Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[2,1]=>1
[[.,.],.]=>[1,2]=>[1,2]=>0
[.,[.,[.,.]]]=>[3,2,1]=>[3,1,2]=>10
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>11
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>01
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>10
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>00
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,1,2,3]=>100
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,1,3,2]=>101
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,1,3]=>110
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>111
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>101
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,4,2,3]=>010
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>011
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>101
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>001
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1,2,4]=>100
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>110
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>010
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>100
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>000
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>1000
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,1,2,4,3]=>1001
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,1,3,2,4]=>1010
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,1,4,3,2]=>1011
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,1,3,4,2]=>1001
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,2,1,3,4]=>1100
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,1,4,3]=>1101
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,1,4]=>1110
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,1,4]=>1010
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,4,2,3,1]=>1101
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>1111
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>1011
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>1101
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>1001
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,5,2,3,4]=>0100
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,5,2,4,3]=>0101
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,5,3,2,4]=>0110
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>0111
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>0101
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,5,3,4]=>1010
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>1011
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,5,3,4]=>0010
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>0011
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,1,2,5,4]=>1001
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>1101
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>0101
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>1001
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>0001
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1,2,3,5]=>1000
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1,3,2,5]=>1010
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,1,3,5]=>1100
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>1110
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>1010
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,2,3,5]=>0100
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>0110
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>1010
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>0010
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,2,4,5]=>1000
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>1100
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>0100
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>10000
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>10001
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,1,2,4,3,5]=>10010
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>10011
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>10001
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,1,3,2,4,5]=>10100
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,1,3,2,5,4]=>10101
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,1,4,3,2,5]=>10110
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,1,3,4,2,5]=>10010
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>10101
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>10111
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,1,3,5,4,2]=>10011
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>10101
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>10001
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,2,1,3,4,5]=>11000
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,2,1,3,5,4]=>11001
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,2,1,4,3,5]=>11010
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,2,1,5,4,3]=>11011
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,1,4,5,3]=>11001
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,3,2,1,4,5]=>11100
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,1,5,4]=>11101
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,2,3,1,4,5]=>10100
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,1,5,4]=>10101
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,2,3,1,5]=>11010
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,3,2,1,5]=>11110
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,2,4,3,1,5]=>10110
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,1,5]=>11010
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,1,5]=>10010
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>11001
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>11011
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,5,3,2,4,1]=>11101
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>11111
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>11011
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,5,3,4,1]=>10101
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>10111
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>11011
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>10011
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>11001
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>11101
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>10101
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>11001
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>10001
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>01000
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,6,2,3,5,4]=>01001
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,6,2,4,3,5]=>01010
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,6,2,5,4,3]=>01011
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,6,2,4,5,3]=>01001
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,6,3,2,4,5]=>01100
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,6,3,2,5,4]=>01101
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,6,4,3,2,5]=>01110
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,6,3,4,2,5]=>01010
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,5,3,4,2]=>01101
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>01111
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>01011
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>01101
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>01001
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,6,3,4,5]=>10100
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>10101
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,6,4,3,5]=>10110
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>10111
