Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[1,2]=>0
[[.,.],.]=>[1,2]=>[2,1]=>1
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>00
[.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>01
[[.,.],[.,.]]=>[1,3,2]=>[2,3,1]=>10
[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>10
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>11
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>000
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>001
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[1,3,4,2]=>010
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>010
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>011
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,3,4,1]=>100
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[2,4,3,1]=>101
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[3,4,1,2]=>100
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[3,4,2,1]=>110
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>100
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>110
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[4,2,3,1]=>110
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>101
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>111
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>0000
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>0001
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[1,2,4,5,3]=>0010
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>0010
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>0011
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[1,3,4,5,2]=>0100
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[1,3,5,4,2]=>0101
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[1,4,5,2,3]=>0100
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[1,4,5,3,2]=>0110
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>0100
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>0110
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[1,5,3,4,2]=>0110
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>0101
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>0111
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,3,4,5,1]=>1000
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[2,3,5,4,1]=>1001
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[2,4,5,3,1]=>1010
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[2,5,3,4,1]=>1010
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[2,5,4,3,1]=>1011
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[3,4,5,1,2]=>1000
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,5,4,1,2]=>1001
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[3,4,5,2,1]=>1100
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[3,5,4,2,1]=>1101
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[4,5,1,2,3]=>1000
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[4,5,1,3,2]=>1100
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[4,5,2,3,1]=>1100
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[4,5,3,1,2]=>1010
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[4,5,3,2,1]=>1110
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>1000
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>1010
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[5,1,3,4,2]=>1100
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>1100
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>1110
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[5,2,3,4,1]=>1100
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[5,2,4,3,1]=>1110
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[5,3,4,1,2]=>1010
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[5,3,4,2,1]=>1110
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>1001
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>1101
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[5,4,2,3,1]=>1101
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>1011
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>1111
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>00001
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>00010
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>00010
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>00011
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>00100
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>00101
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>00100
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>00110
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>00100
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>00110
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>00110
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>00101
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>00111
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>01000
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>01001
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>01010
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>01010
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>01011
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>01000
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>01001
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>01100
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>01101
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>01000
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>01100
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>01100
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>01010
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>01110
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>01000
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>01010
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>01100
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>01100
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>01110
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>01100
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>01110
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>01010
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>01110
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>01001
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>01101
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>01101
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>01011
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>01111
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>10000
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>10001
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>10010
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>10010
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>10011
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>10100
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>10101
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>10100
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>10110
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>10100
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>10110
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>10110
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>10101
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>10111
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>10000
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>10001
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>10010
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>10010
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>10011
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>11000
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>11001
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>11010
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>11010
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>11011
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>10000
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>10001
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>11000
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>11001
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>11000
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>11001
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>10100
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>10101
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>11100
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>11101
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>10000
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>10100
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>11000
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>11000
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>11100
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>11000
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>11100
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>10100
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>11100
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>10010
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>11010
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>11010
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>10110
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>11110
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>10000
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>10010
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>10100
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>10100
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>10110
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>11000
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>11010
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>11000
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>11100
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>11000
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>11100
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>11100
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>11010
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>11110
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>11000
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>11010
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>11100
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>11100
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>11110
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>10100
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>10110
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>11100
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>11110
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>10010
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>11010
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>11010
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>10110
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>11110
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>10001
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>10101
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>11001
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>11001
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>11101
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>11001
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>11101
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>10101
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>11101
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>10011
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>11011
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>11011
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>10111
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>000001
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>000010
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>000010
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>000011
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>000100
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>000101
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>000100
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>000110
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>000100
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>000110
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>000110
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>000101
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>001000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>001001
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>001010
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>001010
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>001000
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>001001
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>001100
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>001101
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>001000
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>001100
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>001100
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>001010
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>001110
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>001000
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>001010
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>001100
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>001100
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>001110
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>001100
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>001110
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>001010
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>001110
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>001001
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>001101
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>001101
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>001011
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>001111
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>010000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>010001
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>010010
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>010010
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>010011
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>010100
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>010101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>010100
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>010110
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>010100
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>010110
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>010110
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>010101
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>010111
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>010000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>010001
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>010010
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>010010
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>010011
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>011000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>011001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>011010
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>011010
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>011011
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>010000
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>010001
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>011000
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>011001
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>011000
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>011001
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>010100
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>010101
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>011100
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>011101
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>010000
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>010100
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>011000
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>011000
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>011100
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>011000
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>011100
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>010100
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>011100
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>010010
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>011010
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>011010
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>010110
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>011110
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>010000
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>010010
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>010100
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>010100
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>010110
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>011000
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>011010
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>011000
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>011100
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>011000
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>011100
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>011100
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>011010
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>011110
