111
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[1,3,2,7,6,4,5]=>010110
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[1,3,2,7,4,6,5]=>010101
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,3,2,7,5,4,6]=>010110
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[1,3,2,7,4,5,6]=>010100
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[1,2,3,7,6,5,4]=>000111
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[1,2,3,7,6,4,5]=>000110
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[1,2,3,7,4,6,5]=>000101
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[1,2,3,7,5,4,6]=>000110
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[1,2,3,7,4,5,6]=>000100
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[1,4,3,2,7,6,5]=>011011
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[1,4,3,2,7,5,6]=>011010
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[1,4,2,3,7,6,5]=>010011
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[1,4,2,3,7,5,6]=>010010
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[1,2,4,3,7,6,5]=>001011
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[1,2,4,3,7,5,6]=>001010
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[1,3,2,4,7,6,5]=>010011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[1,3,2,4,7,5,6]=>010010
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[1,2,3,4,7,6,5]=>000011
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[1,2,3,4,7,5,6]=>000010
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[1,5,4,3,2,7,6]=>011101
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[1,5,4,2,3,7,6]=>011001
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[1,5,2,4,3,7,6]=>010101
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[1,5,3,2,4,7,6]=>011001
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[1,5,2,3,4,7,6]=>010001
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[1,2,5,4,3,7,6]=>001101
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[1,2,5,3,4,7,6]=>001001
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[1,3,2,5,4,7,6]=>010101
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[1,2,3,5,4,7,6]=>000101
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[1,4,3,2,5,7,6]=>011001
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[1,4,2,3,5,7,6]=>010001
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[1,2,4,3,5,7,6]=>001001
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[1,3,2,4,5,7,6]=>010001
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[1,2,3,4,5,7,6]=>000001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,6,5,4,3,2,7]=>011110
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,6,5,4,2,3,7]=>011100
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[1,6,5,2,4,3,7]=>011010
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,6,5,3,2,4,7]=>011100
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,6,5,2,3,4,7]=>011000
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[1,6,2,5,4,3,7]=>010110
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[1,6,2,5,3,4,7]=>010100
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[1,6,3,2,5,4,7]=>011010
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[1,6,2,3,5,4,7]=>010010
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,6,4,3,2,5,7]=>011100
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,6,4,2,3,5,7]=>011000
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[1,6,2,4,3,5,7]=>010100
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,6,3,2,4,5,7]=>011000
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,6,2,3,4,5,7]=>010000
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[1,2,6,5,4,3,7]=>001110
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[1,2,6,5,3,4,7]=>001100
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[1,2,6,3,5,4,7]=>001010
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[1,2,6,4,3,5,7]=>001100
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[1,2,6,3,4,5,7]=>001000
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[1,3,2,6,5,4,7]=>010110
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,3,2,6,4,5,7]=>010100
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[1,2,3,6,5,4,7]=>000110
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[1,2,3,6,4,5,7]=>000100
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,4,3,2,6,5,7]=>011010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[1,4,2,3,6,5,7]=>010010
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[1,2,4,3,6,5,7]=>001010
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,3,2,4,6,5,7]=>010010
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>000010
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,5,4,3,2,6,7]=>011100
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,5,4,2,3,6,7]=>011000
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[1,5,2,4,3,6,7]=>010100
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,5,3,2,4,6,7]=>011000
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,5,2,3,4,6,7]=>010000
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[1,2,5,4,3,6,7]=>001100
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[1,2,5,3,4,6,7]=>001000
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,3,2,5,4,6,7]=>010100
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[1,2,3,5,4,6,7]=>000100
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,4,3,2,5,6,7]=>011000
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,4,2,3,5,6,7]=>010000
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[1,2,4,3,5,6,7]=>001000
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,3,2,4,5,6,7]=>010000
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>000000
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[2,1,7,6,5,4,3]=>101111
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[2,1,7,6,5,3,4]=>101110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[2,1,7,6,3,5,4]=>101101
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[2,1,7,6,4,3,5]=>101110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[2,1,7,6,3,4,5]=>101100
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[2,1,7,3,6,5,4]=>101011
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[2,1,7,3,6,4,5]=>101010
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[2,1,7,4,3,6,5]=>101101
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[2,1,7,3,4,6,5]=>101001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[2,1,7,5,4,3,6]=>101110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[2,1,7,5,3,4,6]=>101100
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[2,1,7,3,5,4,6]=>101010
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[2,1,7,4,3,5,6]=>101100
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[2,1,7,3,4,5,6]=>101000
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[2,1,3,7,6,5,4]=>100111
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[2,1,3,7,6,4,5]=>100110
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[2,1,3,7,4,6,5]=>100101
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[2,1,3,7,5,4,6]=>100110
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[2,1,3,7,4,5,6]=>100100
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[2,1,4,3,7,6,5]=>101011
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[2,1,4,3,7,5,6]=>101010
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[2,1,3,4,7,6,5]=>100011
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[2,1,3,4,7,5,6]=>100010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[2,1,5,4,3,7,6]=>101101
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[2,1,5,3,4,7,6]=>101001
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[2,1,3,5,4,7,6]=>100101
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[2,1,4,3,5,7,6]=>101001
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[2,1,3,4,5,7,6]=>100001
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[2,1,6,5,4,3,7]=>101110
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[2,1,6,5,3,4,7]=>101100
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[2,1,6,3,5,4,7]=>101010
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[2,1,6,4,3,5,7]=>101100
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[2,1,6,3,4,5,7]=>101000
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[2,1,3,6,5,4,7]=>100110
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[2,1,3,6,4,5,7]=>100100
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[2,1,4,3,6,5,7]=>101010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[2,1,3,4,6,5,7]=>100010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[2,1,5,4,3,6,7]=>101100
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[2,1,5,3,4,6,7]=>101000
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[2,1,3,5,4,6,7]=>100100
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[2,1,4,3,5,6,7]=>101000
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,1,3,4,5,6,7]=>100000
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[3,2,1,7,6,5,4]=>110111
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[3,2,1,7,6,4,5]=>110110
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[3,2,1,7,4,6,5]=>110101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[3,2,1,7,5,4,6]=>110110
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[3,2,1,7,4,5,6]=>110100
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[3,2,1,4,7,6,5]=>110011
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[3,2,1,4,7,5,6]=>110010
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[3,2,1,5,4,7,6]=>110101
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[3,2,1,4,5,7,6]=>110001
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[3,2,1,6,5,4,7]=>110110
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[3,2,1,6,4,5,7]=>110100
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[3,2,1,4,6,5,7]=>110010
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[3,2,1,5,4,6,7]=>110100
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,2,1,4,5,6,7]=>110000
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[2,3,1,7,6,5,4]=>010111
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[2,3,1,7,6,4,5]=>010110
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[2,3,1,7,4,6,5]=>010101
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[2,3,1,7,5,4,6]=>010110
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[2,3,1,7,4,5,6]=>010100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[2,3,1,4,7,6,5]=>010011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[2,3,1,4,7,5,6]=>010010
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[2,3,1,5,4,7,6]=>010101
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[2,3,1,4,5,7,6]=>010001
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[2,3,1,6,5,4,7]=>010110
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[2,3,1,6,4,5,7]=>010100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[2,3,1,4,6,5,7]=>010010
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[2,3,1,5,4,6,7]=>010100
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[2,3,1,4,5,6,7]=>010000
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[4,3,2,1,7,6,5]=>111011
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[4,3,2,1,7,5,6]=>111010
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[4,3,2,1,5,7,6]=>111001
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[4,3,2,1,6,5,7]=>111010
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,3,2,1,5,6,7]=>111000
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[4,2,3,1,7,6,5]=>101011
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[4,2,3,1,7,5,6]=>101010
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[4,2,3,1,5,7,6]=>101001
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[4,2,3,1,6,5,7]=>101010
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,2,3,1,5,6,7]=>101000
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[2,4,3,1,7,6,5]=>011011
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[2,4,3,1,7,5,6]=>011010
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[2,4,3,1,5,7,6]=>011001
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[2,4,3,1,6,5,7]=>011010
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[2,4,3,1,5,6,7]=>011000
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[3,2,4,1,7,6,5]=>101011
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[3,2,4,1,7,5,6]=>101010
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[3,2,4,1,5,7,6]=>101001
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[3,2,4,1,6,5,7]=>101010
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[3,2,4,1,5,6,7]=>101000
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[2,3,4,1,7,6,5]=>001011
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[2,3,4,1,7,5,6]=>001010
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[2,3,4,1,5,7,6]=>001001
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[2,3,4,1,6,5,7]=>001010
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[2,3,4,1,5,6,7]=>001000
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[5,4,3,2,1,7,6]=>111101
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,4,3,2,1,6,7]=>111100
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[5,4,2,3,1,7,6]=>110101
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,4,2,3,1,6,7]=>110100
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[5,2,4,3,1,7,6]=>101101
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,2,4,3,1,6,7]=>101100
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[5,3,2,4,1,7,6]=>110101
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,3,2,4,1,6,7]=>110100
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[5,2,3,4,1,7,6]=>100101
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,2,3,4,1,6,7]=>100100
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[2,5,4,3,1,7,6]=>011101
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[2,5,4,3,1,6,7]=>011100
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[2,5,3,4,1,7,6]=>010101
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[2,5,3,4,1,6,7]=>010100
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[3,2,5,4,1,7,6]=>101101
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[3,2,5,4,1,6,7]=>101100
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[2,3,5,4,1,7,6]=>001101
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[2,3,5,4,1,6,7]=>001100
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[4,3,2,5,1,7,6]=>110101
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[4,3,2,5,1,6,7]=>110100
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[4,2,3,5,1,7,6]=>100101
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[4,2,3,5,1,6,7]=>100100
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[2,4,3,5,1,7,6]=>010101
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[2,4,3,5,1,6,7]=>010100
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[3,2,4,5,1,7,6]=>100101
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[3,2,4,5,1,6,7]=>100100
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[2,3,4,5,1,7,6]=>000101
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[2,3,4,5,1,6,7]=>000100
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,1,7]=>111110
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,1,7]=>111010