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>10101
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>00100
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>00101
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,6,4,3,5]=>00110
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>00111
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>00101
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,1,2,6,4,5]=>10010
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,1,2,6,5,4]=>10011
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,6,4,5]=>11010
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>11011
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>01010
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>01011
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,6,4,5]=>10010
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>10011
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>00010
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>00011
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,1,2,3,6,5]=>10001
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>10101
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[4,2,1,3,6,5]=>11001
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>11101
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>10101
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,2,3,6,5]=>01001
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>01101
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>10101
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>00101
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,1,2,4,6,5]=>10001
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>11001
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>01001
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>10001
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>00001
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>10000
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>10010
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,1,3,2,4,6]=>10100
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>10110
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>10010
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,2,1,3,4,6]=>11000
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,2,1,4,3,6]=>11010
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,1,4,6]=>11100
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,1,4,6]=>10100
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>11010
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>11110
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>10110
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>11010
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>10010
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,5,2,3,4,6]=>01000
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>01010
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,5,3,2,4,6]=>01100
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>01110
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>01010
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,5,3,4,6]=>10100
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>10110
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,5,3,4,6]=>00100
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>00110
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,1,2,5,4,6]=>10010
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>11010
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>01010
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>10010
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>00010
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>10000
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>10100
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,1,3,5,6]=>11000
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>11100
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>10100
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,4,2,3,5,6]=>01000
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>01100
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>10100
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>00100
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>10000
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>100000
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,6,5]=>100001
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,1,2,3,5,4,6]=>100010
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,1,2,3,6,5,4]=>100011
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,1,2,3,5,6,4]=>100001
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,1,2,4,3,5,6]=>100100
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,1,2,4,3,6,5]=>100101
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,1,2,5,4,3,6]=>100110
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,1,2,4,5,3,6]=>100010
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,1,2,6,4,5,3]=>100101
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,1,2,6,5,4,3]=>100111
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,1,2,4,6,5,3]=>100011
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,1,2,5,4,6,3]=>100101
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,1,2,4,5,6,3]=>100001
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,1,3,2,4,5,6]=>101000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,1,3,2,4,6,5]=>101001
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,1,3,2,5,4,6]=>101010
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,1,3,2,6,5,4]=>101011
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,1,3,2,5,6,4]=>101001
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,1,4,3,2,5,6]=>101100
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,1,4,3,2,6,5]=>101101
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,1,3,4,2,5,6]=>100100
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,1,3,4,2,6,5]=>100101
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,1,5,3,4,2,6]=>101010
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,1,5,4,3,2,6]=>101110
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,1,3,5,4,2,6]=>100110
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,1,4,3,5,2,6]=>101010
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,1,3,4,5,2,6]=>100010
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,1,6,3,4,5,2]=>101001
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,1,6,3,5,4,2]=>101011
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,1,6,4,3,5,2]=>101101
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,1,6,5,4,3,2]=>101111
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,1,6,4,5,3,2]=>101011
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,1,3,6,4,5,2]=>100101
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,1,3,6,5,4,2]=>100111
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,1,4,3,6,5,2]=>101011
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,1,3,4,6,5,2]=>100011
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,1,5,3,4,6,2]=>101001
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,1,5,4,3,6,2]=>101101
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,1,3,5,4,6,2]=>100101
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,1,4,3,5,6,2]=>101001
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,1,3,4,5,6,2]=>100001
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,2,1,3,4,5,6]=>110000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,2,1,3,4,6,5]=>110001
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,2,1,3,5,4,6]=>110010