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>011000
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>011010
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>011100
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>011100
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>011110
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>010100
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>010110
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>011100
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>011110
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>010010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>011010
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>011010
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>010110
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>011110
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>010001
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>010101
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>011001
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>011001
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>011101
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>011001
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>011101
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>010101
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>011101
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>010011
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>011011
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>011011
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>010111
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>011111
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>100000
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>100001
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>100010
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>100010
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>100011
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>100100
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>100101
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>100100
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>100110
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>100100
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>100110
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>100110
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>100101
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>100111
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>101000
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>101001
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>101010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>101010
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>101011
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>101000
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>101001
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>101100
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>101101
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>101000
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>101100
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>101100
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>101010
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>101110
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>101000
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>101010
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>101100
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>101100
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>101110
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>101100
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>101110
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>101010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>101110
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>101001
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>101101
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>101101
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>101011
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>101111
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>100000
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>100001
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>100010
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>100010
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>100011
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>100100
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>100101
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>100100
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>100110
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>100100
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>100110
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>100110
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>100101
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>100111
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>110000
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>110001
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>110010
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>110010
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>110011
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>110100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>110101
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>110100
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>110110
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>110100
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>110110
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>110110
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>110101
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>110111
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>100000
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>100001
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>100010
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>100010
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>100011
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>110000
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>110001
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>110010
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>110010
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>110011
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>110000
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>110001
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>110010
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>110010
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>110011
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>101000
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>101001
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>101010
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>101010
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>101011
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>111000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>111001
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>111010
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>111010
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>111011
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>100000
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>100001
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>101000
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>101001
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>110000
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>110001
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>110000
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>110001
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>111000
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>111001
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>110000
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>110001
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>111000
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>111001
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>101000
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>101001
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>111000
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>111001
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>100100
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>100101
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>110100
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>110101
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>110100
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>110101
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>101100
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>101101
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>111100
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>111101
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>100000
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>100100
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>101000
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>101000
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>101100
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>110000
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>110100
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>110000
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>111000
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>110000
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>111000
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>111000
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>110100
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>111100
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>110000
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>110100
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>111000
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>111000
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>111100
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>101000
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>101100
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>111000
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>111100
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>100100
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>110100
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>110100
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>101100
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>111100
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>100010
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>101010
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>110010
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>110010
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>111010
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>110010
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>111010
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>101010
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>111010
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>100110
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>110110
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>110110
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>101110
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>111110
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>100000
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>100010
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>100100
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>100100
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>100110
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>101000
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>101010
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>101000
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>101100
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>101000
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>101100
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>101100
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>101010
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>101110
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>110000
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>110010
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>110100
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>110100
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>110110
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>110000
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>110010
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>111000
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>111010
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>110000
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>111000
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>111000
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>110100
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>111100
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>110000
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>110100
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>111000
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>111000
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>111100
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>111000
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>111100
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>110100
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>111100
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>110010
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>111010
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>111010
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>110110
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>111110
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>110000
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>110010
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>110100
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>110100
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>110110
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>111000
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>111010
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>111000
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>111100
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>111000
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>111100
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>111100
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>111010
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>111110
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>101000
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>101010
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>101100
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>101100
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>101110
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>111000
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>111010
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>111100
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>111100
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>111110
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>100100
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>100110
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>110100
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>110110
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>110100
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>110110
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>101100
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>101110
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>111100
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>111110
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>100010
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>101010
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>110010
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>110010
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>111010
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>110010
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>111010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>111010
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>100110
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>110110
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>110110
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>101110
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>111110
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>100001
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>100101
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>101001
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>101001
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>101101
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>110001
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>110101
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>110001
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>111001
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>110001
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>111001
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>111001
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>110101