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,5,2,4,3,1,7]=>110110
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,1,7]=>111010
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,1,7]=>110010
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,2,5,4,3,1,7]=>101110
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,2,5,3,4,1,7]=>101010
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,3,2,5,4,1,7]=>110110
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,2,3,5,4,1,7]=>100110
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,1,7]=>111010
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,1,7]=>110010
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,2,4,3,5,1,7]=>101010
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,1,7]=>110010
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,1,7]=>100010
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[2,6,5,4,3,1,7]=>011110
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[2,6,5,3,4,1,7]=>011010
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[2,6,3,5,4,1,7]=>010110
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[2,6,4,3,5,1,7]=>011010
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[2,6,3,4,5,1,7]=>010010
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[3,2,6,5,4,1,7]=>101110
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[3,2,6,4,5,1,7]=>101010
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[2,3,6,5,4,1,7]=>001110
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[2,3,6,4,5,1,7]=>001010
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[4,3,2,6,5,1,7]=>110110
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[4,2,3,6,5,1,7]=>100110
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[2,4,3,6,5,1,7]=>010110
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[3,2,4,6,5,1,7]=>100110
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[2,3,4,6,5,1,7]=>000110
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,1,7]=>111010
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,1,7]=>110010
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[5,2,4,3,6,1,7]=>101010
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,1,7]=>110010
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,1,7]=>100010
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[2,5,4,3,6,1,7]=>011010
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[2,5,3,4,6,1,7]=>010010
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[3,2,5,4,6,1,7]=>101010
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[2,3,5,4,6,1,7]=>001010
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,1,7]=>110010
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,1,7]=>100010
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[2,4,3,5,6,1,7]=>010010
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,1,7]=>100010
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,1,7]=>000010
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,6,5,4,3,2,1]=>111111
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,6,5,4,2,3,1]=>111101
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[7,6,5,2,4,3,1]=>111011
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,6,5,3,2,4,1]=>111101
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,6,5,2,3,4,1]=>111001
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[7,6,2,5,4,3,1]=>110111
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[7,6,2,5,3,4,1]=>110101
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[7,6,3,2,5,4,1]=>111011
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[7,6,2,3,5,4,1]=>110011
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,6,4,3,2,5,1]=>111101
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,6,4,2,3,5,1]=>111001
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[7,6,2,4,3,5,1]=>110101
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,6,3,2,4,5,1]=>111001
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,6,2,3,4,5,1]=>110001
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[7,2,6,5,4,3,1]=>101111
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[7,2,6,5,3,4,1]=>101101
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[7,2,6,3,5,4,1]=>101011
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[7,2,6,4,3,5,1]=>101101
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[7,2,6,3,4,5,1]=>101001
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[7,3,2,6,5,4,1]=>110111
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[7,3,2,6,4,5,1]=>110101
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[7,2,3,6,5,4,1]=>100111
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[7,2,3,6,4,5,1]=>100101
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[7,4,3,2,6,5,1]=>111011
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[7,4,2,3,6,5,1]=>110011
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[7,2,4,3,6,5,1]=>101011
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[7,3,2,4,6,5,1]=>110011
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[7,2,3,4,6,5,1]=>100011
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,5,4,3,2,6,1]=>111101
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,5,4,2,3,6,1]=>111001
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[7,5,2,4,3,6,1]=>110101
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,5,3,2,4,6,1]=>111001
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,5,2,3,4,6,1]=>110001
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[7,2,5,4,3,6,1]=>101101
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[7,2,5,3,4,6,1]=>101001
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[7,3,2,5,4,6,1]=>110101
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[7,2,3,5,4,6,1]=>100101
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,4,3,2,5,6,1]=>111001
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,4,2,3,5,6,1]=>110001
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[7,2,4,3,5,6,1]=>101001
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,3,2,4,5,6,1]=>110001
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,2,3,4,5,6,1]=>100001
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[2,7,6,5,4,3,1]=>011111
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[2,7,6,5,3,4,1]=>011101
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[2,7,6,3,5,4,1]=>011011
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[2,7,6,4,3,5,1]=>011101
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[2,7,6,3,4,5,1]=>011001
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[2,7,3,6,5,4,1]=>010111
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[2,7,3,6,4,5,1]=>010101
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[2,7,4,3,6,5,1]=>011011
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[2,7,3,4,6,5,1]=>010011
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[2,7,5,4,3,6,1]=>011101
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[2,7,5,3,4,6,1]=>011001
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[2,7,3,5,4,6,1]=>010101
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[2,7,4,3,5,6,1]=>011001
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[2,7,3,4,5,6,1]=>010001
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[3,2,7,6,5,4,1]=>101111
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[3,2,7,6,4,5,1]=>101101
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[3,2,7,4,6,5,1]=>101011
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[3,2,7,5,4,6,1]=>101101
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[3,2,7,4,5,6,1]=>101001
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[2,3,7,6,5,4,1]=>001111
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[2,3,7,6,4,5,1]=>001101
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[2,3,7,4,6,5,1]=>001011
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[2,3,7,5,4,6,1]=>001101
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[2,3,7,4,5,6,1]=>001001
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[4,3,2,7,6,5,1]=>110111
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[4,3,2,7,5,6,1]=>110101
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[4,2,3,7,6,5,1]=>100111
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[4,2,3,7,5,6,1]=>100101
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[2,4,3,7,6,5,1]=>010111
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[2,4,3,7,5,6,1]=>010101
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[3,2,4,7,6,5,1]=>100111
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[3,2,4,7,5,6,1]=>100101
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[2,3,4,7,6,5,1]=>000111
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[2,3,4,7,5,6,1]=>000101
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[5,4,3,2,7,6,1]=>111011
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[5,4,2,3,7,6,1]=>110011
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[5,2,4,3,7,6,1]=>101011
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[5,3,2,4,7,6,1]=>110011
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[5,2,3,4,7,6,1]=>100011
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[2,5,4,3,7,6,1]=>011011
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[2,5,3,4,7,6,1]=>010011
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[3,2,5,4,7,6,1]=>101011
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[2,3,5,4,7,6,1]=>001011
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[4,3,2,5,7,6,1]=>110011
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[4,2,3,5,7,6,1]=>100011
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[2,4,3,5,7,6,1]=>010011
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[3,2,4,5,7,6,1]=>100011
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[2,3,4,5,7,6,1]=>000011
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[6,5,4,3,2,7,1]=>111101
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[6,5,4,2,3,7,1]=>111001
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[6,5,2,4,3,7,1]=>110101
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[6,5,3,2,4,7,1]=>111001
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[6,5,2,3,4,7,1]=>110001
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[6,2,5,4,3,7,1]=>101101
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[6,2,5,3,4,7,1]=>101001
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[6,3,2,5,4,7,1]=>110101
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[6,2,3,5,4,7,1]=>100101
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[6,4,3,2,5,7,1]=>111001
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[6,4,2,3,5,7,1]=>110001
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[6,2,4,3,5,7,1]=>101001
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[6,3,2,4,5,7,1]=>110001
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[6,2,3,4,5,7,1]=>100001
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[2,6,5,4,3,7,1]=>011101
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[2,6,5,3,4,7,1]=>011001
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[2,6,3,5,4,7,1]=>010101
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[2,6,4,3,5,7,1]=>011001
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[2,6,3,4,5,7,1]=>010001
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[3,2,6,5,4,7,1]=>101101
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[3,2,6,4,5,7,1]=>101001
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[2,3,6,5,4,7,1]=>001101
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[2,3,6,4,5,7,1]=>001001
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[4,3,2,6,5,7,1]=>110101
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[4,2,3,6,5,7,1]=>100101
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[2,4,3,6,5,7,1]=>010101
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[3,2,4,6,5,7,1]=>100101
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[2,3,4,6,5,7,1]=>000101
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[5,4,3,2,6,7,1]=>111001
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[5,4,2,3,6,7,1]=>110001
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[5,2,4,3,6,7,1]=>101001
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[5,3,2,4,6,7,1]=>110001
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[5,2,3,4,6,7,1]=>100001
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[2,5,4,3,6,7,1]=>011001
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[2,5,3,4,6,7,1]=>010001
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[3,2,5,4,6,7,1]=>101001
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[2,3,5,4,6,7,1]=>001001
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[4,3,2,5,6,7,1]=>110001
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[4,2,3,5,6,7,1]=>100001
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[2,4,3,5,6,7,1]=>010001
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[3,2,4,5,6,7,1]=>100001
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>000001
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,8,7,6,5,4,3,2]=>0111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,8,7,6,5,4,2,3]=>0111110
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[1,8,7,6,5,2,4,3]=>0111101
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,8,7,6,5,3,2,4]=>0111110
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,8,7,6,5,2,3,4]=>0111100
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[1,8,7,6,2,5,4,3]=>0111011
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[1,8,7,6,3,2,5,4]=>0111101
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,8,7,6,4,3,2,5]=>0111110
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,8,7,6,4,2,3,5]=>0111100
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[1,8,7,6,2,4,3,5]=>0111010
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,8,7,6,3,2,4,5]=>0111100
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,8,7,6,2,3,4,5]=>0111000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[1,8,7,2,6,5,4,3]=>0110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[1,8,7,2,6,5,3,4]=>0110110
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[1,8,7,2,6,3,5,4]=>0110101
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[1,8,7,2,6,3,4,5]=>0110100
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>[1,8,7,3,2,6,4,5]=>0111010
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[1,8,7,2,3,6,5,4]=>0110011
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[1,8,7,2,3,6,4,5]=>0110010
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[1,8,7,4,3,2,6,5]=>0111101
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[1,8,7,4,2,3,6,5]=>0111001
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[5,4,6,8,7,3,2,1]=>[1,8,7,3,2,4,6,5]=>0111001
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[1,8,7,2,3,4,6,5]=>0110001
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,8,7,5,4,3,2,6]=>0111110
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,8,7,5,3,2,4,6]=>0111100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,8,7,5,2,3,4,6]=>0111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[1,8,7,2,5,4,3,6]=>0110110
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[1,8,7,2,5,3,4,6]=>0110100