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,2,1,3,6,5,4]=>110011
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,2,1,3,5,6,4]=>110001
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,2,1,4,3,5,6]=>110100
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,2,1,4,3,6,5]=>110101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,2,1,5,4,3,6]=>110110
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,2,1,4,5,3,6]=>110010
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,2,1,6,4,5,3]=>110101
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,2,1,6,5,4,3]=>110111
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,2,1,4,6,5,3]=>110011
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,2,1,5,4,6,3]=>110101
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,2,1,4,5,6,3]=>110001
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,3,2,1,4,5,6]=>111000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,3,2,1,4,6,5]=>111001
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,3,2,1,5,4,6]=>111010
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,3,2,1,6,5,4]=>111011
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,3,2,1,5,6,4]=>111001
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,2,3,1,4,5,6]=>101000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,2,3,1,4,6,5]=>101001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,2,3,1,5,4,6]=>101010
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,2,3,1,6,5,4]=>101011
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,2,3,1,5,6,4]=>101001
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,4,2,3,1,5,6]=>110100
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,4,2,3,1,6,5]=>110101
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,4,3,2,1,5,6]=>111100
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,4,3,2,1,6,5]=>111101
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,2,4,3,1,5,6]=>101100
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,2,4,3,1,6,5]=>101101
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,3,2,4,1,5,6]=>110100
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,3,2,4,1,6,5]=>110101
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,2,3,4,1,5,6]=>100100
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,2,3,4,1,6,5]=>100101
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,2,3,4,1,6]=>110010
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,5,2,4,3,1,6]=>110110
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,2,4,1,6]=>111010
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,5,4,3,2,1,6]=>111110
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,5,3,4,2,1,6]=>110110
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,2,5,3,4,1,6]=>101010
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,2,5,4,3,1,6]=>101110
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,3,2,5,4,1,6]=>110110
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,2,3,5,4,1,6]=>100110
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,2,3,5,1,6]=>110010
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,4,3,2,5,1,6]=>111010
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,2,4,3,5,1,6]=>101010
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,1,6]=>110010
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,1,6]=>100010
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,6,2,3,4,5,1]=>110001
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,6,2,3,5,4,1]=>110011
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,6,2,4,3,5,1]=>110101
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,6,2,5,4,3,1]=>110111
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,6,2,4,5,3,1]=>110011
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,6,3,2,4,5,1]=>111001
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,6,3,2,5,4,1]=>111011
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,6,4,3,2,5,1]=>111101
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,6,3,4,2,5,1]=>110101
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,5,3,4,2,1]=>111011
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>111111
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>110111
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>111011
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>110011
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,2,6,3,4,5,1]=>101001
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,2,6,3,5,4,1]=>101011
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,2,6,4,3,5,1]=>101101
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>101111
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>101011
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,3,2,6,4,5,1]=>110101
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>110111
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,2,3,6,4,5,1]=>100101
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>100111
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,4,2,3,6,5,1]=>110011
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>111011
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>101011
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>110011
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>100011
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,5,2,3,4,6,1]=>110001
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,5,2,4,3,6,1]=>110101
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,5,3,2,4,6,1]=>111001
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>111101
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>110101
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,2,5,3,4,6,1]=>101001
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>101101
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>110101
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>100101
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,4,2,3,5,6,1]=>110001
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>111001
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>101001
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>110001
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>100001
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>010000
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,7,2,3,4,6,5]=>010001
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,7,2,3,5,4,6]=>010010
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,7,2,3,6,5,4]=>010011
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,7,2,3,5,6,4]=>010001
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,7,2,4,3,5,6]=>010100
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,7,2,4,3,6,5]=>010101
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,7,2,5,4,3,6]=>010110
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,7,2,4,5,3,6]=>010010
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,7,2,6,4,5,3]=>010101
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,7,2,6,5,4,3]=>010111
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,7,2,4,6,5,3]=>010011
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,7,2,5,4,6,3]=>010101
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,7,2,4,5,6,3]=>010001
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,7,3,2,4,5,6]=>011000
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,7,3,2,4,6,5]=>011001
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,7,3,2,5,4,6]=>011010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,7,3,2,6,5,4]=>011011
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,7,3,2,5,6,4]=>011001
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,7,4,3,2,5,6]=>011100
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,7,4,3,2,6,5]=>011101