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>111101
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>110001
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>110101
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>111001
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>111001
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>111101
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>101001
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>101101
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>111001
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>111101
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>100101
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>110101
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>110101
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>101101
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>111101
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>100011
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>101011
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>110011
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>110011
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>111011
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>110011
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>111011
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>101011
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>111011
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>100111
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>110111
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>110111
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>101111
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>0000001
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[1,2,3,4,5,7,8,6]=>0000010
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>0000010
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>0000011
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[1,2,3,4,6,7,8,5]=>0000100
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[1,2,3,4,6,8,7,5]=>0000101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[1,2,3,4,7,8,5,6]=>0000100
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[1,2,3,4,7,8,6,5]=>0000110
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>0000100
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>0000110
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[1,2,3,4,8,6,7,5]=>0000110
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>0000101
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>0000111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[1,2,3,5,6,7,8,4]=>0001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[1,2,3,5,6,8,7,4]=>0001001
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[1,2,3,5,7,8,6,4]=>0001010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[1,2,3,5,8,6,7,4]=>0001010
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[1,2,3,5,8,7,6,4]=>0001011
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[1,2,3,6,7,8,4,5]=>0001000
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[5,4,7,8,6,3,2,1]=>[1,2,3,6,8,7,4,5]=>0001001
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[1,2,3,6,7,8,5,4]=>0001100
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[1,2,3,6,8,7,5,4]=>0001101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[1,2,3,7,8,4,5,6]=>0001000
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[1,2,3,7,8,4,6,5]=>0001100
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[1,2,3,7,8,5,6,4]=>0001100
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[5,4,6,8,7,3,2,1]=>[1,2,3,7,8,6,4,5]=>0001010
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[1,2,3,7,8,6,5,4]=>0001110
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>0001000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>0001010
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[1,2,3,8,4,6,7,5]=>0001100
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>0001100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>0001110
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[1,2,3,8,5,6,7,4]=>0001100
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[1,2,3,8,5,7,6,4]=>0001110
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[1,2,3,8,6,7,4,5]=>0001010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[1,2,3,8,6,7,5,4]=>0001110
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>0001001
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>0001101
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[1,2,3,8,7,5,6,4]=>0001101
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>0001011
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>0001111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[1,2,4,5,6,7,8,3]=>0010000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[1,2,4,5,6,8,7,3]=>0010001
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[1,2,4,5,7,8,6,3]=>0010010
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[1,2,4,5,8,6,7,3]=>0010010
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[3,6,7,8,5,4,2,1]=>[1,2,4,5,8,7,6,3]=>0010011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[1,2,4,6,7,8,5,3]=>0010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[1,2,4,6,8,7,5,3]=>0010101
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[1,2,4,7,8,5,6,3]=>0010100
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[1,2,4,7,8,6,5,3]=>0010110
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[1,2,4,8,5,6,7,3]=>0010100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[1,2,4,8,7,6,5,3]=>0010111
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[1,2,5,6,7,8,3,4]=>0010000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[1,2,5,6,8,7,3,4]=>0010001
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[1,2,5,7,8,6,3,4]=>0010010
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[1,2,5,8,6,7,3,4]=>0010010
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[1,2,5,8,7,6,3,4]=>0010011
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[1,2,5,6,7,8,4,3]=>0011000
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[3,4,7,8,6,5,2,1]=>[1,2,5,6,8,7,4,3]=>0011001
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[1,2,5,8,6,7,4,3]=>0011010
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[1,2,5,8,7,6,4,3]=>0011011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[1,2,6,7,8,3,4,5]=>0010000
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[1,2,6,8,7,3,4,5]=>0010001
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[4,5,3,8,7,6,2,1]=>[1,2,6,7,8,3,5,4]=>0011000
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[1,2,6,8,7,3,5,4]=>0011001
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[3,5,4,8,7,6,2,1]=>[1,2,6,7,8,4,5,3]=>0011000
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[3,5,4,7,8,6,2,1]=>[1,2,6,8,7,4,5,3]=>0011001
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[4,3,5,8,7,6,2,1]=>[1,2,6,7,8,5,3,4]=>0010100
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[1,2,6,8,7,5,3,4]=>0010101
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[1,2,6,7,8,5,4,3]=>0011100
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[1,2,7,8,3,4,5,6]=>0010000
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[5,6,4,3,8,7,2,1]=>[1,2,7,8,3,4,6,5]=>0010100
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[1,2,7,8,3,5,6,4]=>0011000
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[1,2,7,8,3,6,4,5]=>0011000
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[1,2,7,8,3,6,5,4]=>0011100
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[3,6,5,4,8,7,2,1]=>[1,2,7,8,4,5,6,3]=>0011000
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[1,2,7,8,5,6,3,4]=>0010100
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[3,4,6,5,8,7,2,1]=>[1,2,7,8,5,6,4,3]=>0011100
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[1,2,7,8,6,3,4,5]=>0010010
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[1,2,7,8,6,3,5,4]=>0011010
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[3,5,4,6,8,7,2,1]=>[1,2,7,8,6,4,5,3]=>0011010
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[1,2,7,8,6,5,3,4]=>0010110
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[3,4,5,6,8,7,2,1]=>[1,2,7,8,6,5,4,3]=>0011110
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>0010000
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>0010010
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[1,2,8,3,4,6,7,5]=>0010100
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[1,2,8,3,4,7,6,5]=>0010110
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[1,2,8,3,5,6,7,4]=>0011000
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[4,6,7,5,3,8,2,1]=>[1,2,8,3,5,7,6,4]=>0011010
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[5,4,7,6,3,8,2,1]=>[1,2,8,3,6,7,4,5]=>0011000
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>0011000
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[1,2,8,3,7,4,6,5]=>0011100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>0011010
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>0011110
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[1,2,8,4,5,6,7,3]=>0011000
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[3,5,7,6,4,8,2,1]=>[1,2,8,4,6,7,5,3]=>0011100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[1,2,8,4,7,6,5,3]=>0011110
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1]=>[1,2,8,5,6,7,3,4]=>0010100
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[1,2,8,5,6,7,4,3]=>0011100
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[1,2,8,6,7,3,5,4]=>0011010
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[1,2,8,6,7,5,3,4]=>0010110
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[1,2,8,6,7,5,4,3]=>0011110
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>0010001
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[1,2,8,7,3,4,6,5]=>0010101
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>0011101
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[3,6,5,4,7,8,2,1]=>[1,2,8,7,4,5,6,3]=>0011001
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[3,5,6,4,7,8,2,1]=>[1,2,8,7,4,6,5,3]=>0011101
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>[1,2,8,7,5,6,3,4]=>0010101
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>[1,2,8,7,5,6,4,3]=>0011101
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[1,2,8,7,6,3,4,5]=>0010011
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>0011011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,2,8,7,6,5,3,4]=>0010111
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>0011111
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[1,3,4,5,6,7,8,2]=>0100000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[1,3,4,5,6,8,7,2]=>0100001
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[1,3,4,5,7,8,6,2]=>0100010
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[1,3,4,5,8,6,7,2]=>0100010
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[1,3,4,5,8,7,6,2]=>0100011
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[2,5,8,7,6,4,3,1]=>[1,3,4,6,7,8,5,2]=>0100100
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[1,3,4,8,5,6,7,2]=>0100100
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[2,5,7,6,8,4,3,1]=>[1,3,4,8,6,7,5,2]=>0100110
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[1,3,4,8,7,6,5,2]=>0100111
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[1,3,5,6,7,8,4,2]=>0101000
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[1,3,5,6,8,7,4,2]=>0101001
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[1,3,5,7,8,6,4,2]=>0101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[1,3,5,8,7,6,4,2]=>0101011
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[2,5,4,7,8,6,3,1]=>[1,3,6,8,7,4,5,2]=>0101001
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[2,4,5,8,7,6,3,1]=>[1,3,6,7,8,5,4,2]=>0101100
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[1,3,6,8,7,5,4,2]=>0101101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[2,6,5,4,8,7,3,1]=>[1,3,7,8,4,5,6,2]=>0101000
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[1,3,7,8,4,6,5,2]=>0101100
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[1,3,7,8,5,6,4,2]=>0101100
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[2,4,5,6,8,7,3,1]=>[1,3,7,8,6,5,4,2]=>0101110
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[1,3,8,4,5,6,7,2]=>0101000
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[2,5,7,6,4,8,3,1]=>[1,3,8,4,6,7,5,2]=>0101100
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[1,3,8,5,6,7,4,2]=>0101100
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[2,4,6,7,5,8,3,1]=>[1,3,8,5,7,6,4,2]=>0101110
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[2,5,4,7,6,8,3,1]=>[1,3,8,6,7,4,5,2]=>0101010
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[1,3,8,7,4,5,6,2]=>0101001
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[1,3,8,7,4,6,5,2]=>0101101
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>[1,3,8,7,5,6,4,2]=>0101101
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[1,3,8,7,6,5,4,2]=>0101111
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[1,4,5,6,7,8,2,3]=>0100000
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[3,2,7,8,6,5,4,1]=>[1,4,5,6,8,7,2,3]=>0100001
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[3,2,6,7,8,5,4,1]=>[1,4,5,8,7,6,2,3]=>0100011
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[1,4,7,8,5,6,2,3]=>0100100
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[3,2,7,6,5,8,4,1]=>[1,4,8,5,6,7,2,3]=>0100100
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[1,4,8,5,7,6,2,3]=>0100110
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>[1,4,8,6,7,5,2,3]=>0100110
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[1,4,5,6,7,8,3,2]=>0110000
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[2,3,6,8,7,5,4,1]=>[1,4,5,7,8,6,3,2]=>0110010
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[2,3,7,6,8,5,4,1]=>[1,4,5,8,6,7,3,2]=>0110010
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[2,3,6,7,8,5,4,1]=>[1,4,5,8,7,6,3,2]=>0110011
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>[1,4,6,7,8,5,3,2]=>0110100
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[1,4,6,8,7,5,3,2]=>0110101
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[1,4,7,8,5,6,3,2]=>0110100
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[1,4,7,8,6,5,3,2]=>0110110
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[1,4,8,5,6,7,3,2]=>0110100
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[1,4,8,5,7,6,3,2]=>0110110
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>[1,4,8,6,7,5,3,2]=>0110110
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[1,4,8,7,6,5,3,2]=>0110111
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[1,5,6,7,8,2,3,4]=>0100000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[1,5,6,8,7,2,3,4]=>0100001
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[1,5,7,8,6,2,3,4]=>0100010
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[1,5,8,7,6,2,3,4]=>0100011
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[1,5,6,7,8,2,4,3]=>0110000
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[3,4,2,6,8,7,5,1]=>[1,5,7,8,6,2,4,3]=>0110010
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[1,5,8,7,6,2,4,3]=>0110011
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[1,5,6,7,8,3,4,2]=>0110000
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[1,5,7,8,6,3,4,2]=>0110010
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[2,4,3,7,6,8,5,1]=>[1,5,8,6,7,3,4,2]=>0110010
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[2,4,3,6,7,8,5,1]=>[1,5,8,7,6,3,4,2]=>0110011
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[1,5,6,7,8,4,2,3]=>0101000
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[3,2,4,7,8,6,5,1]=>[1,5,6,8,7,4,2,3]=>0101001
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[3,2,4,6,8,7,5,1]=>[1,5,7,8,6,4,2,3]=>0101010
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[3,2,4,7,6,8,5,1]=>[1,5,8,6,7,4,2,3]=>0101010
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[1,5,6,7,8,4,3,2]=>0111000
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[1,5,8,7,6,4,3,2]=>0111011
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[1,6,7,8,2,3,4,5]=>0100000
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[1,6,8,7,2,3,4,5]=>0100001
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[1,6,7,8,2,3,5,4]=>0101000
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[1,6,8,7,2,3,5,4]=>0101001
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[3,5,4,2,8,7,6,1]=>[1,6,7,8,2,4,5,3]=>0110000
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[1,6,7,8,2,5,3,4]=>0110000
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[4,3,5,2,7,8,6,1]=>[1,6,8,7,2,5,3,4]=>0110001
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[3,4,5,2,7,8,6,1]=>[1,6,8,7,2,5,4,3]=>0111001
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[1,6,7,8,3,4,5,2]=>0110000
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[1,6,8,7,3,4,5,2]=>0110001
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>[1,6,7,8,3,5,4,2]=>0111000
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[1,6,8,7,3,5,4,2]=>0111001
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>[1,6,7,8,4,5,3,2]=>0111000
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[1,6,8,7,4,5,3,2]=>0111001
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[1,6,7,8,5,2,3,4]=>0100100
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[4,3,2,5,7,8,6,1]=>[1,6,8,7,5,2,3,4]=>0100101
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[1,6,8,7,5,2,4,3]=>0110101
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[2,4,3,5,8,7,6,1]=>[1,6,7,8,5,3,4,2]=>0110100
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[2,4,3,5,7,8,6,1]=>[1,6,8,7,5,3,4,2]=>0110101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[1,6,7,8,5,4,3,2]=>0111100