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[1,8,7,3,2,5,4,6]=>0111010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[1,8,7,2,3,5,4,6]=>0110010
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,8,7,4,3,2,5,6]=>0111100
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,8,7,4,2,3,5,6]=>0111000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,8,7,3,2,4,5,6]=>0111000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,8,7,2,3,4,5,6]=>0110000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[1,8,2,7,6,5,4,3]=>0101111
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[1,8,2,7,6,3,5,4]=>0101101
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[1,8,2,7,6,4,3,5]=>0101110
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[3,6,7,8,5,4,2,1]=>[1,8,2,7,6,3,4,5]=>0101100
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[1,8,2,7,3,6,5,4]=>0101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[1,8,2,7,3,6,4,5]=>0101010
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[1,8,2,7,4,3,6,5]=>0101101
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[1,8,2,7,3,4,6,5]=>0101001
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[1,8,2,7,5,4,3,6]=>0101110
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[1,8,2,7,5,3,4,6]=>0101100
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[3,5,7,6,8,4,2,1]=>[1,8,2,7,3,5,4,6]=>0101010
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[3,6,5,7,8,4,2,1]=>[1,8,2,7,4,3,5,6]=>0101100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[1,8,2,7,3,4,5,6]=>0101000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[1,8,3,2,7,6,5,4]=>0110111
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[1,8,3,2,7,6,4,5]=>0110110
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[1,8,3,2,7,5,4,6]=>0110110
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[1,8,2,3,7,6,5,4]=>0100111
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[3,4,7,8,6,5,2,1]=>[1,8,2,3,7,6,4,5]=>0100110
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[1,8,2,3,7,5,4,6]=>0100110
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[1,8,4,3,2,7,6,5]=>0111011
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[1,8,4,3,2,7,5,6]=>0111010
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[4,5,3,8,7,6,2,1]=>[1,8,4,2,3,7,6,5]=>0110011
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[1,8,4,2,3,7,5,6]=>0110010
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[3,5,4,8,7,6,2,1]=>[1,8,2,4,3,7,6,5]=>0101011
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[3,5,4,7,8,6,2,1]=>[1,8,2,4,3,7,5,6]=>0101010
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[1,8,3,2,4,7,5,6]=>0110010
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[1,8,2,3,4,7,6,5]=>0100011
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[1,8,2,3,4,7,5,6]=>0100010
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[1,8,5,4,3,2,7,6]=>0111101
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>[1,8,5,4,2,3,7,6]=>0111001
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[1,8,5,3,2,4,7,6]=>0111001
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[1,8,5,2,3,4,7,6]=>0110001
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[3,5,6,4,8,7,2,1]=>[1,8,2,5,3,4,7,6]=>0101001
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[1,8,3,2,5,4,7,6]=>0110101
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[1,8,4,3,2,5,7,6]=>0111001
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[1,8,4,2,3,5,7,6]=>0110001
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[1,8,3,2,4,5,7,6]=>0110001
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[3,4,5,6,8,7,2,1]=>[1,8,2,3,4,5,7,6]=>0100001
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,8,6,5,4,3,2,7]=>0111110
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,8,6,5,4,2,3,7]=>0111100
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[1,8,6,5,3,2,4,7]=>0111100
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[4,6,7,5,3,8,2,1]=>[1,8,6,2,5,3,4,7]=>0110100
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[1,8,6,3,2,5,4,7]=>0111010
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[1,8,6,4,2,3,5,7]=>0111000
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[4,6,5,7,3,8,2,1]=>[1,8,6,2,4,3,5,7]=>0110100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,8,6,3,2,4,5,7]=>0111000
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,8,6,2,3,4,5,7]=>0110000
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[1,8,2,6,5,3,4,7]=>0101100
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[1,8,2,6,3,5,4,7]=>0101010
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[3,6,5,7,4,8,2,1]=>[1,8,2,6,4,3,5,7]=>0101100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[1,8,2,6,3,4,5,7]=>0101000
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[4,3,6,7,5,8,2,1]=>[1,8,3,2,6,4,5,7]=>0110100
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[1,8,2,3,6,5,4,7]=>0100110
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[3,4,6,7,5,8,2,1]=>[1,8,2,3,6,4,5,7]=>0100100
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[1,8,4,2,3,6,5,7]=>0110010
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[1,8,2,4,3,6,5,7]=>0101010
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[1,8,2,3,4,6,5,7]=>0100010
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,8,5,4,3,2,6,7]=>0111100
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[1,8,5,4,2,3,6,7]=>0111000
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[5,4,6,3,7,8,2,1]=>[1,8,5,3,2,4,6,7]=>0111000
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>[1,8,2,5,3,4,6,7]=>0101000
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>[1,8,3,2,5,4,6,7]=>0110100
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[1,8,2,3,5,4,6,7]=>0100100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[1,8,4,3,2,5,6,7]=>0111000
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[1,8,4,2,3,5,6,7]=>0110000
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[3,5,4,6,7,8,2,1]=>[1,8,2,4,3,5,6,7]=>0101000
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,8,3,2,4,5,6,7]=>0110000
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,8,2,3,4,5,6,7]=>0100000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[1,2,8,7,6,5,4,3]=>0011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[1,2,8,7,6,5,3,4]=>0011110
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[1,2,8,7,6,3,5,4]=>0011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[1,2,8,7,6,4,3,5]=>0011110
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[1,2,8,7,6,3,4,5]=>0011100
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[2,5,8,7,6,4,3,1]=>[1,2,8,7,3,6,5,4]=>0011011
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[1,2,8,7,4,3,6,5]=>0011101
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[2,5,6,8,7,4,3,1]=>[1,2,8,7,3,4,6,5]=>0011001
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[1,2,8,7,5,4,3,6]=>0011110
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[2,5,7,6,8,4,3,1]=>[1,2,8,7,3,5,4,6]=>0011010
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[1,2,8,7,3,4,5,6]=>0011000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[1,2,8,3,7,6,5,4]=>0010111
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[1,2,8,3,7,6,4,5]=>0010110
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[1,2,8,3,7,4,6,5]=>0010101
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[1,2,8,3,7,4,5,6]=>0010100
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>[1,2,8,4,3,7,6,5]=>0011011
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[2,5,4,7,8,6,3,1]=>[1,2,8,4,3,7,5,6]=>0011010
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[1,2,8,3,5,4,7,6]=>0010101
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[2,4,5,6,8,7,3,1]=>[1,2,8,3,4,5,7,6]=>0010001
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[1,2,8,6,5,4,3,7]=>0011110
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[2,6,5,7,4,8,3,1]=>[1,2,8,6,4,3,5,7]=>0011100
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[2,5,6,7,4,8,3,1]=>[1,2,8,6,3,4,5,7]=>0011000
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[1,2,8,3,6,5,4,7]=>0010110
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>[1,2,8,3,6,4,5,7]=>0010100
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[2,5,4,7,6,8,3,1]=>[1,2,8,4,3,6,5,7]=>0011010
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[1,2,8,5,4,3,6,7]=>0011100
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[1,2,8,5,3,4,6,7]=>0011000
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>[1,2,8,3,5,4,6,7]=>0010100
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[2,5,4,6,7,8,3,1]=>[1,2,8,4,3,5,6,7]=>0011000
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[1,2,8,3,4,5,6,7]=>0010000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[1,3,2,8,7,6,5,4]=>0101111
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[3,2,7,8,6,5,4,1]=>[1,3,2,8,7,6,4,5]=>0101110
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[1,3,2,8,7,4,6,5]=>0101101
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[3,2,7,6,8,5,4,1]=>[1,3,2,8,7,5,4,6]=>0101110
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[1,3,2,8,5,4,7,6]=>0101101
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[1,3,2,8,4,5,7,6]=>0101001
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[1,3,2,8,6,5,4,7]=>0101110
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[1,3,2,8,6,4,5,7]=>0101100
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>[1,3,2,8,4,6,5,7]=>0101010
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[3,2,6,5,7,8,4,1]=>[1,3,2,8,5,4,6,7]=>0101100
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>[1,3,2,8,4,5,6,7]=>0101000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[1,2,3,8,7,6,5,4]=>0001111
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[2,3,7,8,6,5,4,1]=>[1,2,3,8,7,6,4,5]=>0001110
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[2,3,6,8,7,5,4,1]=>[1,2,3,8,7,4,6,5]=>0001101
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[2,3,7,6,8,5,4,1]=>[1,2,3,8,7,5,4,6]=>0001110
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[1,2,3,8,7,4,5,6]=>0001100
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>[1,2,3,8,4,7,6,5]=>0001011
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[1,2,3,8,4,7,5,6]=>0001010
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[1,2,3,8,5,4,7,6]=>0001101
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[1,2,3,8,4,5,7,6]=>0001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[1,2,3,8,6,5,4,7]=>0001110
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[1,2,3,8,6,4,5,7]=>0001100
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>[1,2,3,8,4,6,5,7]=>0001010
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[2,3,6,5,7,8,4,1]=>[1,2,3,8,5,4,6,7]=>0001100
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[1,2,3,8,4,5,6,7]=>0001000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[1,4,3,2,8,7,6,5]=>0110111
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[1,4,3,2,8,5,6,7]=>0110100
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[1,4,2,3,8,7,6,5]=>0100111
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[1,4,2,3,8,7,5,6]=>0100110
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[3,4,2,6,8,7,5,1]=>[1,4,2,3,8,5,7,6]=>0100101
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[3,4,2,7,6,8,5,1]=>[1,4,2,3,8,6,5,7]=>0100110
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[1,4,2,3,8,5,6,7]=>0100100
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[1,2,4,3,8,7,6,5]=>0010111
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[2,4,3,7,8,6,5,1]=>[1,2,4,3,8,7,5,6]=>0010110
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[1,2,4,3,8,5,7,6]=>0010101
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[2,4,3,7,6,8,5,1]=>[1,2,4,3,8,6,5,7]=>0010110
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>[1,2,4,3,8,5,6,7]=>0010100
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[1,3,2,4,8,7,6,5]=>0100111
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[3,2,4,7,6,8,5,1]=>[1,3,2,4,8,6,5,7]=>0100110
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[3,2,4,6,7,8,5,1]=>[1,3,2,4,8,5,6,7]=>0100100
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[1,2,3,4,8,7,6,5]=>0000111
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[1,2,3,4,8,7,5,6]=>0000110
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[2,3,4,6,8,7,5,1]=>[1,2,3,4,8,5,7,6]=>0000101
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[2,3,4,7,6,8,5,1]=>[1,2,3,4,8,6,5,7]=>0000110
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[1,2,3,4,8,5,6,7]=>0000100
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[1,5,4,3,2,8,7,6]=>0111011
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[1,5,4,2,3,8,7,6]=>0110011
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[1,5,4,2,3,8,6,7]=>0110010
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[1,5,3,2,4,8,7,6]=>0110011
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[3,4,5,2,8,7,6,1]=>[1,5,2,3,4,8,7,6]=>0100011
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[3,4,5,2,7,8,6,1]=>[1,5,2,3,4,8,6,7]=>0100010
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[1,2,5,4,3,8,7,6]=>0011011
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[1,2,5,4,3,8,6,7]=>0011010
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[1,2,5,3,4,8,7,6]=>0010011
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[1,2,5,3,4,8,6,7]=>0010010
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>[1,2,3,5,4,8,7,6]=>0001011
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[1,2,3,5,4,8,6,7]=>0001010
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[1,4,3,2,5,8,7,6]=>0110011
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[4,3,2,5,7,8,6,1]=>[1,4,3,2,5,8,6,7]=>0110010
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[3,4,2,5,8,7,6,1]=>[1,4,2,3,5,8,7,6]=>0100011
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[1,4,2,3,5,8,6,7]=>0100010
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>[1,2,4,3,5,8,7,6]=>0010011
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[2,4,3,5,7,8,6,1]=>[1,2,4,3,5,8,6,7]=>0010010
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[3,2,4,5,7,8,6,1]=>[1,3,2,4,5,8,6,7]=>0100010
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[1,2,3,4,5,8,7,6]=>0000011
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[1,2,3,4,5,8,6,7]=>0000010
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[1,6,5,4,3,2,8,7]=>0111101
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[1,6,5,3,2,4,8,7]=>0111001
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[1,6,5,2,3,4,8,7]=>0110001
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[1,6,2,5,3,4,8,7]=>0101001
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[1,6,4,2,3,5,8,7]=>0110001
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[3,5,4,6,2,8,7,1]=>[1,6,2,4,3,5,8,7]=>0101001
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[3,4,5,6,2,8,7,1]=>[1,6,2,3,4,5,8,7]=>0100001
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>[1,2,6,3,4,5,8,7]=>0010001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[1,3,2,6,5,4,8,7]=>0101101
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[2,3,5,6,4,8,7,1]=>[1,2,3,6,4,5,8,7]=>0001001