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,7,3,4,2,5,6]=>010100
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,7,3,4,2,6,5]=>010101
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,7,5,3,4,2,6]=>011010
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,7,5,4,3,2,6]=>011110
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,7,3,5,4,2,6]=>010110
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,7,4,3,5,2,6]=>011010
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,7,3,4,5,2,6]=>010010
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,6,3,4,5,2]=>011001
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,6,3,5,4,2]=>011011
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,6,4,3,5,2]=>011101
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>011111
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>011011
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,3,6,4,5,2]=>010101
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>010111
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>011011
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>010011
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,5,3,4,6,2]=>011001
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>011101
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>010101
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>011001
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>010001
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,7,3,4,5,6]=>101000
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,7,3,4,6,5]=>101001
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,7,3,5,4,6]=>101010
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,7,3,6,5,4]=>101011
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,7,3,5,6,4]=>101001
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,7,4,3,5,6]=>101100
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,7,4,3,6,5]=>101101
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,7,5,4,3,6]=>101110
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,7,4,5,3,6]=>101010
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,6,4,5,3]=>101101
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>101111
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>101011
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>101101
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>101001
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,7,3,4,5,6]=>001000
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,7,3,4,6,5]=>001001
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,7,3,5,4,6]=>001010
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,7,3,6,5,4]=>001011
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,7,3,5,6,4]=>001001
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,7,4,3,5,6]=>001100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,7,4,3,6,5]=>001101
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,7,5,4,3,6]=>001110
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,7,4,5,3,6]=>001010
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,6,4,5,3]=>001101
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>001111
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>001011
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>001101
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>001001
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[3,1,2,7,4,5,6]=>100100
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,1,2,7,4,6,5]=>100101
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,1,2,7,5,4,6]=>100110
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,1,2,7,6,5,4]=>100111
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[3,1,2,7,5,6,4]=>100101
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,7,4,5,6]=>110100
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,2,1,7,4,6,5]=>110101
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,2,1,7,5,4,6]=>110110
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>110111
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>110101
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6]=>010100
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,7,4,6,5]=>010101
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,7,5,4,6]=>010110
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>010111
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>010101
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,7,4,5,6]=>100100
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,7,4,6,5]=>100101
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,7,5,4,6]=>100110
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>100111
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>100101
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6]=>000100
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,7,4,6,5]=>000101
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,7,5,4,6]=>000110
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>000111
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>000101
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[4,1,2,3,7,5,6]=>100010
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[4,1,2,3,7,6,5]=>100011
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[4,1,3,2,7,5,6]=>101010
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[4,1,3,2,7,6,5]=>101011
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[4,2,1,3,7,5,6]=>110010
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[4,2,1,3,7,6,5]=>110011
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,3,2,1,7,5,6]=>111010
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>111011
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,3,1,7,5,6]=>101010
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>101011
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,4,2,3,7,5,6]=>010010
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,4,2,3,7,6,5]=>010011
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,3,2,7,5,6]=>011010
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>011011
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,5,6]=>101010
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>101011
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,5,6]=>001010
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>001011
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[3,1,2,4,7,5,6]=>100010
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[3,1,2,4,7,6,5]=>100011
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,2,1,4,7,5,6]=>110010
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>110011
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,5,6]=>010010
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>010011
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,5,6]=>100010
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>100011
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,5,6]=>000010
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>000011
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[5,1,2,3,4,7,6]=>100001
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[5,1,2,4,3,7,6]=>100101
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[5,1,3,2,4,7,6]=>101001
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[5,1,4,3,2,7,6]=>101101
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[5,1,3,4,2,7,6]=>100101
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[5,2,1,3,4,7,6]=>110001
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[5,2,1,4,3,7,6]=>110101
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[5,3,2,1,4,7,6]=>111001