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[1,6,8,7,5,4,3,2]=>0111101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[1,7,8,2,3,4,5,6]=>0100000
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[1,7,8,2,3,5,6,4]=>0101000
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[1,7,8,2,3,6,4,5]=>0101000
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[1,7,8,2,3,6,5,4]=>0101100
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[1,7,8,2,4,5,6,3]=>0110000
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[1,7,8,2,4,6,5,3]=>0110100
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[1,7,8,2,5,6,3,4]=>0110000
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[3,5,4,6,2,8,7,1]=>[1,7,8,2,6,4,5,3]=>0111000
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[1,7,8,3,4,5,6,2]=>0110000
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[1,7,8,3,5,6,4,2]=>0111000
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[2,5,4,6,3,8,7,1]=>[1,7,8,3,6,4,5,2]=>0111000
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[2,4,5,6,3,8,7,1]=>[1,7,8,3,6,5,4,2]=>0111100
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[1,7,8,4,5,6,2,3]=>0101000
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[3,2,5,6,4,8,7,1]=>[1,7,8,4,6,5,2,3]=>0101100
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[1,7,8,5,6,3,4,2]=>0110100
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>[1,7,8,5,6,4,2,3]=>0101100
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[1,7,8,5,6,4,3,2]=>0111100
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[1,7,8,6,2,3,4,5]=>0100010
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>[1,7,8,6,2,3,5,4]=>0101010
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[3,4,5,2,6,8,7,1]=>[1,7,8,6,2,5,4,3]=>0111010
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[1,7,8,6,3,4,5,2]=>0110010
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[2,4,5,3,6,8,7,1]=>[1,7,8,6,3,5,4,2]=>0111010
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[2,3,5,4,6,8,7,1]=>[1,7,8,6,4,5,3,2]=>0111010
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[1,7,8,6,5,2,4,3]=>0110110
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[1,7,8,6,5,3,4,2]=>0110110
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>[1,7,8,6,5,4,2,3]=>0101110
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[1,7,8,6,5,4,3,2]=>0111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>0100000
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[1,8,2,3,4,5,7,6]=>0100010
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[1,8,2,3,4,6,7,5]=>0100100
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,8,2,3,4,7,5,6]=>0100100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>0100110
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[1,8,2,3,5,6,7,4]=>0101000
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[1,8,2,3,6,7,5,4]=>0101100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[1,8,2,3,7,5,6,4]=>0101100
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,8,2,3,7,6,4,5]=>0101010
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>0101110
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[3,7,6,5,4,2,8,1]=>[1,8,2,4,5,6,7,3]=>0110000
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[3,6,7,5,4,2,8,1]=>[1,8,2,4,5,7,6,3]=>0110010
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[1,8,2,4,6,7,5,3]=>0110100
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[3,6,5,7,4,2,8,1]=>[1,8,2,4,7,5,6,3]=>0110100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[1,8,2,4,7,6,5,3]=>0110110
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[1,8,2,5,6,7,3,4]=>0110000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>[1,8,2,5,7,6,3,4]=>0110010
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[1,8,2,5,6,7,4,3]=>0111000
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[1,8,2,5,7,6,4,3]=>0111010
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[1,8,2,6,7,3,4,5]=>0110000
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[3,5,4,7,6,2,8,1]=>[1,8,2,6,7,4,5,3]=>0111000
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[3,4,5,7,6,2,8,1]=>[1,8,2,6,7,5,4,3]=>0111100
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>0110000
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[1,8,2,7,3,4,6,5]=>0110100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[1,8,2,7,3,5,6,4]=>0111000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>0111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>0111100
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[1,8,2,7,4,5,6,3]=>0111000
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[1,8,2,7,4,6,5,3]=>0111100
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[1,8,2,7,5,6,3,4]=>0110100
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>0110010
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>0111010
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[1,8,2,7,6,4,5,3]=>0111010
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>0111110
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[1,8,3,4,5,6,7,2]=>0110000
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[2,5,7,6,4,3,8,1]=>[1,8,3,4,6,7,5,2]=>0110100
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[2,5,6,7,4,3,8,1]=>[1,8,3,4,7,6,5,2]=>0110110
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[2,4,7,6,5,3,8,1]=>[1,8,3,5,6,7,4,2]=>0111000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[2,4,6,7,5,3,8,1]=>[1,8,3,5,7,6,4,2]=>0111010
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[1,8,3,6,7,4,5,2]=>0111000
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[1,8,3,6,7,5,4,2]=>0111100
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[2,5,6,4,7,3,8,1]=>[1,8,3,7,4,6,5,2]=>0111100
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[1,8,3,7,5,6,4,2]=>0111100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[1,8,3,7,6,4,5,2]=>0111010
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[1,8,3,7,6,5,4,2]=>0111110
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[3,2,7,6,5,4,8,1]=>[1,8,4,5,6,7,2,3]=>0101000
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[1,8,4,5,7,6,2,3]=>0101010
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[3,2,5,7,6,4,8,1]=>[1,8,4,6,7,5,2,3]=>0101100
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[1,8,4,7,5,6,2,3]=>0101100
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[1,8,4,7,6,5,2,3]=>0101110
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[1,8,4,5,6,7,3,2]=>0111000
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[2,3,5,7,6,4,8,1]=>[1,8,4,6,7,5,3,2]=>0111100
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[1,8,4,7,6,5,3,2]=>0111110
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[1,8,5,6,7,2,3,4]=>0100100
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>[1,8,5,7,6,2,3,4]=>0100110
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>[1,8,5,6,7,2,4,3]=>0110100
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[1,8,5,7,6,2,4,3]=>0110110
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[1,8,5,6,7,3,4,2]=>0110100
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[1,8,5,6,7,4,2,3]=>0101100
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[1,8,5,6,7,4,3,2]=>0111100
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[2,3,4,6,7,5,8,1]=>[1,8,5,7,6,4,3,2]=>0111110
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[1,8,6,7,2,3,4,5]=>0100010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[1,8,6,7,2,5,3,4]=>0110010
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[1,8,6,7,2,5,4,3]=>0111010
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[1,8,6,7,3,4,5,2]=>0110010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[1,8,6,7,4,5,2,3]=>0101010
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[1,8,6,7,4,5,3,2]=>0111010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[1,8,6,7,5,2,3,4]=>0100110
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>[1,8,6,7,5,3,4,2]=>0110110
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[1,8,6,7,5,4,2,3]=>0101110
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[1,8,6,7,5,4,3,2]=>0111110
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>0100001
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[5,6,4,3,2,7,8,1]=>[1,8,7,2,3,4,6,5]=>0100101
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[4,6,5,3,2,7,8,1]=>[1,8,7,2,3,5,6,4]=>0101001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>0101001
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>0101101
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>[1,8,7,2,4,5,6,3]=>0110001
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[4,3,6,5,2,7,8,1]=>[1,8,7,2,5,6,3,4]=>0110001
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[3,4,6,5,2,7,8,1]=>[1,8,7,2,5,6,4,3]=>0111001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>0110001
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>0111001
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>[1,8,7,2,6,4,5,3]=>0111001
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[1,8,7,2,6,5,3,4]=>0110101
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>0111101
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[1,8,7,3,4,5,6,2]=>0110001
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[2,5,6,4,3,7,8,1]=>[1,8,7,3,4,6,5,2]=>0110101
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[1,8,7,3,6,4,5,2]=>0111001
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[2,4,5,6,3,7,8,1]=>[1,8,7,3,6,5,4,2]=>0111101
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[3,2,6,5,4,7,8,1]=>[1,8,7,4,5,6,2,3]=>0101001
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[1,8,7,4,5,6,3,2]=>0111001
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[1,8,7,4,6,5,3,2]=>0111101
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>[1,8,7,5,6,2,3,4]=>0100101
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[1,8,7,5,6,3,4,2]=>0110101
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[3,2,4,6,5,7,8,1]=>[1,8,7,5,6,4,2,3]=>0101101
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>[1,8,7,5,6,4,3,2]=>0111101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>0100011
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[1,8,7,6,2,4,5,3]=>0110011
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>0111011
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[1,8,7,6,3,4,5,2]=>0110011
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[1,8,7,6,3,5,4,2]=>0111011
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>[1,8,7,6,4,5,2,3]=>0101011
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[1,8,7,6,4,5,3,2]=>0111011
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>0100111
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>0110111
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>[1,8,7,6,5,3,4,2]=>0110111
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,8,7,6,5,4,2,3]=>0101111
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>0111111
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1]=>1000000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[2,3,4,5,6,8,7,1]=>1000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[2,3,4,5,7,8,6,1]=>1000010
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[2,3,4,5,8,6,7,1]=>1000010
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[2,3,4,5,8,7,6,1]=>1000011
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[2,3,4,6,7,8,5,1]=>1000100
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,5,7,8,6,4,3,2]=>[2,3,4,6,8,7,5,1]=>1000101
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[2,3,4,7,8,5,6,1]=>1000100
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[2,3,4,7,8,6,5,1]=>1000110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[2,3,4,8,5,6,7,1]=>1000100
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[2,3,4,8,5,7,6,1]=>1000110
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[2,3,4,8,6,7,5,1]=>1000110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[2,3,4,8,7,5,6,1]=>1000101
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[2,3,4,8,7,6,5,1]=>1000111
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[2,3,5,6,7,8,4,1]=>1001000
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[2,3,5,6,8,7,4,1]=>1001001
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[2,3,5,7,8,6,4,1]=>1001010
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[2,3,5,8,6,7,4,1]=>1001010
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>[2,3,5,8,7,6,4,1]=>1001011
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[1,5,4,7,8,6,3,2]=>[2,3,6,8,7,4,5,1]=>1001001
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[1,4,5,8,7,6,3,2]=>[2,3,6,7,8,5,4,1]=>1001100
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,6,5,4,8,7,3,2]=>[2,3,7,8,4,5,6,1]=>1001000
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[2,3,7,8,6,4,5,1]=>1001010
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[2,3,8,4,5,6,7,1]=>1001000
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[1,5,7,6,4,8,3,2]=>[2,3,8,4,6,7,5,1]=>1001100
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,6,5,7,4,8,3,2]=>[2,3,8,4,7,5,6,1]=>1001100
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[2,3,8,5,6,7,4,1]=>1001100
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[2,3,8,5,7,6,4,1]=>1001110
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,4,5,7,6,8,3,2]=>[2,3,8,6,7,5,4,1]=>1001110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>[2,3,8,7,4,5,6,1]=>1001001
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[2,3,8,7,6,5,4,1]=>1001111
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[2,4,5,6,7,8,3,1]=>1010000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>[2,4,5,6,8,7,3,1]=>1010001
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>[2,4,5,7,8,6,3,1]=>1010010
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[2,4,6,7,8,5,3,1]=>1010100
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[2,4,6,8,7,5,3,1]=>1010101
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[1,3,6,5,8,7,4,2]=>[2,4,7,8,5,6,3,1]=>1010100
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[2,4,7,8,6,5,3,1]=>1010110
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,3,7,6,5,8,4,2]=>[2,4,8,5,6,7,3,1]=>1010100
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[2,4,8,5,7,6,3,1]=>1010110
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[2,4,8,6,7,5,3,1]=>1010110
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[2,4,8,7,5,6,3,1]=>1010101
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[2,4,8,7,6,5,3,1]=>1010111
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[2,5,6,7,8,3,4,1]=>1010000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[2,5,6,8,7,3,4,1]=>1010001
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[2,5,7,8,6,3,4,1]=>1010010
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[2,5,8,6,7,3,4,1]=>1010010
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[2,5,6,7,8,4,3,1]=>1011000
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[2,5,8,6,7,4,3,1]=>1011010
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[2,5,8,7,6,4,3,1]=>1011011
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[1,5,4,3,7,8,6,2]=>[2,6,8,7,3,4,5,1]=>1010001
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[1,3,5,4,8,7,6,2]=>[2,6,7,8,4,5,3,1]=>1011000
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[2,6,8,7,4,5,3,1]=>1011001
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>[2,6,7,8,5,3,4,1]=>1010100
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[2,6,8,7,5,3,4,1]=>1010101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[2,6,7,8,5,4,3,1]=>1011100
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>[2,6,8,7,5,4,3,1]=>1011101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[2,7,8,3,4,5,6,1]=>1010000
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[2,7,8,3,4,6,5,1]=>1010100
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,5,4,6,3,8,7,2]=>[2,7,8,3,6,4,5,1]=>1011000
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[2,7,8,4,5,6,3,1]=>1011000
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[2,7,8,5,6,3,4,1]=>1010100
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[2,7,8,6,3,5,4,1]=>1011010
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[2,7,8,6,5,4,3,1]=>1011110
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[2,8,3,4,5,6,7,1]=>1010000
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[2,8,3,4,5,7,6,1]=>1010010
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[2,8,3,4,7,5,6,1]=>1010100
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[2,8,3,5,6,7,4,1]=>1011000
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[2,8,3,5,7,6,4,1]=>1011010
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,5,4,7,6,3,8,2]=>[2,8,3,6,7,4,5,1]=>1011000
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,4,5,7,6,3,8,2]=>[2,8,3,6,7,5,4,1]=>1011100
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[1,6,5,4,7,3,8,2]=>[2,8,3,7,4,5,6,1]=>1011000
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,5,6,4,7,3,8,2]=>[2,8,3,7,4,6,5,1]=>1011100
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[1,4,6,5,7,3,8,2]=>[2,8,3,7,5,6,4,1]=>1011100
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[2,8,3,7,6,5,4,1]=>1011110
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[1,3,7,6,5,4,8,2]=>[2,8,4,5,6,7,3,1]=>1011000
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[2,8,4,6,7,5,3,1]=>1011100
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[2,8,4,7,6,5,3,1]=>1011110
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[1,4,3,6,7,5,8,2]=>[2,8,5,7,6,3,4,1]=>1010110
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[2,8,5,6,7,4,3,1]=>1011100
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[1,3,4,6,7,5,8,2]=>[2,8,5,7,6,4,3,1]=>1011110
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[2,8,6,7,4,5,3,1]=>1011010
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,4,3,5,7,6,8,2]=>[2,8,6,7,5,3,4,1]=>1010110