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>[1,4,2,3,6,5,8,7]=>0100101
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[1,2,4,3,6,5,8,7]=>0010101
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>[1,3,2,4,6,5,8,7]=>0100101
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[1,2,3,4,6,5,8,7]=>0000101
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>[1,5,4,2,3,6,8,7]=>0110001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[3,5,4,2,6,8,7,1]=>[1,5,2,4,3,6,8,7]=>0101001
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[4,3,5,2,6,8,7,1]=>[1,5,3,2,4,6,8,7]=>0110001
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[3,4,5,2,6,8,7,1]=>[1,5,2,3,4,6,8,7]=>0100001
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[1,2,5,4,3,6,8,7]=>0011001
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[2,4,5,3,6,8,7,1]=>[1,2,5,3,4,6,8,7]=>0010001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[1,4,3,2,5,6,8,7]=>0110001
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[1,4,2,3,5,6,8,7]=>0100001
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[1,2,4,3,5,6,8,7]=>0010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>[1,3,2,4,5,6,8,7]=>0100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[1,2,3,4,5,6,8,7]=>0000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,7,6,5,4,3,2,8]=>0111110
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[1,7,6,5,4,2,3,8]=>0111100
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[1,7,6,5,2,4,3,8]=>0111010
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,7,6,5,3,2,4,8]=>0111100
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[5,4,7,6,3,2,8,1]=>[1,7,6,3,2,5,4,8]=>0111010
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[1,7,6,4,2,3,5,8]=>0111000
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[1,7,6,2,4,3,5,8]=>0110100
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,7,6,3,2,4,5,8]=>0111000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,7,6,2,3,4,5,8]=>0110000
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[1,7,2,6,5,4,3,8]=>0101110
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[1,7,2,6,3,5,4,8]=>0101010
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[3,6,5,7,4,2,8,1]=>[1,7,2,6,4,3,5,8]=>0101100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[1,7,2,6,3,4,5,8]=>0101000
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[1,7,2,3,6,4,5,8]=>0100100
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[3,5,4,7,6,2,8,1]=>[1,7,2,4,3,6,5,8]=>0101010
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[4,3,5,7,6,2,8,1]=>[1,7,3,2,4,6,5,8]=>0110010
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[3,4,5,7,6,2,8,1]=>[1,7,2,3,4,6,5,8]=>0100010
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,7,5,4,3,2,6,8]=>0111100
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,7,5,3,2,4,6,8]=>0111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,7,5,2,3,4,6,8]=>0110000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[1,7,2,5,4,3,6,8]=>0101100
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[1,7,2,5,3,4,6,8]=>0101000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[1,7,3,2,5,4,6,8]=>0110100
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[1,7,2,3,5,4,6,8]=>0100100
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,7,4,3,2,5,6,8]=>0111000
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,7,4,2,3,5,6,8]=>0110000
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[1,7,2,4,3,5,6,8]=>0101000
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[1,7,3,2,4,5,6,8]=>0110000
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,7,2,3,4,5,6,8]=>0100000
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[1,2,7,6,5,4,3,8]=>0011110
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[2,6,5,7,4,3,8,1]=>[1,2,7,6,4,3,5,8]=>0011100
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>[1,2,7,6,3,4,5,8]=>0011000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[1,2,7,3,6,4,5,8]=>0010100
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[1,2,7,3,4,6,5,8]=>0010010
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[2,5,6,4,7,3,8,1]=>[1,2,7,5,3,4,6,8]=>0011000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[1,2,7,3,5,4,6,8]=>0010100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[1,2,7,4,3,5,6,8]=>0011000
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[1,2,7,3,4,5,6,8]=>0010000
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[3,2,7,6,5,4,8,1]=>[1,3,2,7,6,5,4,8]=>0101110
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[1,3,2,7,6,4,5,8]=>0101100
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[1,3,2,7,5,4,6,8]=>0101100
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[1,3,2,7,4,5,6,8]=>0101000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[1,2,3,7,6,5,4,8]=>0001110
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[2,3,6,7,5,4,8,1]=>[1,2,3,7,6,4,5,8]=>0001100
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[2,3,5,7,6,4,8,1]=>[1,2,3,7,4,6,5,8]=>0001010
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[1,2,3,7,4,5,6,8]=>0001000
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[1,4,3,2,7,6,5,8]=>0110110
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[1,4,2,3,7,5,6,8]=>0100100
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[2,4,3,6,7,5,8,1]=>[1,2,4,3,7,5,6,8]=>0010100
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[1,3,2,4,7,6,5,8]=>0100110
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[1,2,3,4,7,6,5,8]=>0000110
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[2,3,4,6,7,5,8,1]=>[1,2,3,4,7,5,6,8]=>0000100
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[1,5,4,3,2,7,6,8]=>0111010
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[4,5,3,2,7,6,8,1]=>[1,5,4,2,3,7,6,8]=>0110010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[1,5,3,2,4,7,6,8]=>0110010
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[1,5,2,3,4,7,6,8]=>0100010
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[2,4,5,3,7,6,8,1]=>[1,2,5,3,4,7,6,8]=>0010010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[1,3,2,5,4,7,6,8]=>0101010
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[1,2,3,5,4,7,6,8]=>0001010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[1,4,3,2,5,7,6,8]=>0110010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[1,2,4,3,5,7,6,8]=>0010010
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[1,3,2,4,5,7,6,8]=>0100010
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[1,2,3,4,5,7,6,8]=>0000010
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,6,5,4,3,2,7,8]=>0111100
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,6,5,3,2,4,7,8]=>0111000
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>[1,6,2,5,3,4,7,8]=>0101000
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[4,3,6,5,2,7,8,1]=>[1,6,3,2,5,4,7,8]=>0110100
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,6,4,3,2,5,7,8]=>0111000
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,6,4,2,3,5,7,8]=>0110000
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>[1,6,2,4,3,5,7,8]=>0101000
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[1,6,3,2,4,5,7,8]=>0110000
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,6,2,3,4,5,7,8]=>0100000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[1,2,6,5,4,3,7,8]=>0011100
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[2,5,6,4,3,7,8,1]=>[1,2,6,5,3,4,7,8]=>0011000
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[2,4,6,5,3,7,8,1]=>[1,2,6,3,5,4,7,8]=>0010100
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[1,2,6,4,3,5,7,8]=>0011000
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[2,4,5,6,3,7,8,1]=>[1,2,6,3,4,5,7,8]=>0010000
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[3,2,5,6,4,7,8,1]=>[1,3,2,6,4,5,7,8]=>0101000
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[1,2,3,6,5,4,7,8]=>0001100
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[1,2,3,6,4,5,7,8]=>0001000
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[1,4,2,3,6,5,7,8]=>0100100
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[1,2,4,3,6,5,7,8]=>0010100
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[1,2,3,4,6,5,7,8]=>0000100
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,5,4,3,2,6,7,8]=>0111000
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[1,5,4,2,3,6,7,8]=>0110000
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[1,5,2,4,3,6,7,8]=>0101000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[1,5,3,2,4,6,7,8]=>0110000
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,5,2,3,4,6,7,8]=>0100000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[1,2,5,4,3,6,7,8]=>0011000
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[1,2,5,3,4,6,7,8]=>0010000
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[1,3,2,5,4,6,7,8]=>0101000
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[1,2,3,5,4,6,7,8]=>0001000
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,4,3,2,5,6,7,8]=>0110000
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,4,2,3,5,6,7,8]=>0100000
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[1,2,4,3,5,6,7,8]=>0010000
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,3,2,4,5,6,7,8]=>0100000
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>0000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[2,1,8,7,6,5,4,3]=>1011111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[2,1,8,7,6,5,3,4]=>1011110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[2,1,8,7,6,3,5,4]=>1011101
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[2,1,8,7,6,4,3,5]=>1011110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[2,1,8,7,6,3,4,5]=>1011100
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[2,1,8,7,3,6,5,4]=>1011011
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,5,7,8,6,4,3,2]=>[2,1,8,7,3,6,4,5]=>1011010
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[2,1,8,7,4,3,6,5]=>1011101
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[2,1,8,7,3,4,6,5]=>1011001
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[2,1,8,7,5,4,3,6]=>1011110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[2,1,8,7,5,3,4,6]=>1011100
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[2,1,8,7,3,5,4,6]=>1011010
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[2,1,8,7,4,3,5,6]=>1011100
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[2,1,8,7,3,4,5,6]=>1011000
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[2,1,8,3,7,6,5,4]=>1010111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[2,1,8,3,7,6,4,5]=>1010110
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[2,1,8,3,7,4,6,5]=>1010101
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[2,1,8,3,7,5,4,6]=>1010110
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[2,1,8,3,7,4,5,6]=>1010100
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,5,4,8,7,6,3,2]=>[2,1,8,4,3,7,6,5]=>1011011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>[2,1,8,4,3,7,5,6]=>1011010
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[2,1,8,3,4,7,6,5]=>1010011
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[2,1,8,3,4,7,5,6]=>1010010
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,6,5,4,8,7,3,2]=>[2,1,8,5,4,3,7,6]=>1011101
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[2,1,8,4,3,5,7,6]=>1011001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[2,1,8,6,5,4,3,7]=>1011110
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,6,5,7,4,8,3,2]=>[2,1,8,6,4,3,5,7]=>1011100
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[2,1,8,3,6,4,5,7]=>1010100
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[2,1,8,5,4,3,6,7]=>1011100
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[1,5,6,4,7,8,3,2]=>[2,1,8,5,3,4,6,7]=>1011000
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[2,1,8,3,4,5,6,7]=>1010000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[2,1,3,8,7,6,5,4]=>1001111
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>[2,1,3,8,7,6,4,5]=>1001110
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[2,1,3,8,7,4,6,5]=>1001101
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[1,3,7,6,8,5,4,2]=>[2,1,3,8,7,5,4,6]=>1001110
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[2,1,3,8,7,4,5,6]=>1001100
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[2,1,3,8,4,7,6,5]=>1001011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[2,1,3,8,4,7,5,6]=>1001010
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,3,6,5,8,7,4,2]=>[2,1,3,8,5,4,7,6]=>1001101
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[2,1,3,8,4,5,7,6]=>1001001
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,3,7,6,5,8,4,2]=>[2,1,3,8,6,5,4,7]=>1001110
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[2,1,3,8,6,4,5,7]=>1001100
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[2,1,3,8,4,6,5,7]=>1001010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[2,1,3,8,5,4,6,7]=>1001100
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[2,1,3,8,4,5,6,7]=>1001000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[2,1,4,3,8,7,6,5]=>1010111
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[2,1,4,3,8,7,5,6]=>1010110
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[2,1,4,3,8,5,7,6]=>1010101
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[2,1,4,3,8,6,5,7]=>1010110
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[2,1,4,3,8,5,6,7]=>1010100
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[2,1,3,4,8,7,6,5]=>1000111
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[1,3,4,7,8,6,5,2]=>[2,1,3,4,8,7,5,6]=>1000110
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[1,3,4,6,8,7,5,2]=>[2,1,3,4,8,5,7,6]=>1000101
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[2,1,3,4,8,6,5,7]=>1000110
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[2,1,3,4,8,5,6,7]=>1000100
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[2,1,5,4,3,8,7,6]=>1011011
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[2,1,3,5,4,8,7,6]=>1001011
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[2,1,4,3,5,8,7,6]=>1010011
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[2,1,4,3,5,8,6,7]=>1010010
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[2,1,3,4,5,8,7,6]=>1000011
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>[2,1,3,4,5,8,6,7]=>1000010
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[2,1,6,5,4,3,8,7]=>1011101
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[2,1,6,5,3,4,8,7]=>1011001
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[1,4,5,6,3,8,7,2]=>[2,1,6,3,4,5,8,7]=>1010001
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[1,3,5,6,4,8,7,2]=>[2,1,3,6,4,5,8,7]=>1001001
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[2,1,4,3,6,5,8,7]=>1010101
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[1,3,4,6,5,8,7,2]=>[2,1,3,4,6,5,8,7]=>1000101
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[2,1,5,3,4,6,8,7]=>1010001
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[1,3,5,4,6,8,7,2]=>[2,1,3,5,4,6,8,7]=>1001001
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[1,4,3,5,6,8,7,2]=>[2,1,4,3,5,6,8,7]=>1010001
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[2,1,3,4,5,6,8,7]=>1000001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[2,1,7,6,5,4,3,8]=>1011110