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[5,2,3,1,4,7,6]=>101001
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,4,2,3,1,7,6]=>110101
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>111101
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>101101
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>110101
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>100101
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,5,2,3,4,7,6]=>010001
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,5,2,4,3,7,6]=>010101
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,5,3,2,4,7,6]=>011001
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>011101
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>010101
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,5,3,4,7,6]=>101001
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>101101
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,5,3,4,7,6]=>001001
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>001101
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>100101
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>110101
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>010101
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>100101
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>000101
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[4,1,2,3,5,7,6]=>100001
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[4,1,3,2,5,7,6]=>101001
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[4,2,1,3,5,7,6]=>110001
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>111001
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>101001
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,4,2,3,5,7,6]=>010001
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>011001
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>101001
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>001001
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>100001
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>110001
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>010001
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>100001
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>000001
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>100000
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,1,2,3,5,4,7]=>100010
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,1,2,4,3,5,7]=>100100
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,1,2,5,4,3,7]=>100110
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,1,2,4,5,3,7]=>100010
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,1,3,2,4,5,7]=>101000
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,1,3,2,5,4,7]=>101010
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,1,4,3,2,5,7]=>101100
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,1,3,4,2,5,7]=>100100
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,1,5,3,4,2,7]=>101010
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,1,5,4,3,2,7]=>101110
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,1,3,5,4,2,7]=>100110
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,1,4,3,5,2,7]=>101010
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,1,3,4,5,2,7]=>100010
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,2,1,3,4,5,7]=>110000
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,2,1,3,5,4,7]=>110010
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,2,1,4,3,5,7]=>110100
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,2,1,5,4,3,7]=>110110
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,2,1,4,5,3,7]=>110010
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,3,2,1,4,5,7]=>111000
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,3,2,1,5,4,7]=>111010
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,2,3,1,4,5,7]=>101000
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,3,1,5,4,7]=>101010
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,2,3,1,5,7]=>110100
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,4,3,2,1,5,7]=>111100
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,2,4,3,1,5,7]=>101100
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,1,5,7]=>110100
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,1,5,7]=>100100
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,5,2,3,4,1,7]=>110010
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,5,2,4,3,1,7]=>110110
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,5,3,2,4,1,7]=>111010
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>111110
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>110110
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,2,5,3,4,1,7]=>101010
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>101110
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>110110
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>100110
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,4,2,3,5,1,7]=>110010
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>111010
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>101010
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>110010
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>100010
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,6,2,3,4,5,7]=>010000
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,6,2,3,5,4,7]=>010010
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,6,2,4,3,5,7]=>010100
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,6,2,5,4,3,7]=>010110
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,6,2,4,5,3,7]=>010010
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,6,3,2,4,5,7]=>011000
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,6,3,2,5,4,7]=>011010
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,6,4,3,2,5,7]=>011100
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,6,3,4,2,5,7]=>010100
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,5,3,4,2,7]=>011010
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>011110
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>010110
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>011010
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>010010
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,6,3,4,5,7]=>101000
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,6,3,5,4,7]=>101010
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,6,4,3,5,7]=>101100
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>101110
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>101010
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,6,3,4,5,7]=>001000
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,6,3,5,4,7]=>001010
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,6,4,3,5,7]=>001100
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>001110
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>001010
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[3,1,2,6,4,5,7]=>100100
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[3,1,2,6,5,4,7]=>100110
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,6,4,5,7]=>110100
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>110110
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,6,4,5,7]=>010100
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>010110
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,6,4,5,7]=>100100
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>100110
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,6,4,5,7]=>000100
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>000110
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[4,1,2,3,6,5,7]=>100010
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[4,1,3,2,6,5,7]=>101010