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[1,3,4,5,7,6,8,2]=>[2,8,6,7,5,4,3,1]=>1011110
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[1,6,5,4,3,7,8,2]=>[2,8,7,3,4,5,6,1]=>1010001
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[1,5,6,4,3,7,8,2]=>[2,8,7,3,4,6,5,1]=>1010101
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[1,3,6,5,4,7,8,2]=>[2,8,7,4,5,6,3,1]=>1011001
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>[2,8,7,4,6,5,3,1]=>1011101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[2,8,7,5,6,3,4,1]=>1010101
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[1,3,4,6,5,7,8,2]=>[2,8,7,5,6,4,3,1]=>1011101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[2,8,7,6,3,4,5,1]=>1010011
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[2,8,7,6,3,5,4,1]=>1011011
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[2,8,7,6,4,5,3,1]=>1011011
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[2,8,7,6,5,3,4,1]=>1010111
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>1011111
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>1000000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[3,4,5,6,8,7,1,2]=>1000001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[3,4,5,7,8,6,1,2]=>1000010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[3,4,5,8,6,7,1,2]=>1000010
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[3,4,5,8,7,6,1,2]=>1000011
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[3,4,6,7,8,5,1,2]=>1000100
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[3,4,6,8,7,5,1,2]=>1000101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[3,4,7,8,5,6,1,2]=>1000100
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[2,1,5,6,8,7,4,3]=>[3,4,7,8,6,5,1,2]=>1000110
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[3,4,8,5,6,7,1,2]=>1000100
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[3,4,8,5,7,6,1,2]=>1000110
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[3,4,8,7,5,6,1,2]=>1000101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[3,4,8,7,6,5,1,2]=>1000111
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[3,5,6,7,8,4,1,2]=>1001000
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[3,5,6,8,7,4,1,2]=>1001001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[3,5,7,8,6,4,1,2]=>1001010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[2,1,4,7,6,8,5,3]=>[3,5,8,6,7,4,1,2]=>1001010
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[3,5,8,7,6,4,1,2]=>1001011
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[3,6,7,8,4,5,1,2]=>1001000
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[3,6,7,8,5,4,1,2]=>1001100
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[2,1,6,5,4,8,7,3]=>[3,7,8,4,5,6,1,2]=>1001000
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[3,7,8,5,6,4,1,2]=>1001100
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[3,8,4,7,5,6,1,2]=>1001100
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[3,8,4,7,6,5,1,2]=>1001110
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[3,8,5,6,7,4,1,2]=>1001100
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[3,8,6,7,4,5,1,2]=>1001010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[2,1,4,5,7,6,8,3]=>[3,8,6,7,5,4,1,2]=>1001110
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[3,8,7,4,5,6,1,2]=>1001001
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[3,8,7,4,6,5,1,2]=>1001101
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[2,1,4,6,5,7,8,3]=>[3,8,7,5,6,4,1,2]=>1001101
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[3,8,7,6,4,5,1,2]=>1001011
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[3,8,7,6,5,4,1,2]=>1001111
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[3,4,5,6,7,8,2,1]=>1100000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[3,4,5,6,8,7,2,1]=>1100001
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,2,6,8,7,5,4,3]=>[3,4,5,7,8,6,2,1]=>1100010
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>[3,4,5,8,6,7,2,1]=>1100010
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[3,4,5,8,7,6,2,1]=>1100011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[3,4,6,7,8,5,2,1]=>1100100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[3,4,8,5,6,7,2,1]=>1100100
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[3,4,8,7,5,6,2,1]=>1100101
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[3,4,8,7,6,5,2,1]=>1100111
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[3,5,6,7,8,4,2,1]=>1101000
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[3,5,6,8,7,4,2,1]=>1101001
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[3,5,7,8,6,4,2,1]=>1101010
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,2,4,7,6,8,5,3]=>[3,5,8,6,7,4,2,1]=>1101010
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[3,5,8,7,6,4,2,1]=>1101011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[3,6,7,8,4,5,2,1]=>1101000
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[3,6,8,7,5,4,2,1]=>1101101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[3,7,8,4,5,6,2,1]=>1101000
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[3,7,8,5,6,4,2,1]=>1101100
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[3,7,8,6,5,4,2,1]=>1101110
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[3,8,4,5,6,7,2,1]=>1101000
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,2,6,5,7,4,8,3]=>[3,8,4,7,5,6,2,1]=>1101100
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[3,8,4,7,6,5,2,1]=>1101110
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[3,8,5,7,6,4,2,1]=>1101110
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[1,2,4,5,7,6,8,3]=>[3,8,6,7,5,4,2,1]=>1101110
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[3,8,7,4,5,6,2,1]=>1101001
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[3,8,7,4,6,5,2,1]=>1101101
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[1,2,4,6,5,7,8,3]=>[3,8,7,5,6,4,2,1]=>1101101
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[3,8,7,6,4,5,2,1]=>1101011
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>1101111
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[4,5,6,7,8,1,2,3]=>1000000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[4,5,6,8,7,1,2,3]=>1000001
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[4,5,7,8,6,1,2,3]=>1000010
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[4,5,8,6,7,1,2,3]=>1000010
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[4,5,8,7,6,1,2,3]=>1000011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[4,6,7,8,5,1,2,3]=>1000100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[4,6,8,7,5,1,2,3]=>1000101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[4,7,8,5,6,1,2,3]=>1000100
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[4,7,8,6,5,1,2,3]=>1000110
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[4,8,5,6,7,1,2,3]=>1000100
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[4,8,5,7,6,1,2,3]=>1000110
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[4,8,6,7,5,1,2,3]=>1000110
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[4,8,7,5,6,1,2,3]=>1000101
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[4,8,7,6,5,1,2,3]=>1000111
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[4,5,6,7,8,1,3,2]=>1100000
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[4,5,8,6,7,1,3,2]=>1100010
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[4,5,8,7,6,1,3,2]=>1100011
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[4,6,7,8,5,1,3,2]=>1100100
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[4,7,8,5,6,1,3,2]=>1100100
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[4,7,8,6,5,1,3,2]=>1100110
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[4,8,5,6,7,1,3,2]=>1100100
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[4,8,5,7,6,1,3,2]=>1100110
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[4,8,6,7,5,1,3,2]=>1100110
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[4,8,7,5,6,1,3,2]=>1100101
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[4,8,7,6,5,1,3,2]=>1100111
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[4,5,6,7,8,2,3,1]=>1100000
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[1,3,2,7,6,8,5,4]=>[4,5,8,6,7,2,3,1]=>1100010
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[4,6,7,8,5,2,3,1]=>1100100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[4,6,8,7,5,2,3,1]=>1100101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[4,7,8,5,6,2,3,1]=>1100100
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>[4,8,5,6,7,2,3,1]=>1100100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[4,8,6,7,5,2,3,1]=>1100110
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[4,8,7,5,6,2,3,1]=>1100101
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[1,3,2,5,6,7,8,4]=>[4,8,7,6,5,2,3,1]=>1100111
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[4,5,6,7,8,3,1,2]=>1010000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[4,5,6,8,7,3,1,2]=>1010001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[4,5,7,8,6,3,1,2]=>1010010
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[4,5,8,7,6,3,1,2]=>1010011
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[4,6,8,7,5,3,1,2]=>1010101
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[2,1,3,7,6,5,8,4]=>[4,8,5,6,7,3,1,2]=>1010100
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[4,8,5,7,6,3,1,2]=>1010110
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[4,8,6,7,5,3,1,2]=>1010110
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[4,8,7,5,6,3,1,2]=>1010101
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[4,8,7,6,5,3,1,2]=>1010111
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[4,5,6,7,8,3,2,1]=>1110000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[4,5,6,8,7,3,2,1]=>1110001
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[4,5,7,8,6,3,2,1]=>1110010
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[4,5,8,6,7,3,2,1]=>1110010
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[4,5,8,7,6,3,2,1]=>1110011
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[4,6,7,8,5,3,2,1]=>1110100
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[4,6,8,7,5,3,2,1]=>1110101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[4,7,8,5,6,3,2,1]=>1110100
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[4,7,8,6,5,3,2,1]=>1110110
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[4,8,5,6,7,3,2,1]=>1110100
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[4,8,5,7,6,3,2,1]=>1110110
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[4,8,6,7,5,3,2,1]=>1110110
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[4,8,7,5,6,3,2,1]=>1110101
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>1110111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>1000000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[5,6,8,7,1,2,3,4]=>1000001
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[5,7,8,6,1,2,3,4]=>1000010
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[5,8,6,7,1,2,3,4]=>1000010
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[5,8,7,6,1,2,3,4]=>1000011
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[5,6,7,8,1,2,4,3]=>1010000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>1010001
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[5,7,8,6,1,2,4,3]=>1010010
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[5,8,6,7,1,2,4,3]=>1010010
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[5,8,7,6,1,2,4,3]=>1010011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[5,6,7,8,1,3,4,2]=>1100000
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[5,6,8,7,1,3,4,2]=>1100001
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[5,7,8,6,1,3,4,2]=>1100010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>1100010
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[5,8,7,6,1,3,4,2]=>1100011
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[5,6,7,8,1,4,2,3]=>1100000
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[5,6,8,7,1,4,2,3]=>1100001
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>1100010
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[5,8,6,7,1,4,2,3]=>1100010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[5,8,7,6,1,4,2,3]=>1100011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[5,6,7,8,1,4,3,2]=>1110000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[5,6,8,7,1,4,3,2]=>1110001
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[5,7,8,6,1,4,3,2]=>1110010
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[5,8,6,7,1,4,3,2]=>1110010
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>1110011
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[5,6,7,8,2,3,4,1]=>1100000
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[5,7,8,6,2,3,4,1]=>1100010
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[5,8,6,7,2,3,4,1]=>1100010
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[5,8,7,6,2,3,4,1]=>1100011
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[5,6,7,8,2,4,3,1]=>1110000
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[5,6,8,7,2,4,3,1]=>1110001
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[5,8,6,7,2,4,3,1]=>1110010
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[5,8,7,6,2,4,3,1]=>1110011
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>1010000
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[5,6,8,7,3,4,1,2]=>1010001
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[5,7,8,6,3,4,1,2]=>1010010
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[5,8,6,7,3,4,1,2]=>1010010
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[5,8,7,6,3,4,1,2]=>1010011
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[5,6,7,8,3,4,2,1]=>1110000
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[5,7,8,6,3,4,2,1]=>1110010
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[5,8,6,7,3,4,2,1]=>1110010
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>1110011
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[5,6,7,8,4,1,2,3]=>1001000
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[5,6,8,7,4,1,2,3]=>1001001
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[5,7,8,6,4,1,2,3]=>1001010
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[5,8,6,7,4,1,2,3]=>1001010
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[5,8,7,6,4,1,2,3]=>1001011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[5,6,7,8,4,1,3,2]=>1101000
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[5,8,6,7,4,1,3,2]=>1101010
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[5,8,7,6,4,1,3,2]=>1101011
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[5,6,7,8,4,2,3,1]=>1101000
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[5,7,8,6,4,2,3,1]=>1101010
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[5,8,6,7,4,2,3,1]=>1101010
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[5,8,7,6,4,2,3,1]=>1101011
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[5,6,7,8,4,3,1,2]=>1011000
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[5,6,8,7,4,3,1,2]=>1011001
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[5,8,6,7,4,3,1,2]=>1011010
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[5,8,7,6,4,3,1,2]=>1011011
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[5,6,7,8,4,3,2,1]=>1111000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[5,6,8,7,4,3,2,1]=>1111001
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[5,7,8,6,4,3,2,1]=>1111010
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[5,8,6,7,4,3,2,1]=>1111010
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>1111011
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[6,7,8,1,2,3,4,5]=>1000000
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[6,8,7,1,2,3,4,5]=>1000001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[6,7,8,1,2,3,5,4]=>1001000
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[6,7,8,1,2,4,5,3]=>1010000
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[6,7,8,1,2,5,3,4]=>1010000
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[6,7,8,1,2,5,4,3]=>1011000
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[6,7,8,1,3,4,5,2]=>1100000
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[6,8,7,1,3,4,5,2]=>1100001
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[6,7,8,1,3,5,4,2]=>1101000
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[6,8,7,1,3,5,4,2]=>1101001
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[6,7,8,1,4,5,2,3]=>1100000
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[6,8,7,1,4,5,2,3]=>1100001
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[6,7,8,1,4,5,3,2]=>1110000
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[6,7,8,1,5,2,3,4]=>1100000
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[6,8,7,1,5,2,3,4]=>1100001
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[6,7,8,1,5,2,4,3]=>1110000
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[6,7,8,1,5,3,4,2]=>1110000
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[6,8,7,1,5,3,4,2]=>1110001
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[6,7,8,1,5,4,2,3]=>1101000
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[6,8,7,1,5,4,2,3]=>1101001
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[6,7,8,1,5,4,3,2]=>1111000
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[6,8,7,1,5,4,3,2]=>1111001
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[6,7,8,2,3,4,5,1]=>1100000
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[6,8,7,2,3,4,5,1]=>1100001
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[6,7,8,2,3,5,4,1]=>1101000
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,4,5,3,2,7,8,6]=>[6,8,7,2,3,5,4,1]=>1101001
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,3,5,4,2,8,7,6]=>[6,7,8,2,4,5,3,1]=>1110000
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[6,8,7,2,4,5,3,1]=>1110001
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[1,3,4,5,2,8,7,6]=>[6,7,8,2,5,4,3,1]=>1111000