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[2,1,7,6,5,3,4,8]=>1011100
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[1,5,6,7,4,3,8,2]=>[2,1,7,6,3,4,5,8]=>1011000
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[2,1,7,3,4,5,6,8]=>1010000
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,3,4,6,7,5,8,2]=>[2,1,3,4,7,5,6,8]=>1000100
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,5,4,3,7,6,8,2]=>[2,1,5,4,3,7,6,8]=>1011010
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,3,4,5,7,6,8,2]=>[2,1,3,4,5,7,6,8]=>1000010
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[2,1,6,4,3,5,7,8]=>1011000
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>[2,1,3,6,4,5,7,8]=>1001000
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[2,1,4,3,6,5,7,8]=>1010100
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[2,1,3,4,6,5,7,8]=>1000100
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[2,1,5,4,3,6,7,8]=>1011000
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[2,1,5,3,4,6,7,8]=>1010000
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[2,1,4,3,5,6,7,8]=>1010000
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[2,1,3,4,5,6,7,8]=>1000000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[3,2,1,8,7,6,5,4]=>1101111
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[3,2,1,8,7,6,4,5]=>1101110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[3,2,1,8,7,4,6,5]=>1101101
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[3,2,1,8,7,5,4,6]=>1101110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[3,2,1,8,7,4,5,6]=>1101100
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[3,2,1,8,4,7,6,5]=>1101011
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[3,2,1,8,4,7,5,6]=>1101010
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[3,2,1,8,5,4,7,6]=>1101101
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[2,1,5,6,8,7,4,3]=>[3,2,1,8,4,5,7,6]=>1101001
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[3,2,1,8,6,5,4,7]=>1101110
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[3,2,1,8,6,4,5,7]=>1101100
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[3,2,1,8,4,6,5,7]=>1101010
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[3,2,1,8,5,4,6,7]=>1101100
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[3,2,1,8,4,5,6,7]=>1101000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[3,2,1,4,8,7,6,5]=>1100111
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[3,2,1,4,8,7,5,6]=>1100110
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[3,2,1,4,8,5,7,6]=>1100101
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[2,1,4,7,6,8,5,3]=>[3,2,1,4,8,6,5,7]=>1100110
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[3,2,1,4,8,5,6,7]=>1100100
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[3,2,1,4,5,8,7,6]=>1100011
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[3,2,1,4,5,8,6,7]=>1100010
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[2,1,6,5,4,8,7,3]=>[3,2,1,6,5,4,8,7]=>1101101
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[3,2,1,4,5,6,8,7]=>1100001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[2,1,7,6,5,4,8,3]=>[3,2,1,7,6,5,4,8]=>1101110
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[2,1,6,7,5,4,8,3]=>[3,2,1,7,6,4,5,8]=>1101100
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[3,2,1,7,4,6,5,8]=>1101010
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[3,2,1,7,5,4,6,8]=>1101100
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[3,2,1,4,7,6,5,8]=>1100110
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[3,2,1,5,4,7,6,8]=>1101010
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[3,2,1,6,5,4,7,8]=>1101100
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[3,2,1,5,4,6,7,8]=>1101000
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[3,2,1,4,5,6,7,8]=>1100000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[2,3,1,8,7,6,5,4]=>0101111
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[2,3,1,8,7,6,4,5]=>0101110
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>[2,3,1,8,7,5,4,6]=>0101110
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[2,3,1,8,7,4,5,6]=>0101100
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[2,3,1,8,4,7,6,5]=>0101011
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[2,3,1,8,4,7,5,6]=>0101010
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[2,3,1,8,5,4,7,6]=>0101101
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[2,3,1,8,4,5,7,6]=>0101001
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[2,3,1,8,6,5,4,7]=>0101110
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[2,3,1,8,6,4,5,7]=>0101100
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[2,3,1,8,4,6,5,7]=>0101010
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[2,3,1,8,5,4,6,7]=>0101100
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[2,3,1,8,4,5,6,7]=>0101000
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[2,3,1,4,8,7,6,5]=>0100111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[2,3,1,4,8,5,7,6]=>0100101
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,2,4,7,6,8,5,3]=>[2,3,1,4,8,6,5,7]=>0100110
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[2,3,1,4,8,5,6,7]=>0100100
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[2,3,1,4,5,8,6,7]=>0100010
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[2,3,1,6,5,4,8,7]=>0101101
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[2,3,1,4,6,5,8,7]=>0100101
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[2,3,1,4,5,6,8,7]=>0100001
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[2,3,1,4,7,5,6,8]=>0100100
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[2,3,1,6,5,4,7,8]=>0101100
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[2,3,1,6,4,5,7,8]=>0101000
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[2,3,1,5,4,6,7,8]=>0101000
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[2,3,1,4,5,6,7,8]=>0100000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[4,3,2,1,8,7,6,5]=>1110111
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[4,3,2,1,8,7,5,6]=>1110110
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[4,3,2,1,8,5,7,6]=>1110101
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[4,3,2,1,8,6,5,7]=>1110110
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[4,3,2,1,8,5,6,7]=>1110100
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[4,3,2,1,5,8,7,6]=>1110011
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[4,3,2,1,5,8,6,7]=>1110010
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[4,3,2,1,6,5,8,7]=>1110101
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[4,3,2,1,5,6,8,7]=>1110001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[4,3,2,1,7,6,5,8]=>1110110
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[4,3,2,1,7,5,6,8]=>1110100
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[4,3,2,1,5,7,6,8]=>1110010
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[4,3,2,1,6,5,7,8]=>1110100
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[4,3,2,1,5,6,7,8]=>1110000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[4,2,3,1,8,7,6,5]=>1010111
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[4,2,3,1,8,7,5,6]=>1010110
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[4,2,3,1,8,5,7,6]=>1010101
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[4,2,3,1,8,6,5,7]=>1010110
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[4,2,3,1,8,5,6,7]=>1010100
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[4,2,3,1,5,8,6,7]=>1010010
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[4,2,3,1,6,5,8,7]=>1010101
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[4,2,3,1,5,7,6,8]=>1010010
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[4,2,3,1,5,6,7,8]=>1010000
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[2,4,3,1,8,7,6,5]=>0110111
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,3,2,7,8,6,5,4]=>[2,4,3,1,8,7,5,6]=>0110110
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>[2,4,3,1,8,5,7,6]=>0110101
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>[2,4,3,1,8,6,5,7]=>0110110
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,3,2,6,7,8,5,4]=>[2,4,3,1,8,5,6,7]=>0110100
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[2,4,3,1,5,8,7,6]=>0110011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[2,4,3,1,5,8,6,7]=>0110010
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[2,4,3,1,6,5,8,7]=>0110101
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[2,4,3,1,6,5,7,8]=>0110100
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[2,4,3,1,5,6,7,8]=>0110000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[3,2,4,1,8,7,6,5]=>1010111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[3,2,4,1,8,7,5,6]=>1010110
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[3,2,4,1,8,5,7,6]=>1010101
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[2,1,3,7,6,8,5,4]=>[3,2,4,1,8,6,5,7]=>1010110
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[3,2,4,1,8,5,6,7]=>1010100
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[3,2,4,1,5,8,7,6]=>1010011
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[3,2,4,1,5,8,6,7]=>1010010
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[2,1,3,6,5,8,7,4]=>[3,2,4,1,6,5,8,7]=>1010101
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[2,1,3,5,6,8,7,4]=>[3,2,4,1,5,6,8,7]=>1010001
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[3,2,4,1,7,5,6,8]=>1010100
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[3,2,4,1,5,7,6,8]=>1010010
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[3,2,4,1,6,5,7,8]=>1010100
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[3,2,4,1,5,6,7,8]=>1010000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[2,3,4,1,8,7,6,5]=>0010111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[2,3,4,1,8,7,5,6]=>0010110
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[2,3,4,1,8,5,7,6]=>0010101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[2,3,4,1,8,6,5,7]=>0010110
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[2,3,4,1,8,5,6,7]=>0010100
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[2,3,4,1,5,8,7,6]=>0010011
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[2,3,4,1,5,8,6,7]=>0010010
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[2,3,4,1,6,5,8,7]=>0010101
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[2,3,4,1,5,6,8,7]=>0010001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[2,3,4,1,7,6,5,8]=>0010110
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[2,3,4,1,7,5,6,8]=>0010100
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[2,3,4,1,5,7,6,8]=>0010010
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[2,3,4,1,6,5,7,8]=>0010100
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[2,3,4,1,5,6,7,8]=>0010000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[5,4,3,2,1,8,7,6]=>1111011
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[5,4,3,2,1,8,6,7]=>1111010
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[5,4,3,2,1,6,8,7]=>1111001
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[5,4,3,2,1,7,6,8]=>1111010
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[5,4,3,2,1,6,7,8]=>1111000
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[5,4,2,3,1,8,7,6]=>1101011
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[5,4,2,3,1,8,6,7]=>1101010
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[5,4,2,3,1,6,8,7]=>1101001
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,4,2,3,1,6,7,8]=>1101000
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[5,2,4,3,1,8,7,6]=>1011011
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[5,2,4,3,1,6,8,7]=>1011001
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[5,2,4,3,1,7,6,8]=>1011010
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[5,2,4,3,1,6,7,8]=>1011000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[5,3,2,4,1,8,7,6]=>1101011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[5,3,2,4,1,6,8,7]=>1101001
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[5,3,2,4,1,7,6,8]=>1101010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,3,2,4,1,6,7,8]=>1101000
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[5,2,3,4,1,8,7,6]=>1001011
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[5,2,3,4,1,8,6,7]=>1001010
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[5,2,3,4,1,6,8,7]=>1001001
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,2,3,4,1,6,7,8]=>1001000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[2,5,4,3,1,8,7,6]=>0111011
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,4,3,2,7,8,6,5]=>[2,5,4,3,1,8,6,7]=>0111010
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[2,5,4,3,1,6,8,7]=>0111001
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[2,5,4,3,1,7,6,8]=>0111010
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[2,5,4,3,1,6,7,8]=>0111000
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[2,5,3,4,1,8,7,6]=>0101011
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[2,5,3,4,1,8,6,7]=>0101010
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[2,5,3,4,1,6,7,8]=>0101000
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[3,2,5,4,1,8,7,6]=>1011011
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[3,2,5,4,1,8,6,7]=>1011010
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[3,2,5,4,1,6,8,7]=>1011001
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[3,2,5,4,1,7,6,8]=>1011010
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[3,2,5,4,1,6,7,8]=>1011000
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[2,3,5,4,1,8,7,6]=>0011011
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[2,3,5,4,1,8,6,7]=>0011010
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[2,3,5,4,1,6,8,7]=>0011001
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[2,3,5,4,1,7,6,8]=>0011010
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[2,3,5,4,1,6,7,8]=>0011000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[4,3,2,5,1,8,7,6]=>1101011
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[4,3,2,5,1,8,6,7]=>1101010
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[4,3,2,5,1,6,7,8]=>1101000
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[4,2,3,5,1,8,7,6]=>1001011
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[4,2,3,5,1,8,6,7]=>1001010
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[2,3,1,4,6,8,7,5]=>[4,2,3,5,1,6,8,7]=>1001001
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[4,2,3,5,1,6,7,8]=>1001000
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[2,4,3,5,1,8,7,6]=>0101011
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,3,2,4,7,8,6,5]=>[2,4,3,5,1,8,6,7]=>0101010
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[2,4,3,5,1,6,8,7]=>0101001
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[2,4,3,5,1,7,6,8]=>0101010
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[2,4,3,5,1,6,7,8]=>0101000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[3,2,4,5,1,8,7,6]=>1001011
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[3,2,4,5,1,6,7,8]=>1001000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[2,3,4,5,1,8,7,6]=>0001011
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[2,3,4,5,1,8,6,7]=>0001010