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[4,2,1,3,6,5,7]=>110010
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>111010
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>101010
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,4,2,3,6,5,7]=>010010
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>011010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>001010
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>100010
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>110010
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>010010
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>100010
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>000010
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>100000
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,1,2,4,3,6,7]=>100100
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,1,3,2,4,6,7]=>101000
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,1,4,3,2,6,7]=>101100
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,1,3,4,2,6,7]=>100100
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,2,1,3,4,6,7]=>110000
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,2,1,4,3,6,7]=>110100
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,1,4,6,7]=>111000
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,1,4,6,7]=>101000
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>110100
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>101100
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>110100
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>100100
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,5,2,3,4,6,7]=>010000
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,5,2,4,3,6,7]=>010100
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,5,3,2,4,6,7]=>011000
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>011100
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>010100
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,5,3,4,6,7]=>101000
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>101100
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,5,3,4,6,7]=>001000
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>001100
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>100100
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>110100
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>010100
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>100100
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>100000
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,1,3,5,6,7]=>110000
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>101000
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,4,2,3,5,6,7]=>010000
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>101000
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7]=>1000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,1,2,3,4,5,7,6]=>1000001
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[8,1,2,3,4,6,5,7]=>1000010
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,1,2,3,4,7,6,5]=>1000011
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,1,2,3,4,6,7,5]=>1000001
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,1,2,3,5,4,6,7]=>1000100
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[8,1,2,3,5,4,7,6]=>1000101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,1,2,3,6,5,4,7]=>1000110
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,1,2,3,5,6,4,7]=>1000010
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,1,2,3,7,5,6,4]=>1000101
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,1,2,3,7,6,5,4]=>1000111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[8,1,2,3,5,7,6,4]=>1000011
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,1,2,3,6,5,7,4]=>1000101
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,1,2,3,5,6,7,4]=>1000001
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,1,2,4,3,5,6,7]=>1001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[8,1,2,4,3,5,7,6]=>1001001
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,1,2,4,3,6,5,7]=>1001010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[8,1,2,4,3,7,6,5]=>1001011
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[8,1,2,4,3,6,7,5]=>1001001
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[8,1,2,5,4,3,6,7]=>1001100
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[8,1,2,4,5,3,6,7]=>1000100
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[8,1,2,4,5,3,7,6]=>1000101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[6,5,4,8,7,3,2,1]=>[8,1,2,6,4,5,3,7]=>1001010
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[8,1,2,6,5,4,3,7]=>1001110
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,1,2,4,6,5,3,7]=>1000110
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[5,4,6,8,7,3,2,1]=>[8,1,2,5,4,6,3,7]=>1001010
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[8,1,2,4,5,6,3,7]=>1000010
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,1,2,7,4,5,6,3]=>1001001
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,1,2,7,4,6,5,3]=>1001011
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,1,2,7,6,5,4,3]=>1001111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[8,1,2,4,7,5,6,3]=>1000101
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[8,1,2,4,7,6,5,3]=>1000111
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,1,2,6,4,5,7,3]=>1001001
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[8,1,2,4,6,5,7,3]=>1000101
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,1,2,4,5,6,7,3]=>1000001
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[8,1,3,2,4,5,6,7]=>1010000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[3,7,8,6,5,4,2,1]=>[8,1,3,2,4,5,7,6]=>1010001
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[3,6,8,7,5,4,2,1]=>[8,1,3,2,4,6,5,7]=>1010010
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[8,1,3,2,4,7,6,5]=>1010011
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[3,6,7,8,5,4,2,1]=>[8,1,3,2,4,6,7,5]=>1010001
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,1,3,2,5,4,6,7]=>1010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[8,1,3,2,5,4,7,6]=>1010101
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[8,1,3,2,6,5,4,7]=>1010110
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[8,1,3,2,5,6,4,7]=>1010010
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[8,1,3,2,7,5,6,4]=>1010101
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[8,1,3,2,7,6,5,4]=>1010111
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[3,6,5,7,8,4,2,1]=>[8,1,3,2,6,5,7,4]=>1010101
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[8,1,3,2,5,6,7,4]=>1010001
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[4,3,8,7,6,5,2,1]=>[8,1,4,3,2,5,6,7]=>1011000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[4,3,7,8,6,5,2,1]=>[8,1,4,3,2,5,7,6]=>1011001
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[4,3,6,8,7,5,2,1]=>[8,1,4,3,2,6,5,7]=>1011010
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[4,3,7,6,8,5,2,1]=>[8,1,4,3,2,7,6,5]=>1011011
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[8,1,4,3,2,6,7,5]=>1011001
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[3,4,7,8,6,5,2,1]=>[8,1,3,4,2,5,7,6]=>1001001
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[3,4,6,8,7,5,2,1]=>[8,1,3,4,2,6,5,7]=>1001010
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[3,4,7,6,8,5,2,1]=>[8,1,3,4,2,7,6,5]=>1001011
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[8,1,3,4,2,6,7,5]=>1001001
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[8,1,5,3,4,2,6,7]=>1010100
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[8,1,5,3,4,2,7,6]=>1010101