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[6,8,7,2,5,4,3,1]=>1111001
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]=>[6,7,8,3,4,5,1,2]=>1010000
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[2,1,5,4,3,7,8,6]=>[6,8,7,3,4,5,1,2]=>1010001
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[6,7,8,3,4,5,2,1]=>1110000
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[6,8,7,3,4,5,2,1]=>1110001
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[6,7,8,3,5,4,2,1]=>1111000
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>[6,8,7,3,5,4,2,1]=>1111001
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]=>[6,7,8,4,5,1,2,3]=>1001000
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[2,3,1,5,4,7,8,6]=>[6,8,7,4,5,1,3,2]=>1101001
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[6,7,8,4,5,2,3,1]=>1101000
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[6,8,7,4,5,2,3,1]=>1101001
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[6,7,8,4,5,3,1,2]=>1011000
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[2,1,3,5,4,7,8,6]=>[6,8,7,4,5,3,1,2]=>1011001
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[6,7,8,4,5,3,2,1]=>1111000
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[6,8,7,4,5,3,2,1]=>1111001
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[6,7,8,5,1,2,3,4]=>1000100
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[6,8,7,5,1,2,3,4]=>1000101
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[6,7,8,5,1,2,4,3]=>1010100
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[3,4,2,1,5,7,8,6]=>[6,8,7,5,1,2,4,3]=>1010101
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[6,8,7,5,1,3,4,2]=>1100101
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[6,7,8,5,1,4,2,3]=>1100100
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[6,8,7,5,1,4,2,3]=>1100101
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[6,7,8,5,1,4,3,2]=>1110100
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[6,8,7,5,1,4,3,2]=>1110101
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[6,7,8,5,2,3,4,1]=>1100100
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[6,8,7,5,2,4,3,1]=>1110101
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]=>[6,7,8,5,3,4,1,2]=>1010100
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[2,1,4,3,5,7,8,6]=>[6,8,7,5,3,4,1,2]=>1010101
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[6,8,7,5,3,4,2,1]=>1110101
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>1001100
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[6,8,7,5,4,1,2,3]=>1001101
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>1101101
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[6,8,7,5,4,2,3,1]=>1101101
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>[6,7,8,5,4,3,1,2]=>1011100
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>[6,8,7,5,4,3,1,2]=>1011101
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[6,7,8,5,4,3,2,1]=>1111100
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>1111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>1000000
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[7,8,1,2,3,4,6,5]=>1000100
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[7,8,1,2,3,5,6,4]=>1001000
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[7,8,1,2,3,6,4,5]=>1001000
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[7,8,1,2,3,6,5,4]=>1001100
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[7,8,1,2,4,5,6,3]=>1010000
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[7,8,1,2,4,6,5,3]=>1010100
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[7,8,1,2,5,6,3,4]=>1010000
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[3,4,6,5,2,1,8,7]=>[7,8,1,2,5,6,4,3]=>1011000
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[7,8,1,2,6,3,4,5]=>1010000
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[7,8,1,2,6,3,5,4]=>1011000
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[7,8,1,2,6,5,3,4]=>1010100
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[7,8,1,2,6,5,4,3]=>1011100
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[7,8,1,3,4,5,6,2]=>1100000
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[7,8,1,3,5,6,4,2]=>1101000
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[2,5,4,6,3,1,8,7]=>[7,8,1,3,6,4,5,2]=>1101000
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[3,2,6,5,4,1,8,7]=>[7,8,1,4,5,6,2,3]=>1100000
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[7,8,1,4,5,6,3,2]=>1110000
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>[7,8,1,4,6,5,3,2]=>1110100
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[4,3,2,6,5,1,8,7]=>[7,8,1,5,6,2,3,4]=>1100000
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[7,8,1,5,6,3,4,2]=>1110000
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[3,2,4,6,5,1,8,7]=>[7,8,1,5,6,4,2,3]=>1101000
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[2,3,4,6,5,1,8,7]=>[7,8,1,5,6,4,3,2]=>1111000
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[7,8,1,6,2,3,4,5]=>1100000
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[7,8,1,6,2,3,5,4]=>1101000
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>[7,8,1,6,2,4,5,3]=>1110000
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[7,8,1,6,2,5,3,4]=>1110000
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[7,8,1,6,2,5,4,3]=>1111000
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[7,8,1,6,3,4,5,2]=>1110000
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[7,8,1,6,3,5,4,2]=>1111000
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[7,8,1,6,4,5,2,3]=>1101000
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[7,8,1,6,5,2,3,4]=>1100100
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[7,8,1,6,5,2,4,3]=>1110100
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[2,4,3,5,6,1,8,7]=>[7,8,1,6,5,3,4,2]=>1110100
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[7,8,1,6,5,4,3,2]=>1111100
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>[7,8,2,3,4,5,6,1]=>1100000
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,5,6,4,3,2,8,7]=>[7,8,2,3,4,6,5,1]=>1100100
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>[7,8,2,3,6,4,5,1]=>1101000
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[1,4,5,3,6,2,8,7]=>[7,8,2,6,3,5,4,1]=>1111000
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[1,3,5,4,6,2,8,7]=>[7,8,2,6,4,5,3,1]=>1111000
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[1,3,4,5,6,2,8,7]=>[7,8,2,6,5,4,3,1]=>1111100
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>1010000
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[7,8,3,4,6,5,1,2]=>1010100
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[7,8,3,5,6,4,1,2]=>1011000
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[7,8,3,6,4,5,1,2]=>1011000
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[7,8,3,6,5,4,1,2]=>1011100
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[7,8,3,4,5,6,2,1]=>1110000
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[1,2,5,6,4,3,8,7]=>[7,8,3,4,6,5,2,1]=>1110100
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[7,8,4,5,6,1,2,3]=>1001000
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[7,8,4,5,6,1,3,2]=>1101000
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]=>[7,8,4,5,6,2,3,1]=>1101000
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>[7,8,4,5,6,3,1,2]=>1011000
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[2,1,3,5,6,4,8,7]=>[7,8,4,6,5,3,1,2]=>1011100
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>1000100
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[7,8,5,6,1,2,4,3]=>1010100
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[7,8,5,6,1,3,4,2]=>1100100
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[7,8,5,6,1,4,2,3]=>1100100
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[7,8,5,6,1,4,3,2]=>1110100
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[7,8,5,6,2,3,4,1]=>1100100
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,3,4,2,6,5,8,7]=>[7,8,5,6,2,4,3,1]=>1110100
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>1010100
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>1110100
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[7,8,5,6,4,1,2,3]=>1001100
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[2,3,1,4,6,5,8,7]=>[7,8,5,6,4,1,3,2]=>1101100
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[7,8,5,6,4,3,1,2]=>1011100
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1]=>1111100
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[7,8,6,1,2,3,4,5]=>1000010
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[7,8,6,1,2,4,5,3]=>1010010
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[7,8,6,1,3,4,5,2]=>1100010
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[7,8,6,1,3,5,4,2]=>1101010
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[7,8,6,1,4,5,2,3]=>1100010
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>[7,8,6,1,4,5,3,2]=>1110010
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[4,3,2,5,1,6,8,7]=>[7,8,6,1,5,2,3,4]=>1100010
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[2,4,3,5,1,6,8,7]=>[7,8,6,1,5,3,4,2]=>1110010
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[7,8,6,1,5,4,3,2]=>1111010
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]=>[7,8,6,2,3,4,5,1]=>1100010
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,4,5,3,2,6,8,7]=>[7,8,6,2,3,5,4,1]=>1101010
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[7,8,6,3,4,5,1,2]=>1010010
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[7,8,6,3,4,5,2,1]=>1110010
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[7,8,6,3,5,4,2,1]=>1111010
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>1011010
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[7,8,6,4,5,3,2,1]=>1111010
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[7,8,6,5,1,2,3,4]=>1000110
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[3,4,2,1,5,6,8,7]=>[7,8,6,5,1,2,4,3]=>1010110
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[7,8,6,5,1,4,2,3]=>1100110
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[7,8,6,5,1,4,3,2]=>1110110
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[7,8,6,5,2,4,3,1]=>1110110
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[7,8,6,5,3,4,1,2]=>1010110
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>1110110
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[7,8,6,5,4,1,2,3]=>1001110
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[7,8,6,5,4,1,3,2]=>1101110
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]=>[7,8,6,5,4,2,3,1]=>1101110
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>1011110
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>1111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>1000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6]=>1000010
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[8,1,2,3,4,6,7,5]=>1000100
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[8,1,2,3,4,7,5,6]=>1000100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>1000110
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[8,1,2,3,5,6,7,4]=>1001000
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[8,1,2,3,5,7,6,4]=>1001010
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[5,4,7,6,3,2,1,8]=>[8,1,2,3,6,7,4,5]=>1001000
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[8,1,2,3,6,7,5,4]=>1001100
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>1001000
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[8,1,2,3,7,5,6,4]=>1001100
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>1001110
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[3,7,6,5,4,2,1,8]=>[8,1,2,4,5,6,7,3]=>1010000
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[8,1,2,4,6,7,5,3]=>1010100
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[8,1,2,4,7,6,5,3]=>1010110
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[8,1,2,5,6,7,3,4]=>1010000
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[8,1,2,5,6,7,4,3]=>1011000
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[8,1,2,6,7,3,5,4]=>1011000
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[8,1,2,6,7,4,5,3]=>1011000
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[8,1,2,6,7,5,3,4]=>1010100
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[3,4,5,7,6,2,1,8]=>[8,1,2,6,7,5,4,3]=>1011100
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>1010000
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[8,1,2,7,3,4,6,5]=>1010100
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[4,6,5,3,7,2,1,8]=>[8,1,2,7,3,5,6,4]=>1011000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>1011000
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>1011100
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>[8,1,2,7,4,5,6,3]=>1011000
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[8,1,2,7,4,6,5,3]=>1011100
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[4,3,6,5,7,2,1,8]=>[8,1,2,7,5,6,3,4]=>1010100
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>1010010
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>1011010
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[3,5,4,6,7,2,1,8]=>[8,1,2,7,6,4,5,3]=>1011010
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>1011110
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[8,1,3,4,5,6,7,2]=>1100000
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[2,6,7,5,4,3,1,8]=>[8,1,3,4,5,7,6,2]=>1100010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[2,5,7,6,4,3,1,8]=>[8,1,3,4,6,7,5,2]=>1100100
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[8,1,3,5,6,7,4,2]=>1101000
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[8,1,3,5,7,6,4,2]=>1101010
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[2,5,4,7,6,3,1,8]=>[8,1,3,6,7,4,5,2]=>1101000
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[8,1,3,6,7,5,4,2]=>1101100
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[2,6,5,4,7,3,1,8]=>[8,1,3,7,4,5,6,2]=>1101000
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[8,1,3,7,4,6,5,2]=>1101100
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[2,4,6,5,7,3,1,8]=>[8,1,3,7,5,6,4,2]=>1101100
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>[8,1,3,7,6,4,5,2]=>1101010
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[2,4,5,6,7,3,1,8]=>[8,1,3,7,6,5,4,2]=>1101110
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[8,1,4,5,6,7,2,3]=>1100000
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[8,1,4,5,7,6,2,3]=>1100010
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[8,1,4,6,7,5,2,3]=>1100100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[8,1,4,7,6,5,2,3]=>1100110
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[8,1,4,5,6,7,3,2]=>1110000
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[8,1,4,5,7,6,3,2]=>1110010
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[8,1,4,7,6,5,3,2]=>1110110
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[8,1,5,6,7,2,3,4]=>1100000
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[4,3,2,6,7,5,1,8]=>[8,1,5,7,6,2,3,4]=>1100010
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[8,1,5,6,7,2,4,3]=>1110000
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[8,1,5,7,6,2,4,3]=>1110010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[2,4,3,7,6,5,1,8]=>[8,1,5,6,7,3,4,2]=>1110000
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[3,2,4,7,6,5,1,8]=>[8,1,5,6,7,4,2,3]=>1101000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[8,1,5,6,7,4,3,2]=>1111000
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[8,1,6,7,2,3,4,5]=>1100000
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[8,1,6,7,2,3,5,4]=>1101000
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[8,1,6,7,2,4,5,3]=>1110000
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>[8,1,6,7,2,5,3,4]=>1110000
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[3,4,5,2,7,6,1,8]=>[8,1,6,7,2,5,4,3]=>1111000
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[8,1,6,7,4,5,2,3]=>1101000
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[2,3,5,4,7,6,1,8]=>[8,1,6,7,4,5,3,2]=>1111000
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[8,1,6,7,5,2,3,4]=>1100100
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[3,4,2,5,7,6,1,8]=>[8,1,6,7,5,2,4,3]=>1110100
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[2,4,3,5,7,6,1,8]=>[8,1,6,7,5,3,4,2]=>1110100
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[3,2,4,5,7,6,1,8]=>[8,1,6,7,5,4,2,3]=>1101100
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[8,1,6,7,5,4,3,2]=>1111100
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,1,7,2,3,4,5,6]=>1100000
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>1101000
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>1101100
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[8,1,7,2,4,5,6,3]=>1110000
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[8,1,7,2,4,6,5,3]=>1110100
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[8,1,7,2,5,6,3,4]=>1110000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[8,1,7,2,5,6,4,3]=>1111000
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>1110000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>1111000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[8,1,7,2,6,4,5,3]=>1111000
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>1111100
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[2,6,5,4,3,7,1,8]=>[8,1,7,3,4,5,6,2]=>1110000
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[2,4,6,5,3,7,1,8]=>[8,1,7,3,5,6,4,2]=>1111000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[8,1,7,3,6,4,5,2]=>1111000
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[2,4,5,6,3,7,1,8]=>[8,1,7,3,6,5,4,2]=>1111100
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[8,1,7,4,5,6,2,3]=>1101000
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[8,1,7,4,6,5,3,2]=>1111100