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[2,3,4,5,1,6,8,7]=>0001001
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[2,3,4,5,1,7,6,8]=>0001010
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[2,3,4,5,1,6,7,8]=>0001000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[6,5,4,3,2,1,8,7]=>1111101
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[6,5,4,3,2,1,7,8]=>1111100
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[6,5,4,2,3,1,8,7]=>1110101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[6,5,3,2,4,1,8,7]=>1110101
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[6,5,2,3,4,1,7,8]=>1100100
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[6,2,5,4,3,1,8,7]=>1011101
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[6,2,5,4,3,1,7,8]=>1011100
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[6,2,5,3,4,1,8,7]=>1010101
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[6,3,2,5,4,1,8,7]=>1101101
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[6,3,2,5,4,1,7,8]=>1101100
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[6,2,3,5,4,1,8,7]=>1001101
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[2,3,5,4,1,7,8,6]=>[6,2,3,5,4,1,7,8]=>1001100
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[6,4,3,2,5,1,8,7]=>1110101
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[6,4,3,2,5,1,7,8]=>1110100
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[6,4,2,3,5,1,8,7]=>1100101
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[6,2,4,3,5,1,8,7]=>1010101
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[6,2,3,4,5,1,8,7]=>1000101
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[6,2,3,4,5,1,7,8]=>1000100
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[2,6,5,4,3,1,8,7]=>0111101
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[2,6,5,3,4,1,8,7]=>0110101
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,4,5,3,2,7,8,6]=>[2,6,5,3,4,1,7,8]=>0110100
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,3,5,4,2,8,7,6]=>[2,6,3,5,4,1,8,7]=>0101101
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[2,6,3,5,4,1,7,8]=>0101100
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[1,4,3,5,2,8,7,6]=>[2,6,4,3,5,1,8,7]=>0110101
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[2,6,3,4,5,1,7,8]=>0100100
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]=>[3,2,6,5,4,1,8,7]=>1011101
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[2,1,4,5,3,8,7,6]=>[3,2,6,4,5,1,8,7]=>1010101
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[2,3,6,5,4,1,8,7]=>0011101
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[2,3,6,5,4,1,7,8]=>0011100
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[2,3,6,4,5,1,8,7]=>0010101
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>[2,3,6,4,5,1,7,8]=>0010100
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]=>[4,3,2,6,5,1,8,7]=>1101101
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[3,2,1,5,4,7,8,6]=>[4,3,2,6,5,1,7,8]=>1101100
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[2,3,1,5,4,7,8,6]=>[4,2,3,6,5,1,7,8]=>1001100
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[2,4,3,6,5,1,8,7]=>0101101
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[2,4,3,6,5,1,7,8]=>0101100
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[2,3,4,6,5,1,7,8]=>0001100
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[5,4,3,2,6,1,8,7]=>1110101
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[5,4,3,2,6,1,7,8]=>1110100
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[5,4,2,3,6,1,8,7]=>1100101
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[2,4,3,1,5,8,7,6]=>[5,2,4,3,6,1,8,7]=>1010101
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[5,2,4,3,6,1,7,8]=>1010100
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[5,3,2,4,6,1,8,7]=>1100101
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[5,3,2,4,6,1,7,8]=>1100100
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[5,2,3,4,6,1,8,7]=>1000101
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[5,2,3,4,6,1,7,8]=>1000100
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[2,5,4,3,6,1,8,7]=>0110101
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]=>[3,2,5,4,6,1,8,7]=>1010101
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[2,3,5,4,6,1,7,8]=>0010100
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[4,3,2,5,6,1,8,7]=>1100101
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[4,3,2,5,6,1,7,8]=>1100100
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[2,3,1,4,5,8,7,6]=>[4,2,3,5,6,1,8,7]=>1000101
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[4,2,3,5,6,1,7,8]=>1000100
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]=>[2,4,3,5,6,1,8,7]=>0100101
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>[3,2,4,5,6,1,7,8]=>1000100
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[2,3,4,5,6,1,8,7]=>0000101
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[2,3,4,5,6,1,7,8]=>0000100
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[7,6,5,4,2,3,1,8]=>1111010
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[7,6,5,3,2,4,1,8]=>1111010
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[7,6,5,2,3,4,1,8]=>1110010
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[7,6,2,5,4,3,1,8]=>1101110
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[7,6,2,5,3,4,1,8]=>1101010
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[7,6,3,2,5,4,1,8]=>1110110
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[3,4,6,5,2,1,8,7]=>[7,6,2,3,5,4,1,8]=>1100110
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[7,6,4,3,2,5,1,8]=>1111010
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[7,6,4,2,3,5,1,8]=>1110010
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[3,5,4,6,2,1,8,7]=>[7,6,2,4,3,5,1,8]=>1101010
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[7,6,3,2,4,5,1,8]=>1110010
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[7,6,2,3,4,5,1,8]=>1100010
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[7,2,6,5,4,3,1,8]=>1011110
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>[7,2,6,5,3,4,1,8]=>1011010
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[2,4,5,6,3,1,8,7]=>[7,2,6,3,4,5,1,8]=>1010010
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[7,2,3,6,5,4,1,8]=>1001110
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[4,3,2,6,5,1,8,7]=>[7,4,3,2,6,5,1,8]=>1110110
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[7,4,2,3,6,5,1,8]=>1100110
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[7,2,4,3,6,5,1,8]=>1010110
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[2,3,4,6,5,1,8,7]=>[7,2,3,4,6,5,1,8]=>1000110
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[7,5,4,3,2,6,1,8]=>1111010
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[7,5,4,2,3,6,1,8]=>1110010
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[7,5,3,2,4,6,1,8]=>1110010
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[7,2,5,4,3,6,1,8]=>1011010
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[7,2,5,3,4,6,1,8]=>1010010
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[7,3,2,5,4,6,1,8]=>1101010
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[7,4,2,3,5,6,1,8]=>1100010
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[7,2,3,4,5,6,1,8]=>1000010
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>[2,7,6,5,4,3,1,8]=>0111110
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[1,4,5,6,3,2,8,7]=>[2,7,6,3,4,5,1,8]=>0110010
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>[2,7,3,6,5,4,1,8]=>0101110
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[1,3,5,6,4,2,8,7]=>[2,7,3,6,4,5,1,8]=>0101010
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,3,4,5,6,2,8,7]=>[2,7,3,4,5,6,1,8]=>0100010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[3,2,7,6,5,4,1,8]=>1011110
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[3,2,7,6,4,5,1,8]=>1011010
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[3,2,7,4,6,5,1,8]=>1010110
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[3,2,7,5,4,6,1,8]=>1011010
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[3,2,7,4,5,6,1,8]=>1010010
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[2,3,7,6,5,4,1,8]=>0011110
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[1,2,5,4,6,3,8,7]=>[2,3,7,5,4,6,1,8]=>0011010
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[2,3,1,5,6,4,8,7]=>[4,2,3,7,5,6,1,8]=>1001010
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[2,3,4,7,6,5,1,8]=>0001110
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[2,3,4,7,5,6,1,8]=>0001010
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[5,4,3,2,7,6,1,8]=>1110110
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[5,4,2,3,7,6,1,8]=>1100110
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[5,2,4,3,7,6,1,8]=>1010110
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[5,3,2,4,7,6,1,8]=>1100110
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[5,2,3,4,7,6,1,8]=>1000110
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[3,2,5,4,7,6,1,8]=>1010110
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[4,3,2,5,7,6,1,8]=>1100110
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[2,3,1,4,6,5,8,7]=>[4,2,3,5,7,6,1,8]=>1000110
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[2,3,4,5,7,6,1,8]=>0000110
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[6,5,4,3,2,7,1,8]=>1111010
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[6,5,2,4,3,7,1,8]=>1101010
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[4,3,5,2,1,6,8,7]=>[6,5,3,2,4,7,1,8]=>1110010
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[6,2,5,4,3,7,1,8]=>1011010
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[6,2,5,3,4,7,1,8]=>1010010
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[6,3,2,5,4,7,1,8]=>1101010
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>[6,2,3,5,4,7,1,8]=>1001010
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[3,4,2,5,1,6,8,7]=>[6,4,2,3,5,7,1,8]=>1100010
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[3,2,4,5,1,6,8,7]=>[6,3,2,4,5,7,1,8]=>1100010
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[6,2,3,4,5,7,1,8]=>1000010
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[3,2,6,5,4,7,1,8]=>1011010
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[3,2,6,4,5,7,1,8]=>1010010
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[4,3,2,6,5,7,1,8]=>1101010
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]=>[2,4,3,6,5,7,1,8]=>0101010
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[2,3,4,6,5,7,1,8]=>0001010
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[5,4,3,2,6,7,1,8]=>1110010
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[3,4,2,1,5,6,8,7]=>[5,4,2,3,6,7,1,8]=>1100010
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[2,4,3,1,5,6,8,7]=>[5,2,4,3,6,7,1,8]=>1010010
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[5,2,3,4,6,7,1,8]=>1000010
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[2,5,4,3,6,7,1,8]=>0110010
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[2,5,3,4,6,7,1,8]=>0100010
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[2,3,5,4,6,7,1,8]=>0010010
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[4,3,2,5,6,7,1,8]=>1100010
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[4,2,3,5,6,7,1,8]=>1000010
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[3,2,4,5,6,7,1,8]=>1000010
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[2,3,4,5,6,7,1,8]=>0000010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,1]=>1111111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[8,7,6,5,4,2,3,1]=>1111101
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[8,7,6,5,2,4,3,1]=>1111011
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[8,7,6,5,3,2,4,1]=>1111101
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,7,6,5,2,3,4,1]=>1111001
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[8,7,6,2,5,4,3,1]=>1110111
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[8,7,6,2,5,3,4,1]=>1110101
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[8,7,6,3,2,5,4,1]=>1111011
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[8,7,6,2,3,5,4,1]=>1110011
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,7,6,4,3,2,5,1]=>1111101
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[8,7,6,4,2,3,5,1]=>1111001
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[8,7,6,3,2,4,5,1]=>1111001
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,7,6,2,3,4,5,1]=>1110001
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[3,7,6,5,4,2,1,8]=>[8,7,2,6,5,4,3,1]=>1101111
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[8,7,2,6,3,5,4,1]=>1101011
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[8,7,2,3,6,5,4,1]=>1100111
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[8,7,4,2,3,6,5,1]=>1110011
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[8,7,2,4,3,6,5,1]=>1101011
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[8,7,3,2,4,6,5,1]=>1110011
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,7,5,4,3,2,6,1]=>1111101
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[4,6,5,3,7,2,1,8]=>[8,7,5,2,4,3,6,1]=>1110101
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,7,5,3,2,4,6,1]=>1111001
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>[8,7,2,5,4,3,6,1]=>1101101
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[4,3,6,5,7,2,1,8]=>[8,7,3,2,5,4,6,1]=>1110101
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,7,4,3,2,5,6,1]=>1111001
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,7,2,3,4,5,6,1]=>1100001
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[8,2,7,6,5,4,3,1]=>1011111
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[2,6,7,5,4,3,1,8]=>[8,2,7,6,5,3,4,1]=>1011101
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[2,5,7,6,4,3,1,8]=>[8,2,7,6,3,5,4,1]=>1011011
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[8,2,7,6,3,4,5,1]=>1011001
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[8,2,7,3,6,5,4,1]=>1010111
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[8,2,7,3,6,4,5,1]=>1010101
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[8,2,7,3,4,6,5,1]=>1010011
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[2,4,5,6,7,3,1,8]=>[8,2,7,3,4,5,6,1]=>1010001
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[8,3,2,7,6,5,4,1]=>1101111
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[8,3,2,7,6,4,5,1]=>1101101
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[8,3,2,7,4,6,5,1]=>1101011
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[8,2,3,7,6,5,4,1]=>1001111
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[8,2,3,7,6,4,5,1]=>1001101
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[8,2,3,7,4,5,6,1]=>1001001
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[8,4,3,2,7,6,5,1]=>1110111
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[4,3,2,6,7,5,1,8]=>[8,4,3,2,7,5,6,1]=>1110101
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[8,4,2,3,7,6,5,1]=>1100111
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[8,4,2,3,7,5,6,1]=>1100101
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[2,4,3,7,6,5,1,8]=>[8,2,4,3,7,6,5,1]=>1010111