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[4,5,3,8,7,6,2,1]=>[8,1,5,4,3,2,6,7]=>1011100
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[8,1,5,4,3,2,7,6]=>1011101
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[3,5,4,8,7,6,2,1]=>[8,1,3,5,4,2,6,7]=>1001100
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[4,3,5,8,7,6,2,1]=>[8,1,4,3,5,2,6,7]=>1010100
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[8,1,4,3,5,2,7,6]=>1010101
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[8,1,3,4,5,2,6,7]=>1000100
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[8,1,6,3,4,5,2,7]=>1010010
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[8,1,6,4,3,5,2,7]=>1011010
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[5,4,6,3,8,7,2,1]=>[8,1,6,5,4,3,2,7]=>1011110
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[8,1,6,4,5,3,2,7]=>1010110
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[3,6,5,4,8,7,2,1]=>[8,1,3,6,4,5,2,7]=>1001010
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[3,5,6,4,8,7,2,1]=>[8,1,3,6,5,4,2,7]=>1001110
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,1,4,3,6,5,2,7]=>1010110
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[3,4,6,5,8,7,2,1]=>[8,1,3,4,6,5,2,7]=>1000110
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>[8,1,5,3,4,6,2,7]=>1010010
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>[8,1,5,4,3,6,2,7]=>1011010
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[3,5,4,6,8,7,2,1]=>[8,1,3,5,4,6,2,7]=>1001010
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>[8,1,4,3,5,6,2,7]=>1010010
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,1,7,3,4,5,6,2]=>1010001
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[8,1,7,3,5,4,6,2]=>1010101
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[8,1,7,3,6,5,4,2]=>1010111
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,1,7,3,5,6,4,2]=>1010011
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>[8,1,7,4,3,5,6,2]=>1011001
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[4,6,7,5,3,8,2,1]=>[8,1,7,4,3,6,5,2]=>1011011
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,1,7,6,4,5,3,2]=>1011011
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[8,1,7,6,5,4,3,2]=>1011111
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[4,6,5,7,3,8,2,1]=>[8,1,7,4,6,5,3,2]=>1010111
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[3,7,6,5,4,8,2,1]=>[8,1,3,7,4,5,6,2]=>1001001
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[8,1,3,7,4,6,5,2]=>1001011
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[3,6,5,7,4,8,2,1]=>[8,1,3,7,6,5,4,2]=>1001111
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[3,5,6,7,4,8,2,1]=>[8,1,3,7,5,6,4,2]=>1001011
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[4,3,7,6,5,8,2,1]=>[8,1,4,3,7,5,6,2]=>1010101
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[4,3,6,7,5,8,2,1]=>[8,1,4,3,7,6,5,2]=>1010111
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>[8,1,5,4,3,7,6,2]=>1011011
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[3,5,4,7,6,8,2,1]=>[8,1,3,5,4,7,6,2]=>1001011
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>[8,1,4,3,5,7,6,2]=>1010011
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[3,4,5,7,6,8,2,1]=>[8,1,3,4,5,7,6,2]=>1000011
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,1,6,3,4,5,7,2]=>1010001
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[8,1,6,3,5,4,7,2]=>1010101
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[4,6,5,3,7,8,2,1]=>[8,1,6,4,3,5,7,2]=>1011001
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[4,3,6,5,7,8,2,1]=>[8,1,4,3,6,5,7,2]=>1010101
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[8,1,5,4,3,6,7,2]=>1011001
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,1,4,3,5,6,7,2]=>1010001
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,1,3,4,5,6,7,2]=>1000001
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,2,1,3,4,5,6,7]=>1100000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[8,2,1,3,4,5,7,6]=>1100001
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,2,1,3,4,6,5,7]=>1100010
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[8,2,1,3,4,6,7,5]=>1100001
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[2,5,7,8,6,4,3,1]=>[8,2,1,3,5,4,7,6]=>1100101
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[2,6,5,8,7,4,3,1]=>[8,2,1,3,6,5,4,7]=>1100110
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[2,5,6,8,7,4,3,1]=>[8,2,1,3,5,6,4,7]=>1100010
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[2,6,7,5,8,4,3,1]=>[8,2,1,3,7,6,5,4]=>1100111
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[2,6,5,7,8,4,3,1]=>[8,2,1,3,6,5,7,4]=>1100101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[8,2,1,3,5,6,7,4]=>1100001
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[2,4,7,8,6,5,3,1]=>[8,2,1,4,3,5,7,6]=>1101001
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,2,1,4,3,6,5,7]=>1101010
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[2,5,4,7,8,6,3,1]=>[8,2,1,5,4,3,7,6]=>1101101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[8,2,1,4,6,5,3,7]=>1100110
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[2,6,5,7,4,8,3,1]=>[8,2,1,7,6,5,4,3]=>1101111
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[2,5,6,7,4,8,3,1]=>[8,2,1,7,5,6,4,3]=>1101011
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[2,5,6,4,7,8,3,1]=>[8,2,1,6,5,4,7,3]=>1101101
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[2,4,6,5,7,8,3,1]=>[8,2,1,4,6,5,7,3]=>1100101
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[2,4,5,6,7,8,3,1]=>[8,2,1,4,5,6,7,3]=>1100001
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>[8,3,2,1,4,5,6,7]=>1110000
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[3,2,7,8,6,5,4,1]=>[8,3,2,1,4,5,7,6]=>1110001
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>[8,3,2,1,4,6,5,7]=>1110010
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[3,2,7,6,8,5,4,1]=>[8,3,2,1,4,7,6,5]=>1110011
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[3,2,5,7,8,6,4,1]=>[8,3,2,1,5,4,7,6]=>1110101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[3,2,6,5,8,7,4,1]=>[8,3,2,1,6,5,4,7]=>1110110
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[8,3,2,1,5,6,4,7]=>1110010
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[3,2,6,7,5,8,4,1]=>[8,3,2,1,7,6,5,4]=>1110111
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[3,2,5,7,6,8,4,1]=>[8,3,2,1,5,7,6,4]=>1110011
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[3,2,6,5,7,8,4,1]=>[8,3,2,1,6,5,7,4]=>1110101
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,2,3,1,4,5,6,7]=>1010000
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[2,3,7,8,6,5,4,1]=>[8,2,3,1,4,5,7,6]=>1010001
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>[8,2,3,1,5,4,7,6]=>1010101
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[2,3,6,5,8,7,4,1]=>[8,2,3,1,6,5,4,7]=>1010110
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,2,3,1,5,6,4,7]=>1010010
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>[8,2,3,1,7,5,6,4]=>1010101
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[2,3,6,7,5,8,4,1]=>[8,2,3,1,7,6,5,4]=>1010111
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[2,3,5,7,6,8,4,1]=>[8,2,3,1,5,7,6,4]=>1010011
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[2,3,6,5,7,8,4,1]=>[8,2,3,1,6,5,7,4]=>1010101
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[8,2,3,1,5,6,7,4]=>1010001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,4,2,3,1,5,6,7]=>1101000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[8,4,2,3,1,5,7,6]=>1101001
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[8,4,2,3,1,6,5,7]=>1101010