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[4,3,2,6,5,7,1,8]=>[8,1,7,5,6,2,3,4]=>1100100
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[8,1,7,5,6,2,4,3]=>1110100
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[8,1,7,5,6,3,4,2]=>1110100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[3,2,4,6,5,7,1,8]=>[8,1,7,5,6,4,2,3]=>1101100
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[8,1,7,5,6,4,3,2]=>1111100
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>1100010
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[8,1,7,6,2,4,5,3]=>1110010
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>1111010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[8,1,7,6,3,4,5,2]=>1110010
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[2,4,5,3,6,7,1,8]=>[8,1,7,6,3,5,4,2]=>1111010
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[3,2,5,4,6,7,1,8]=>[8,1,7,6,4,5,2,3]=>1101010
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[8,1,7,6,4,5,3,2]=>1111010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>1100110
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[8,1,7,6,5,2,4,3]=>1110110
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[2,4,3,5,6,7,1,8]=>[8,1,7,6,5,3,4,2]=>1110110
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[8,1,7,6,5,4,2,3]=>1101110
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>1111110
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>1100000
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,6,7,5,4,3,2,8]=>[8,2,3,4,5,7,6,1]=>1100010
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>[8,2,3,4,7,6,5,1]=>1100110
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,4,7,6,5,3,2,8]=>[8,2,3,5,6,7,4,1]=>1101000
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[1,4,6,7,5,3,2,8]=>[8,2,3,5,7,6,4,1]=>1101010
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,5,4,7,6,3,2,8]=>[8,2,3,6,7,4,5,1]=>1101000
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[1,6,5,4,7,3,2,8]=>[8,2,3,7,4,5,6,1]=>1101000
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[8,2,3,7,5,6,4,1]=>1101100
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,5,4,6,7,3,2,8]=>[8,2,3,7,6,4,5,1]=>1101010
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[8,2,3,7,6,5,4,1]=>1101110
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>[8,2,4,5,6,7,3,1]=>1110000
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[8,2,4,5,7,6,3,1]=>1110010
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[8,2,4,6,7,5,3,1]=>1110100
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[1,3,6,5,7,4,2,8]=>[8,2,4,7,5,6,3,1]=>1110100
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[8,2,4,7,6,5,3,1]=>1110110
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[1,3,4,7,6,5,2,8]=>[8,2,5,6,7,4,3,1]=>1111000
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[8,2,5,7,6,4,3,1]=>1111010
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[8,2,6,7,4,5,3,1]=>1111000
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[8,2,6,7,5,3,4,1]=>1110100
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[8,2,6,7,5,4,3,1]=>1111100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,6,5,4,3,7,2,8]=>[8,2,7,3,4,5,6,1]=>1110000
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,5,6,4,3,7,2,8]=>[8,2,7,3,4,6,5,1]=>1110100
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[8,2,7,3,6,4,5,1]=>1111000
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>[8,2,7,3,6,5,4,1]=>1111100
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[8,2,7,4,5,6,3,1]=>1111000
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[8,2,7,4,6,5,3,1]=>1111100
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[8,2,7,5,6,3,4,1]=>1110100
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[1,3,4,6,5,7,2,8]=>[8,2,7,5,6,4,3,1]=>1111100
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[8,2,7,6,3,4,5,1]=>1110010
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,4,5,3,6,7,2,8]=>[8,2,7,6,3,5,4,1]=>1111010
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,3,5,4,6,7,2,8]=>[8,2,7,6,4,5,3,1]=>1111010
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[1,4,3,5,6,7,2,8]=>[8,2,7,6,5,3,4,1]=>1110110
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>1111110
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>[8,3,4,5,6,7,1,2]=>1010000
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[2,1,6,7,5,4,3,8]=>[8,3,4,5,7,6,1,2]=>1010010
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[2,1,5,7,6,4,3,8]=>[8,3,4,6,7,5,1,2]=>1010100
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[2,1,6,5,4,7,3,8]=>[8,3,7,4,5,6,1,2]=>1011000
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[2,1,5,6,4,7,3,8]=>[8,3,7,4,6,5,1,2]=>1011100
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[8,3,7,6,4,5,1,2]=>1011010
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[8,3,4,5,6,7,2,1]=>1110000
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,2,6,7,5,4,3,8]=>[8,3,4,5,7,6,2,1]=>1110010
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>[8,3,4,7,6,5,2,1]=>1110110
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[1,2,4,6,7,5,3,8]=>[8,3,5,7,6,4,2,1]=>1111010
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[1,2,6,5,4,7,3,8]=>[8,3,7,4,5,6,2,1]=>1111000
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[8,3,7,4,6,5,2,1]=>1111100
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[1,2,4,6,5,7,3,8]=>[8,3,7,5,6,4,2,1]=>1111100
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[8,3,7,6,5,4,2,1]=>1111110
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]=>[8,4,5,6,7,1,2,3]=>1001000
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[3,2,1,6,7,5,4,8]=>[8,4,5,7,6,1,2,3]=>1001010
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[8,4,6,7,5,1,2,3]=>1001100
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[8,4,7,6,5,1,2,3]=>1001110
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[8,4,5,7,6,1,3,2]=>1101010
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[2,3,1,5,7,6,4,8]=>[8,4,6,7,5,1,3,2]=>1101100
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[8,4,7,5,6,1,3,2]=>1101100
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[8,4,7,6,5,1,3,2]=>1101110
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[8,4,5,6,7,2,3,1]=>1101000
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[8,4,5,7,6,2,3,1]=>1101010
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[8,4,6,7,5,2,3,1]=>1101100
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[8,4,7,5,6,2,3,1]=>1101100
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[1,3,2,5,6,7,4,8]=>[8,4,7,6,5,2,3,1]=>1101110
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[2,1,3,5,7,6,4,8]=>[8,4,6,7,5,3,1,2]=>1011100
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[2,1,3,5,6,7,4,8]=>[8,4,7,6,5,3,1,2]=>1011110
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[8,4,5,6,7,3,2,1]=>1111000
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[8,4,5,7,6,3,2,1]=>1111010
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[8,4,6,7,5,3,2,1]=>1111100
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[8,4,7,5,6,3,2,1]=>1111100
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>1111110
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[8,5,6,7,1,2,3,4]=>1000100
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[8,5,7,6,1,2,3,4]=>1000110
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[3,4,2,1,6,7,5,8]=>[8,5,7,6,1,2,4,3]=>1010110
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[8,5,6,7,1,4,2,3]=>1100100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[8,5,7,6,1,4,2,3]=>1100110
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[8,5,6,7,1,4,3,2]=>1110100
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[8,5,7,6,1,4,3,2]=>1110110
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>1100100
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[8,5,7,6,2,3,4,1]=>1100110
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,3,4,2,7,6,5,8]=>[8,5,6,7,2,4,3,1]=>1110100
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>1110110
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]=>[8,5,6,7,3,4,1,2]=>1010100
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>[8,5,7,6,3,4,1,2]=>1010110
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]=>[8,5,6,7,3,4,2,1]=>1110100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[8,5,6,7,4,1,2,3]=>1001100
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[3,2,1,4,6,7,5,8]=>[8,5,7,6,4,1,2,3]=>1001110
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[2,3,1,4,7,6,5,8]=>[8,5,6,7,4,1,3,2]=>1101100
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[8,5,7,6,4,1,3,2]=>1101110
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>[8,5,6,7,4,2,3,1]=>1101100
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,3,2,4,6,7,5,8]=>[8,5,7,6,4,2,3,1]=>1101110
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[2,1,3,4,6,7,5,8]=>[8,5,7,6,4,3,1,2]=>1011110
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[8,5,6,7,4,3,2,1]=>1111100
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>1111110
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[8,6,7,1,2,3,4,5]=>1000010
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[4,3,5,2,1,7,6,8]=>[8,6,7,1,2,5,3,4]=>1010010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[8,6,7,1,4,5,2,3]=>1100010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[8,6,7,1,4,5,3,2]=>1110010
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[4,3,2,5,1,7,6,8]=>[8,6,7,1,5,2,3,4]=>1100010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[8,6,7,1,5,2,4,3]=>1110010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[8,6,7,1,5,3,4,2]=>1110010
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[8,6,7,1,5,4,3,2]=>1111010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[8,6,7,2,3,4,5,1]=>1100010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[8,6,7,2,3,5,4,1]=>1101010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[8,6,7,2,4,5,3,1]=>1110010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[8,6,7,2,5,3,4,1]=>1110010
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[8,6,7,2,5,4,3,1]=>1111010
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]=>[8,6,7,3,4,5,1,2]=>1010010
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]=>[8,6,7,3,4,5,2,1]=>1110010
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[1,2,4,5,3,7,6,8]=>[8,6,7,3,5,4,2,1]=>1111010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[8,6,7,4,5,1,2,3]=>1001010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[8,6,7,4,5,1,3,2]=>1101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>1101010
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[2,1,3,5,4,7,6,8]=>[8,6,7,4,5,3,1,2]=>1011010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1]=>1111010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[8,6,7,5,1,2,3,4]=>1000110
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[8,6,7,5,1,4,2,3]=>1100110
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[8,6,7,5,1,4,3,2]=>1110110
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[8,6,7,5,2,3,4,1]=>1100110
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[8,6,7,5,2,4,3,1]=>1110110
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]=>[8,6,7,5,3,4,2,1]=>1110110
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[2,3,1,4,5,7,6,8]=>[8,6,7,5,4,1,3,2]=>1101110
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>1101110
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>[8,6,7,5,4,3,1,2]=>1011110
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>1111110
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>1000001
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>1000101
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>1001001
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[8,7,1,2,3,6,5,4]=>1001101
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>[8,7,1,2,4,5,6,3]=>1010001
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[3,5,6,4,2,1,7,8]=>[8,7,1,2,4,6,5,3]=>1010101
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>1010001
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>1010101
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>1011101
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[8,7,1,3,6,5,4,2]=>1101101
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[3,2,6,5,4,1,7,8]=>[8,7,1,4,5,6,2,3]=>1100001
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[3,2,5,6,4,1,7,8]=>[8,7,1,4,6,5,2,3]=>1100101
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[2,3,6,5,4,1,7,8]=>[8,7,1,4,5,6,3,2]=>1110001
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[2,3,5,6,4,1,7,8]=>[8,7,1,4,6,5,3,2]=>1110101
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[8,7,1,5,6,2,3,4]=>1100001
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[8,7,1,5,6,2,4,3]=>1110001
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[8,7,1,5,6,4,3,2]=>1111001
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>1100001
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>1101001
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>[8,7,1,6,2,4,5,3]=>1110001
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[8,7,1,6,2,5,3,4]=>1110001
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>1111001
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[2,4,5,3,6,1,7,8]=>[8,7,1,6,3,5,4,2]=>1111001
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[3,2,5,4,6,1,7,8]=>[8,7,1,6,4,5,2,3]=>1101001
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[8,7,1,6,4,5,3,2]=>1111001
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>1100101
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[8,7,1,6,5,2,4,3]=>1110101
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>1111101
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[8,7,2,3,4,5,6,1]=>1100001
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>[8,7,2,3,6,5,4,1]=>1101101
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[8,7,2,4,5,6,3,1]=>1110001
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[8,7,2,4,6,5,3,1]=>1110101
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,3,4,6,5,2,7,8]=>[8,7,2,5,6,4,3,1]=>1111001
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,4,5,3,6,2,7,8]=>[8,7,2,6,3,5,4,1]=>1111001
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>[8,7,2,6,4,5,3,1]=>1111001
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,3,4,5,6,2,7,8]=>[8,7,2,6,5,4,3,1]=>1111101
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[2,1,6,5,4,3,7,8]=>[8,7,3,4,5,6,1,2]=>1010001
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[8,7,3,4,6,5,1,2]=>1010101
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>1110001
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[8,7,3,4,6,5,2,1]=>1110101
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[8,7,3,5,6,4,2,1]=>1111001
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,2,5,4,6,3,7,8]=>[8,7,3,6,4,5,2,1]=>1111001
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>1111101
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]=>[8,7,4,5,6,1,2,3]=>1001001
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>[8,7,4,5,6,1,3,2]=>1101001
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[2,3,1,5,6,4,7,8]=>[8,7,4,6,5,1,3,2]=>1101101
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[8,7,4,5,6,2,3,1]=>1101001
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>[8,7,4,6,5,2,3,1]=>1101101
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[2,1,3,5,6,4,7,8]=>[8,7,4,6,5,3,1,2]=>1011101
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[8,7,4,5,6,3,2,1]=>1111001
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[8,7,4,6,5,3,2,1]=>1111101
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[8,7,5,6,1,2,3,4]=>1000101
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[3,4,2,1,6,5,7,8]=>[8,7,5,6,1,2,4,3]=>1010101
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[2,4,3,1,6,5,7,8]=>[8,7,5,6,1,3,4,2]=>1100101
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[8,7,5,6,1,4,2,3]=>1100101
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[8,7,5,6,1,4,3,2]=>1110101
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[8,7,5,6,2,3,4,1]=>1100101
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[8,7,5,6,3,4,1,2]=>1010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>1110101
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[2,3,1,4,6,5,7,8]=>[8,7,5,6,4,1,3,2]=>1101101
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[8,7,5,6,4,2,3,1]=>1101101
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[8,7,5,6,4,3,1,2]=>1011101
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>1111101
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>1000011
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>1001011
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[8,7,6,1,2,4,5,3]=>1010011
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>1010011
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>1011011
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[8,7,6,1,3,4,5,2]=>1100011
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[8,7,6,1,3,5,4,2]=>1101011
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[8,7,6,1,4,5,2,3]=>1100011
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[8,7,6,1,4,5,3,2]=>1110011
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>1100011
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>1110011
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[8,7,6,1,5,3,4,2]=>1110011
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>1101011
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>1111011
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[8,7,6,2,3,4,5,1]=>1100011
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>[8,7,6,2,3,5,4,1]=>1101011
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[8,7,6,2,4,5,3,1]=>1110011
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,4,3,5,2,6,7,8]=>[8,7,6,2,5,3,4,1]=>1110011