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[3,2,4,7,6,5,1,8]=>[8,3,2,4,7,6,5,1]=>1100111
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[8,2,3,4,7,6,5,1]=>1000111
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[8,5,4,3,2,7,6,1]=>1111011
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[8,5,4,2,3,7,6,1]=>1110011
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[2,5,4,3,7,6,1,8]=>[8,2,5,4,3,7,6,1]=>1011011
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[8,3,2,5,4,7,6,1]=>1101011
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[2,3,5,4,7,6,1,8]=>[8,2,3,5,4,7,6,1]=>1001011
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[8,4,3,2,5,7,6,1]=>1110011
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[3,4,2,5,7,6,1,8]=>[8,4,2,3,5,7,6,1]=>1100011
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[8,2,3,4,5,7,6,1]=>1000011
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,6,5,4,3,2,7,1]=>1111101
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[8,6,5,4,2,3,7,1]=>1111001
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,6,5,3,2,4,7,1]=>1111001
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[8,6,2,5,4,3,7,1]=>1101101
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[8,6,2,5,3,4,7,1]=>1101001
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[8,6,3,2,5,4,7,1]=>1110101
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,6,4,3,2,5,7,1]=>1111001
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,6,4,2,3,5,7,1]=>1110001
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,6,2,3,4,5,7,1]=>1100001
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[2,6,5,4,3,7,1,8]=>[8,2,6,5,4,3,7,1]=>1011101
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[2,4,5,6,3,7,1,8]=>[8,2,6,3,4,5,7,1]=>1010001
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[4,3,2,6,5,7,1,8]=>[8,4,3,2,6,5,7,1]=>1110101
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[8,4,2,3,6,5,7,1]=>1100101
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[8,2,4,3,6,5,7,1]=>1010101
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[3,2,4,6,5,7,1,8]=>[8,3,2,4,6,5,7,1]=>1100101
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,5,4,3,2,6,7,1]=>1111001
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[8,5,4,2,3,6,7,1]=>1110001
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,5,2,3,4,6,7,1]=>1100001
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[8,2,5,4,3,6,7,1]=>1011001
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[8,2,3,5,4,6,7,1]=>1001001
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,4,3,2,5,6,7,1]=>1110001
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[8,4,2,3,5,6,7,1]=>1100001
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[8,3,2,4,5,6,7,1]=>1100001
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,2,3,4,5,6,7,1]=>1000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[2,8,7,6,5,4,3,1]=>0111111
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,6,7,5,4,3,2,8]=>[2,8,7,6,5,3,4,1]=>0111101
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,5,7,6,4,3,2,8]=>[2,8,7,6,3,5,4,1]=>0111011
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[1,6,5,7,4,3,2,8]=>[2,8,7,6,4,3,5,1]=>0111101
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[2,8,7,6,3,4,5,1]=>0111001
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,4,5,7,6,3,2,8]=>[2,8,7,3,4,6,5,1]=>0110011
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[2,8,7,3,4,5,6,1]=>0110001
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>[2,8,3,7,6,5,4,1]=>0101111
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[2,8,3,7,4,6,5,1]=>0101011
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[2,8,3,7,4,5,6,1]=>0101001
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,4,3,7,6,5,2,8]=>[2,8,4,3,7,6,5,1]=>0110111
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[2,8,3,4,7,5,6,1]=>0100101
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,4,5,3,7,6,2,8]=>[2,8,5,3,4,7,6,1]=>0110011
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[2,8,3,5,4,7,6,1]=>0101011
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[2,8,4,3,5,7,6,1]=>0110011
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[2,8,3,4,5,7,6,1]=>0100011
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[1,4,6,5,3,7,2,8]=>[2,8,6,3,5,4,7,1]=>0110101
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[2,8,6,4,3,5,7,1]=>0111001
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>[2,8,6,3,4,5,7,1]=>0110001
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[2,8,3,6,4,5,7,1]=>0101001
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[2,8,4,3,6,5,7,1]=>0110101
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[2,8,5,4,3,6,7,1]=>0111001
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,4,5,3,6,7,2,8]=>[2,8,5,3,4,6,7,1]=>0110001
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,4,3,5,6,7,2,8]=>[2,8,4,3,5,6,7,1]=>0110001
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[2,8,3,4,5,6,7,1]=>0100001
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>[3,2,8,7,6,5,4,1]=>1011111
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>[3,2,8,7,4,5,6,1]=>1011001
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[3,2,8,4,7,5,6,1]=>1010101
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[2,1,5,4,7,6,3,8]=>[3,2,8,5,4,7,6,1]=>1011011
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[2,1,4,6,5,7,3,8]=>[3,2,8,4,6,5,7,1]=>1010101
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[3,2,8,5,4,6,7,1]=>1011001
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[2,1,4,5,6,7,3,8]=>[3,2,8,4,5,6,7,1]=>1010001
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[2,3,8,7,6,5,4,1]=>0011111
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[2,3,8,7,4,5,6,1]=>0011001
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,2,4,6,7,5,3,8]=>[2,3,8,4,7,5,6,1]=>0010101
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[2,3,8,6,4,5,7,1]=>0011001
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[2,3,8,5,4,6,7,1]=>0011001
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[2,3,8,4,5,6,7,1]=>0010001
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[4,3,2,8,7,6,5,1]=>1101111
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[4,3,2,8,5,7,6,1]=>1101011
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[4,3,2,8,5,6,7,1]=>1101001
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[4,2,3,8,5,6,7,1]=>1001001
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[2,4,3,8,7,6,5,1]=>0101111
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[2,4,3,8,7,5,6,1]=>0101101
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[2,4,3,8,5,7,6,1]=>0101011
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[2,4,3,8,6,5,7,1]=>0101101
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[2,4,3,8,5,6,7,1]=>0101001
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>[3,2,4,8,7,5,6,1]=>1001101
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[2,3,4,8,7,6,5,1]=>0001111
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[2,3,4,8,7,5,6,1]=>0001101
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[2,3,4,8,5,7,6,1]=>0001011
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[2,3,4,8,6,5,7,1]=>0001101
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[2,3,4,8,5,6,7,1]=>0001001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[5,4,3,2,8,7,6,1]=>1110111
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[5,4,3,2,8,6,7,1]=>1110101
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[5,2,3,4,8,7,6,1]=>1000111
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[5,2,3,4,8,6,7,1]=>1000101
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[2,5,4,3,8,7,6,1]=>0110111
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[2,5,4,3,8,6,7,1]=>0110101
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,3,4,2,7,6,5,8]=>[2,5,3,4,8,7,6,1]=>0100111
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[2,5,3,4,8,6,7,1]=>0100101
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>[3,2,5,4,8,6,7,1]=>1010101
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]=>[2,3,5,4,8,7,6,1]=>0010111
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[2,3,5,4,8,6,7,1]=>0010101
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[4,3,2,5,8,7,6,1]=>1100111
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>[2,4,3,5,8,7,6,1]=>0100111
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,3,2,4,6,7,5,8]=>[2,4,3,5,8,6,7,1]=>0100101
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[2,1,3,4,6,7,5,8]=>[3,2,4,5,8,6,7,1]=>1000101
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[2,3,4,5,8,7,6,1]=>0000111
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[2,3,4,5,8,6,7,1]=>0000101
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[6,5,4,3,2,8,7,1]=>1111011
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[6,5,2,4,3,8,7,1]=>1101011
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[6,2,5,3,4,8,7,1]=>1010011
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[6,3,2,5,4,8,7,1]=>1101011
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[4,3,2,5,1,7,6,8]=>[6,4,3,2,5,8,7,1]=>1110011
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[6,2,3,4,5,8,7,1]=>1000011
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[2,6,5,4,3,8,7,1]=>0111011
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[2,6,5,3,4,8,7,1]=>0110011
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[2,6,3,5,4,8,7,1]=>0101011
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[2,6,4,3,5,8,7,1]=>0110011
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[2,6,3,4,5,8,7,1]=>0100011
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]=>[3,2,6,5,4,8,7,1]=>1011011
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,2,4,5,3,7,6,8]=>[2,3,6,4,5,8,7,1]=>0010011
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[4,3,2,6,5,8,7,1]=>1101011
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[4,2,3,6,5,8,7,1]=>1001011
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[2,4,3,6,5,8,7,1]=>0101011
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[2,1,3,5,4,7,6,8]=>[3,2,4,6,5,8,7,1]=>1001011
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[2,3,4,6,5,8,7,1]=>0001011
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[5,4,3,2,6,8,7,1]=>1110011
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[2,5,4,3,6,8,7,1]=>0110011
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[2,5,3,4,6,8,7,1]=>0100011
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[4,3,2,5,6,8,7,1]=>1100011
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>[4,2,3,5,6,8,7,1]=>1000011
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[2,4,3,5,6,8,7,1]=>0100011
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>[3,2,4,5,6,8,7,1]=>1000011
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[2,3,4,5,6,8,7,1]=>0000011
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[7,6,5,4,3,2,8,1]=>1111101
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[7,6,5,4,2,3,8,1]=>1111001
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[7,6,5,3,2,4,8,1]=>1111001
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[7,6,5,2,3,4,8,1]=>1110001
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[4,5,3,6,2,1,7,8]=>[7,6,4,2,3,5,8,1]=>1110001
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[7,6,3,2,4,5,8,1]=>1110001
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[7,6,2,3,4,5,8,1]=>1100001
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[7,2,6,3,5,4,8,1]=>1010101
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[7,2,6,4,3,5,8,1]=>1011001
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[7,2,6,3,4,5,8,1]=>1010001
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[7,4,3,2,6,5,8,1]=>1110101
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[2,4,3,6,5,1,7,8]=>[7,2,4,3,6,5,8,1]=>1010101
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[7,5,4,3,2,6,8,1]=>1111001
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[7,5,4,2,3,6,8,1]=>1110001
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>[7,5,2,4,3,6,8,1]=>1101001
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[7,5,3,2,4,6,8,1]=>1110001
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[7,5,2,3,4,6,8,1]=>1100001
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[7,4,3,2,5,6,8,1]=>1110001
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[7,4,2,3,5,6,8,1]=>1100001
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[7,3,2,4,5,6,8,1]=>1100001
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[7,2,3,4,5,6,8,1]=>1000001
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[2,7,6,5,4,3,8,1]=>0111101
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>[2,7,6,5,3,4,8,1]=>0111001
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>[2,7,6,3,4,5,8,1]=>0110001
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[2,7,4,3,6,5,8,1]=>0110101
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[2,7,5,4,3,6,8,1]=>0111001
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>[2,7,3,5,4,6,8,1]=>0101001
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,4,3,5,6,2,7,8]=>[2,7,4,3,5,6,8,1]=>0110001
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[3,2,7,6,4,5,8,1]=>1011001
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[3,2,7,4,6,5,8,1]=>1010101
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[2,3,7,6,5,4,8,1]=>0011101
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[2,3,7,6,4,5,8,1]=>0011001
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[2,3,7,4,6,5,8,1]=>0010101
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,2,5,4,6,3,7,8]=>[2,3,7,5,4,6,8,1]=>0011001
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[2,3,7,4,5,6,8,1]=>0010001
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[4,3,2,7,6,5,8,1]=>1101101
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[4,3,2,7,5,6,8,1]=>1101001
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>[4,2,3,7,6,5,8,1]=>1001101
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[2,3,1,5,6,4,7,8]=>[4,2,3,7,5,6,8,1]=>1001001
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[2,4,3,7,6,5,8,1]=>0101101
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>[2,4,3,7,5,6,8,1]=>0101001
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[2,1,3,6,5,4,7,8]=>[3,2,4,7,6,5,8,1]=>1001101
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[2,1,3,5,6,4,7,8]=>[3,2,4,7,5,6,8,1]=>1001001
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[2,3,4,7,6,5,8,1]=>0001101
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[2,3,4,7,5,6,8,1]=>0001001
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[5,4,3,2,7,6,8,1]=>1110101
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[3,4,2,1,6,5,7,8]=>[5,4,2,3,7,6,8,1]=>1100101
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[2,5,4,3,7,6,8,1]=>0110101
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[3,2,5,4,7,6,8,1]=>1010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[2,3,5,4,7,6,8,1]=>0010101
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[3,2,1,4,6,5,7,8]=>[4,3,2,5,7,6,8,1]=>1100101
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[2,4,3,5,7,6,8,1]=>0100101
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[3,2,4,5,7,6,8,1]=>1000101