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[8,7,6,2,5,4,3,1]=>1111011
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[8,7,6,3,4,5,1,2]=>1010011
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[8,7,6,3,5,4,1,2]=>1011011
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[8,7,6,3,4,5,2,1]=>1110011
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[8,7,6,3,5,4,2,1]=>1111011
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]=>[8,7,6,4,5,1,2,3]=>1001011
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[8,7,6,4,5,1,3,2]=>1101011
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1]=>1101011
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]=>[8,7,6,4,5,3,1,2]=>1011011
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>1111011
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>1000111
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>1010111
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[8,7,6,5,1,3,4,2]=>1100111
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>1100111
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>1110111
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[8,7,6,5,2,3,4,1]=>1100111
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>1110111
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[8,7,6,5,3,4,1,2]=>1010111
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1]=>1110111
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>1001111
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>1101111
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1]=>1101111
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>1011111
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>00000001
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,9,8,7]=>00000011
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[1,2,3,4,5,9,8,7,6]=>00000111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[1,2,3,4,9,8,7,6,5]=>00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[1,2,3,9,8,7,6,5,4]=>00011111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[1,2,9,8,7,6,5,4,3]=>00111111
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2]=>01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,9,7]=>00000010
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[6,8,9,7,5,4,3,2,1]=>[1,2,3,4,5,7,9,8,6]=>00000101
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[1,2,3,4,5,6,10,9,8,7]=>000000111
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[5,7,8,9,6,4,3,2,1]=>[1,2,3,4,6,9,8,7,5]=>00001011
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[4,6,7,8,9,5,3,2,1]=>[1,2,3,5,9,8,7,6,4]=>00010111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[1,2,3,4,10,9,8,7,6,5]=>000011111
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[3,5,6,7,8,9,4,2,1]=>[1,2,4,9,8,7,6,5,3]=>00101111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[1,2,3,10,9,8,7,6,5,4]=>000111111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[2,4,5,6,7,8,9,3,1]=>[1,3,9,8,7,6,5,4,2]=>01011111
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[1,2,10,9,8,7,6,5,4,3]=>001111111
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[2,9,8,7,6,5,4,3,1]=>10111111
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,9,7,8]=>00000010
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[1,2,3,4,5,9,6,7,8]=>00000100
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[1,2,3,4,9,5,6,7,8]=>00001000
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[1,2,3,9,4,5,6,7,8]=>00010000
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[1,2,9,3,4,5,6,7,8]=>00100000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[1,9,2,3,4,5,6,7,8]=>01000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8]=>10000000
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,10,8,9]=>000000010
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[6,8,7,9,5,4,3,2,1]=>[1,2,3,4,5,9,7,8,6]=>00000110
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[1,2,3,4,5,6,10,7,8,9]=>000000100
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[5,8,7,6,9,4,3,2,1]=>[1,2,3,4,9,6,7,8,5]=>00001100
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[1,2,3,4,5,10,6,7,8,9]=>000001000
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[4,8,7,6,5,9,3,2,1]=>[1,2,3,9,5,6,7,8,4]=>00011000
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[1,2,3,4,10,5,6,7,8,9]=>000010000
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[3,8,7,6,5,4,9,2,1]=>[1,2,9,4,5,6,7,8,3]=>00110000
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[1,2,3,10,4,5,6,7,8,9]=>000100000
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[2,8,7,6,5,4,3,9,1]=>[1,9,3,4,5,6,7,8,2]=>01100000
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[1,2,10,3,4,5,6,7,8,9]=>001000000
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>[9,2,3,4,5,6,7,8,1]=>11000000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[10,1,9,2,8,3,7,4,6,5]=>111110000
[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,9,8,1,10]=>[10,1,8,9,6,7,4,5,2,3]=>110101000
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>101010100
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>10101010100
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1]=>11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,2,1]=>111111110
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,1,2]=>10111110
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,2,3]=>01011111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,11,9,8,7,6,5,4,3,2,1]=>1111111110
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,1,2]=>101111110
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]=>[8,9,7,6,5,4,2,3,1]=>11011110
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[2,3,1,4,5,6,7,9,8]=>[8,9,7,6,5,4,1,3,2]=>11011110
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[1,9,8,7,6,5,2,4,3]=>01101111
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,2,3]=>010111111
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[7,9,8,6,5,4,3,2,1]=>11111101
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[6,9,8,7,5,4,3,2,1]=>11111011
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[5,9,8,7,6,4,3,2,1]=>11110111
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[4,9,8,7,6,5,3,2,1]=>11101111
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[3,9,8,7,6,5,4,2,1]=>11011111
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[7,8,9,6,5,4,3,2,1]=>11111100
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[8,10,9,7,6,5,4,3,2,1]=>111111101
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>[6,9,7,8,5,4,3,2,1]=>11111010
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[7,10,9,8,6,5,4,3,2,1]=>111111011
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,4,7,6,8,9,5]=>[5,9,8,6,7,4,3,2,1]=>11110101
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[6,10,9,8,7,5,4,3,2,1]=>111110111
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,3,6,5,7,8,9,4]=>[4,9,8,7,5,6,3,2,1]=>11101011
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[5,10,9,8,7,6,4,3,2,1]=>111101111
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[1,2,5,4,6,7,8,9,3]=>[3,9,8,7,6,4,5,2,1]=>11010111
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[4,10,9,8,7,6,5,3,2,1]=>111011111
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>[2,9,8,7,6,5,3,4,1]=>10101111
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[3,10,9,8,7,6,5,4,2,1]=>110111111
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[2,10,9,8,7,6,5,4,3,1]=>101111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,1]=>10000000
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,8,7]=>10000010
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[2,3,4,5,6,7,9,8,1]=>10000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,10,1]=>100000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,9,8]=>100000010
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[9,1,2,3,4,5,8,6,7]=>10000100
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>[2,3,4,5,6,9,7,8,1]=>10000010
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,10,9,1]=>100000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,10,11,1]=>1000000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,1,2]=>10000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>[4,5,6,7,8,9,1,2,3]=>10000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>[5,6,7,8,9,1,2,3,4]=>10000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>[6,7,8,9,1,2,3,4,5]=>10000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>[7,8,9,1,2,3,4,5,6]=>10000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[8,9,1,2,3,4,5,6,7]=>10000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,2,1]=>11000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,10,1,2]=>100000000
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>[4,5,6,7,8,9,1,3,2]=>11000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>[4,5,6,7,8,9,10,1,2,3]=>100000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[5,6,7,8,9,10,1,2,3,4]=>100000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]=>[6,7,8,9,10,1,2,3,4,5]=>100000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[7,8,9,10,1,2,3,4,5,6]=>100000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>[8,9,10,1,2,3,4,5,6,7]=>100000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[9,10,1,2,3,4,5,6,7,8]=>100000000
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[9,8,1,2,3,4,5,6,7]=>10000001
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[9,8,7,1,2,3,4,5,6]=>10000011
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[9,8,7,6,1,2,3,4,5]=>10000111
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[9,8,7,6,5,1,2,3,4]=>10001111
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3]=>10011111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2]=>10111111
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[10,9,1,2,3,4,5,6,7,8]=>100000001
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[10,9,8,1,2,3,4,5,6,7]=>100000011
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,7,6,5,4,3,2,8,9]=>[9,8,2,3,4,5,6,7,1]=>11000001
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[10,9,8,7,1,2,3,4,5,6]=>100000111
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>100001111
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,2,3,4]=>100011111
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>[9,8,7,6,5,2,3,4,1]=>11001111
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,2,3]=>100111111
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,3,1]=>11011111
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2]=>101111111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[4,9,8,7,6,5,3,2,1]=>[1,2,3,5,6,7,8,9,4]=>00010000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[3,9,8,7,6,5,4,2,1]=>[1,2,4,5,6,7,8,9,3]=>00100000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[1,3,4,5,6,7,8,9,2]=>01000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[6,10,9,8,7,5,4,3,2,1]=>[1,2,3,4,5,7,8,9,10,6]=>000001000
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[2,4,6,8,10,9,7,5,3,1]=>[1,3,5,7,9,10,8,6,4,2]=>010101010
[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,8,7,1,10,9]=>[9,10,1,7,8,5,6,3,4,2]=>111010000
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>[1,8,9,7,6,5,4,3,2]=>01111110
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,1,2]=>1011111111
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]=>[9,7,8,6,5,4,3,1,2]=>10111110
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[2,3,4,5,6,8,9,7,1]=>[1,7,9,8,6,5,4,3,2]=>01111101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>[1,9,10,8,7,6,5,4,3,2]=>011111110
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]=>[9,8,7,6,5,3,4,1,2]=>10101111
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]=>[9,7,8,1,2,3,4,5,6]=>10000010
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]=>[7,8,6,9,5,4,3,2,1]=>[1,2,3,4,5,9,6,8,7]=>00000110
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[1,9,2,8,7,6,5,4,3]=>01111110
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[9,1,8,7,6,5,4,3,2]=>11111110
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,3,2]=>11011111
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[9,8,1,7,6,5,4,3,2]=>11111101
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,3,2]=>110111111
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[2,4,3,1,5,6,7,8,9]=>[9,8,7,6,5,1,3,4,2]=>11001111
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[2,3,5,4,1,6,7,8,9]=>[9,8,7,6,1,4,5,3,2]=>11100111
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[2,3,4,6,5,1,7,8,9]=>[9,8,7,1,5,6,4,3,2]=>11110011
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[2,3,4,5,7,6,1,8,9]=>[9,8,1,6,7,5,4,3,2]=>11111001
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[2,3,4,5,6,8,7,1,9]=>[9,1,7,8,6,5,4,3,2]=>11111100
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[10,1,9,8,7,6,5,4,3,2]=>111111110
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]=>[9,8,7,6,5,3,4,2,1]=>11101111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>11110111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>11111011
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>[9,7,8,6,5,4,3,2,1]=>11111110
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,3,1]=>110111111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>111110111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>111111011
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[10,8,9,7,6,5,4,3,2,1]=>111111110
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,3,4,5,6,7,9,8,2]=>[2,8,9,7,6,5,4,3,1]=>10111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[7,6,5,4,3,2,9,8,1]=>[1,8,9,2,3,4,5,6,7]=>01000000
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1]=>[1,9,8,7,6,5,2,3,4]=>01001111
[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]=>[6,5,4,3,2,7,8,9,10,1]=>[1,10,9,8,7,2,3,4,5,6]=>010000111
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>[8,9,2,3,4,5,6,7,1]=>11000000
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,10,2,1]=>110000000
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]=>[4,5,6,7,8,9,2,3,1]=>11000000
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>[9,3,4,5,6,7,8,1,2]=>10100000
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[10,2,3,4,5,6,7,8,9,1]=>110000000
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>[9,8,7,6,4,5,2,3,1]=>11010111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[8,7,6,5,4,3,2,10,9,1]=>[1,9,10,2,3,4,5,6,7,8]=>010000000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>[3,9,8,7,6,5,4,1,2]=>10011111
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[1,3,4,5,6,7,8,2,9]=>[9,2,8,7,6,5,4,3,1]=>11111110
[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]=>[6,7,8,5,4,3,2,9,1]=>[1,9,2,3,4,5,8,7,6]=>01000110
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>[8,9,10,7,6,5,4,3,2,1]=>111111100
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[9,1,2,3,4,5,8,7,6]=>10000110
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,9,8,7]=>100000110
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>[6,7,8,9,5,4,3,2,1]=>11111000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>[5,6,7,8,9,4,3,2,1]=>11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]=>[4,5,6,7,8,9,3,2,1]=>11100000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>[8,9,6,7,5,4,3,2,1]=>11111100
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]=>[7,8,9,10,6,5,4,3,2,1]=>111111000
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]=>[6,7,8,9,10,5,4,3,2,1]=>111110000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]=>[5,6,7,8,9,10,4,3,2,1]=>111100000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]=>[4,5,6,7,8,9,10,3,2,1]=>111000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]=>[9,10,7,8,6,5,4,3,2,1]=>111111100
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,11,9,10]=>0000000010
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[1,9,8,10,7,6,5,4,3,2]=>[2,3,4,5,6,7,10,8,9,1]=>100000010
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[2,8,9,7,6,5,4,3,1]=>[1,3,4,5,6,7,9,8,2]=>01000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[1,9,2,3,4,5,6,8,7]=>01000010
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[9,1,8,2,3,4,5,6,7]=>11000000
[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]=>[5,8,7,6,4,3,2,1,9]=>[9,1,2,3,4,6,7,8,5]=>10001000
[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]=>[6,5,8,7,4,3,2,1,9]=>[9,1,2,3,4,7,8,5,6]=>10001000
[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[9,1,2,3,4,8,5,6,7]=>10001000
[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]=>[4,3,2,9,8,7,6,5,1]=>[1,5,6,7,8,9,2,3,4]=>01000000
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,5,8,7,6,9]=>[9,6,7,8,5,4,3,2,1]=>11111100
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]=>[9,6,7,8,1,2,3,4,5]=>10000100
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[1,4,5,6,7,8,9,3,2]=>01100000
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,8,7,6,5,4,3,9,2]=>[2,9,3,4,5,6,7,8,1]=>10100000
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[9,1,3,4,5,6,7,8,2]=>11000000
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[8,9,1,7,6,5,4,3,2]=>11111100
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[9,8,7,6,5,2,4,3,1]=>11101111
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9]=>[9,3,4,5,6,7,8,2,1]=>11100000
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[11,9,10,8,7,6,5,4,3,2,1]=>1111111110
[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]=>[2,3,1,4,5,6,8,7,9]=>[9,7,8,6,5,4,1,3,2]=>11011110
[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]]=>[2,1,3,4,6,7,8,9,5]=>[5,9,8,7,6,4,3,1,2]=>10110111
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]=>[9,10,11,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,11,10,9]=>0000000011
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
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
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