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[2,3,4,5,7,6,8,1]=>0000101
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[6,5,4,3,2,7,8,1]=>1111001
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[6,5,4,2,3,7,8,1]=>1110001
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[6,5,2,4,3,7,8,1]=>1101001
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[6,5,3,2,4,7,8,1]=>1110001
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[6,5,2,3,4,7,8,1]=>1100001
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[6,2,5,4,3,7,8,1]=>1011001
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[6,3,2,5,4,7,8,1]=>1101001
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[6,2,3,5,4,7,8,1]=>1001001
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[6,2,3,4,5,7,8,1]=>1000001
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[2,6,5,4,3,7,8,1]=>0111001
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>[2,6,5,3,4,7,8,1]=>0110001
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[2,6,3,5,4,7,8,1]=>0101001
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,4,3,5,2,6,7,8]=>[2,6,4,3,5,7,8,1]=>0110001
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[2,6,3,4,5,7,8,1]=>0100001
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[2,3,6,5,4,7,8,1]=>0011001
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[2,3,6,4,5,7,8,1]=>0010001
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]=>[4,3,2,6,5,7,8,1]=>1101001
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[2,4,3,6,5,7,8,1]=>0101001
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[2,3,4,6,5,7,8,1]=>0001001
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[5,4,3,2,6,7,8,1]=>1110001
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[5,4,2,3,6,7,8,1]=>1100001
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[5,3,2,4,6,7,8,1]=>1100001
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[5,2,3,4,6,7,8,1]=>1000001
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[2,5,4,3,6,7,8,1]=>0110001
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[2,5,3,4,6,7,8,1]=>0100001
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[3,2,5,4,6,7,8,1]=>1010001
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[2,3,5,4,6,7,8,1]=>0010001
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[4,3,2,5,6,7,8,1]=>1100001
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,1]=>1000001
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[2,4,3,5,6,7,8,1]=>0100001
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,1]=>1000001
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>0000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,3,2]=>01111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,2,3]=>01111110
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[1,9,8,7,6,5,2,3,4]=>01111100
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[1,9,2,3,4,5,6,7,8]=>01000000
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,8,9]=>00000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,1]=>00000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,2,3]=>011111110
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>[1,9,8,7,6,5,2,4,3]=>01111101
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[1,10,9,8,7,2,3,4,5,6]=>011110000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[2,4,5,6,7,8,9,3,1]=>[1,2,9,3,4,5,6,7,8]=>00100000
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[2,1,3,4,5,6,7,8,9]=>10000000
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[1,9,8,7,6,5,3,2,4]=>01111110
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[1,9,8,7,6,4,3,2,5]=>01111110
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[1,9,8,7,5,4,3,2,6]=>01111110
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[1,9,8,6,5,4,3,2,7]=>01111110
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[1,9,7,6,5,4,3,2,8]=>01111110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[1,8,7,6,5,4,3,2,9]=>01111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,3,2,4]=>011111110
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[1,10,9,8,7,6,4,3,2,5]=>011111110
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[1,10,9,8,7,5,4,3,2,6]=>011111110
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[1,10,9,8,6,5,4,3,2,7]=>011111110
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[1,10,9,7,6,5,4,3,2,8]=>011111110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[1,10,8,7,6,5,4,3,2,9]=>011111110
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>[2,9,8,7,6,5,4,3,1]=>01111111
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,10,9,1]=>[1,2,4,3,6,5,8,7,10,9]=>001010101
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,9,8,1,10]=>[10,3,2,5,4,7,6,9,8,1]=>110101011
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[3,2,5,4,7,6,9,8,1,10]=>101010110
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,9,8,11,10,1,12]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>11010101011
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[3,2,5,4,7,6,9,8,11,10,1,12]=>10101010110
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[2,3,4,5,6,7,8,1,9]=>00000010
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[2,3,4,5,6,7,8,9,1,10]=>000000010
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>[3,2,4,5,6,7,8,1,9]=>10000010
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[1,3,2,4,5,6,7,8,9]=>01000000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[2,3,4,5,6,7,8,9,10,1,11]=>0000000010
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[2,3,1,4,5,6,7,9,8]=>[4,2,3,5,6,7,8,1,9]=>10000010
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[2,4,3,5,6,7,8,9,1]=>[1,2,4,3,5,6,7,8,9]=>00100000
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[1,4,2,3,5,6,7,8,9]=>01000000
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[2,3,4,5,6,7,1,8,9]=>00000100
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[2,3,4,5,6,1,7,8,9]=>00001000
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[2,3,4,5,1,6,7,8,9]=>00010000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[2,3,4,1,5,6,7,8,9]=>00100000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[2,3,1,4,5,6,7,8,9]=>01000000
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[2,3,4,5,6,7,1,9,8]=>00000101
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[2,3,4,5,6,7,8,1,9,10]=>000000100
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>[2,3,4,5,6,1,8,7,9]=>00001010
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[2,3,4,5,6,7,1,8,9,10]=>000001000
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,4,7,6,8,9,5]=>[2,3,4,5,1,7,6,8,9]=>00010100
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[2,3,4,5,6,1,7,8,9,10]=>000010000
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,3,6,5,7,8,9,4]=>[2,3,4,1,6,5,7,8,9]=>00101000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[2,3,4,5,1,6,7,8,9,10]=>000100000
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[1,2,5,4,6,7,8,9,3]=>[2,3,1,5,4,6,7,8,9]=>01010000
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[2,3,4,1,5,6,7,8,9,10]=>001000000
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>[2,1,4,3,5,6,7,8,9]=>10100000
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[2,3,1,4,5,6,7,8,9,10]=>010000000
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[2,1,9,8,7,6,5,4,3]=>10111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,2,3,1]=>11111101
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[2,1,9,8,7,6,5,3,4]=>10111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,10,9,8,7,6,5,4,3]=>101111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,2,3,1]=>111111101
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[9,8,7,6,5,3,2,4,1]=>11111101
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>[2,1,9,8,7,6,4,3,5]=>10111110
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[2,1,10,9,8,7,6,5,3,4]=>101111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,11,10,9,8,7,6,5,4,3]=>1011111111
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,10,1]=>[1,3,2,5,4,7,6,9,8,10]=>010101010
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,10,3]=>[3,2,1,5,4,7,6,9,8,10]=>110101010
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[3,2,1,9,8,7,6,5,4]=>11011111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>[4,3,2,1,9,8,7,6,5]=>11101111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>[5,4,3,2,1,9,8,7,6]=>11110111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>[6,5,4,3,2,1,9,8,7]=>11111011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>[7,6,5,4,3,2,1,9,8]=>11111101
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[8,7,6,5,4,3,2,1,9]=>11111110
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>[2,3,1,9,8,7,6,5,4]=>01011111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[3,2,1,10,9,8,7,6,5,4]=>110111111
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>[4,2,3,1,9,8,7,6,5]=>10101111
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>[4,3,2,1,10,9,8,7,6,5]=>111011111
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[5,4,3,2,1,10,9,8,7,6]=>111101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]=>[6,5,4,3,2,1,10,9,8,7]=>111110111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[7,6,5,4,3,2,1,10,9,8]=>111111011
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[6,7,5,4,3,2,1,9,8]=>[8,7,6,5,4,2,3,1,9]=>11111010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>[8,7,6,5,4,3,2,1,10,9]=>111111101
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,2,9,1]=>11111101
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[7,6,5,4,3,2,8,9,1]=>11111001
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[6,5,4,3,2,7,8,9,1]=>11110001
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[5,4,3,2,6,7,8,9,1]=>11100001
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[4,3,2,5,6,7,8,9,1]=>11000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,1]=>10000001
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[9,8,7,6,5,4,3,2,10,1]=>111111101
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[8,7,6,5,4,3,2,9,10,1]=>111111001
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,7,6,5,4,3,2,8,9]=>[2,8,7,6,5,4,3,9,1]=>01111101
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[7,6,5,4,3,2,8,9,10,1]=>111110001
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[6,5,4,3,2,7,8,9,10,1]=>111100001
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[5,4,3,2,6,7,8,9,10,1]=>111000001
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[4,3,2,5,6,7,8,9,10,1]=>110000001
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[2,4,3,5,6,7,8,9,1]=>01000001
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[3,2,4,5,6,7,8,9,10,1]=>100000001
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[4,9,8,7,6,5,3,2,1]=>[1,9,8,2,7,6,5,4,3]=>01101111
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[3,9,8,7,6,5,4,2,1]=>[1,9,2,8,7,6,5,4,3]=>01011111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[1,2,9,8,7,6,5,4,3]=>00111111
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>[1,2,3,4,5,6,7,9,8]=>00000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[3,2,4,5,6,7,8,9,10,11,1]=>1000000001
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[2,3,4,5,6,8,9,7,1]=>[1,2,3,4,5,6,9,7,8]=>00000010
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]=>[7,6,5,4,3,2,9,8,1]=>11111011
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[1,8,2,3,4,5,6,7,9]=>01000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[9,2,3,4,5,6,7,8,1]=>10000001
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[4,2,3,5,6,7,8,9,1]=>10000001
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[8,2,3,4,5,6,7,9,1]=>10000001
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[4,2,3,5,6,7,8,9,10,1]=>100000001
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[10,2,3,4,5,6,7,8,9,1]=>100000001
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>[2,3,4,6,5,7,8,9,1]=>00010001
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>[2,3,4,5,7,6,8,9,1]=>00001001
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]=>[2,3,4,5,6,8,7,9,1]=>00000101
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>[2,3,4,5,6,7,9,8,1]=>00000011
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>[2,3,4,6,5,7,8,9,10,1]=>000100001
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[2,3,4,5,7,6,8,9,10,1]=>000010001
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[2,3,4,5,6,7,8,10,9,1]=>000000011
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,3,4,5,6,7,9,8,2]=>[2,1,3,4,5,6,7,9,8]=>10000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>[1,7,6,5,4,3,2,9,8]=>01111101
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1]=>[1,4,3,2,5,6,7,8,9]=>01100000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>[2,8,7,6,5,4,3,1,9]=>01111110
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7]=>[7,6,5,4,3,2,1,8,9]=>11111100
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>[3,2,9,8,7,6,5,4,1]=>10111111
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[2,10,9,8,7,6,5,4,3,1]=>011111111
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[1,2,4,5,3,6,7,8,9]=>[2,3,6,4,5,7,8,9,1]=>00100001
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[1,3,4,5,6,7,8,2,9]=>[2,9,3,4,5,6,7,8,1]=>01000001
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>[2,3,4,5,6,7,8,1,10,9]=>000000101
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[9,8,7,6,5,2,3,4,1]=>11111001
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>[2,3,4,5,6,1,9,8,7]=>00001011
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>[2,3,4,5,1,9,8,7,6]=>00010111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>[2,3,4,5,6,8,7,1,9]=>00000110
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]=>[2,3,4,5,6,7,9,8,1,10]=>000000110
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[5,4,2,3,6,7,8,9,1]=>11000001
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[9,7,6,5,4,3,2,8,1]=>11111101
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[9,8,7,6,4,3,2,5,1]=>11111101
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[6,5,4,2,3,7,8,9,1]=>11100001
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[9,3,2,4,5,6,7,8,1]=>11000001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10]=>[8,7,6,5,4,3,2,10,9,1]=>111111011
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[1,2,3,9,8,7,6,5,4]=>00011111
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[9,2,8,7,6,5,4,3,1]=>10111111
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[8,2,3,4,5,6,7,1,9]=>10000010
[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>[10,8,7,6,5,4,3,2,9,1]=>111111101
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,4,5,6,7,8,3,9,2]=>[2,1,8,3,4,5,6,7,9]=>10100000
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9]=>[2,3,9,8,7,6,5,4,1]=>00111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[2,3,4,5,6,7,8,9,11,10,1]=>0000000011
[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[2,1,3,5,6,7,8,9,4]=>[3,2,4,1,5,6,7,8,9]=>10100000
[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[5,6,4,3,2,1,7,8,9]=>[7,6,5,4,2,3,8,9,1]=>11110001
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
searching the database
Sorry, this map was not found in the database.