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[4,3,2,6,7,8,5,1]=>[8,4,2,3,1,6,7,5]=>1101001
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,4,3,2,1,5,6,7]=>1111000
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[8,4,3,2,1,5,7,6]=>1111001
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[3,4,2,6,7,8,5,1]=>[8,4,3,2,1,6,7,5]=>1111001
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,2,4,3,1,6,5,7]=>1011010
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,2,3,4,1,5,6,7]=>1001000
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[2,3,4,7,8,6,5,1]=>[8,2,3,4,1,5,7,6]=>1001001
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>[8,2,3,4,1,6,7,5]=>1001001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[8,5,2,3,4,1,6,7]=>1100100
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>[8,5,2,4,3,1,6,7]=>1101100
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[4,5,3,2,7,8,6,1]=>[8,5,2,4,3,1,7,6]=>1101101
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[3,5,4,2,7,8,6,1]=>[8,5,3,2,4,1,7,6]=>1110101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[8,5,4,3,2,1,6,7]=>1111100
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[8,2,5,3,4,1,7,6]=>1010101
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[2,3,5,4,7,8,6,1]=>[8,2,3,5,4,1,7,6]=>1001101
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>[8,4,2,3,5,1,6,7]=>1100100
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[8,4,3,2,5,1,7,6]=>1110101
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[2,4,3,5,7,8,6,1]=>[8,2,4,3,5,1,7,6]=>1010101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>[8,2,3,4,5,1,6,7]=>1000100
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[8,2,3,4,5,1,7,6]=>1000101
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[5,6,4,3,2,8,7,1]=>[8,6,2,3,5,4,1,7]=>1100110
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[8,6,2,4,3,5,1,7]=>1101010
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[8,6,2,4,5,3,1,7]=>1100110
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[8,6,3,2,4,5,1,7]=>1110010
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,6,4,3,2,5,1,7]=>1111010
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[8,6,5,3,4,2,1,7]=>1110110
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[4,5,3,6,2,8,7,1]=>[8,6,5,4,3,2,1,7]=>1111110
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[8,2,6,3,4,5,1,7]=>1010010
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[8,2,6,4,3,5,1,7]=>1011010
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[8,3,2,6,4,5,1,7]=>1101010
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,2,4,3,6,5,1,7]=>1010110
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[3,2,4,6,5,8,7,1]=>[8,3,2,4,6,5,1,7]=>1100110
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[8,5,2,3,4,6,1,7]=>1100010
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[4,5,3,2,6,8,7,1]=>[8,5,2,4,3,6,1,7]=>1101010
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[3,5,4,2,6,8,7,1]=>[8,5,3,2,4,6,1,7]=>1110010
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[4,3,5,2,6,8,7,1]=>[8,5,4,3,2,6,1,7]=>1111010
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[3,2,4,5,6,8,7,1]=>[8,3,2,4,5,6,1,7]=>1100010
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,6,1,7]=>1000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,7,2,3,4,5,6,1]=>1100001
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[5,7,6,4,3,2,8,1]=>[8,7,2,3,5,4,6,1]=>1100101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,7,2,3,6,5,4,1]=>1100111
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[8,7,2,4,3,5,6,1]=>1101001
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[4,6,7,5,3,2,8,1]=>[8,7,2,4,3,6,5,1]=>1101011
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[5,4,7,6,3,2,8,1]=>[8,7,2,5,4,3,6,1]=>1101101
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[8,7,2,4,5,3,6,1]=>1100101
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,7,2,6,4,5,3,1]=>1101011
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[5,6,4,7,3,2,8,1]=>[8,7,2,6,5,4,3,1]=>1101111
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[8,7,2,4,6,5,3,1]=>1100111
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,7,2,4,5,6,3,1]=>1100011
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[3,6,7,5,4,2,8,1]=>[8,7,3,2,4,6,5,1]=>1110011
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[8,7,3,2,5,4,6,1]=>1110101
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[8,7,3,2,5,6,4,1]=>1110011
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[8,7,4,3,2,5,6,1]=>1111001
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[3,4,6,7,5,2,8,1]=>[8,7,3,4,2,6,5,1]=>1101011
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>[8,7,5,3,4,2,6,1]=>1110101
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[4,5,3,7,6,2,8,1]=>[8,7,5,4,3,2,6,1]=>1111101
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[3,5,4,7,6,2,8,1]=>[8,7,3,5,4,2,6,1]=>1101101
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[4,3,5,7,6,2,8,1]=>[8,7,4,3,5,2,6,1]=>1110101
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>1110011
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>1110111
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[8,7,6,4,3,5,2,1]=>1111011
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>1110111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[8,7,3,6,4,5,2,1]=>1101011
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>1101111
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>1110111
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[3,4,6,5,7,2,8,1]=>[8,7,3,4,6,5,2,1]=>1100111
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,7,5,3,4,6,2,1]=>1110011
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>1111011
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]=>1101011
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[8,7,4,3,5,6,2,1]=>1110011
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>1100011
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[8,2,7,3,4,5,6,1]=>1010001
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[2,6,5,7,4,3,8,1]=>[8,2,7,3,6,5,4,1]=>1010111
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[8,2,7,5,4,3,6,1]=>1011101
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[8,2,7,4,5,3,6,1]=>1010101
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[2,5,6,4,7,3,8,1]=>[8,2,7,6,5,4,3,1]=>1011111
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>1010111
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[8,2,7,5,4,6,3,1]=>1011011
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>1010011
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[8,3,2,7,4,6,5,1]=>1101011
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>1101111
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[3,2,5,6,7,4,8,1]=>[8,3,2,7,5,6,4,1]=>1101011
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[8,2,3,7,4,5,6,1]=>1001001
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[2,3,5,6,7,4,8,1]=>[8,2,3,7,5,6,4,1]=>1001011
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[8,4,2,3,7,5,6,1]=>1100101
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>[8,4,2,3,7,6,5,1]=>1100111
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>[8,4,3,2,7,5,6,1]=>1110101
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[8,4,3,2,7,6,5,1]=>1110111
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[8,2,4,3,7,5,6,1]=>1010101
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[2,4,3,6,7,5,8,1]=>[8,2,4,3,7,6,5,1]=>1010111
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[3,2,4,6,7,5,8,1]=>[8,3,2,4,7,6,5,1]=>1100111
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[2,3,4,6,7,5,8,1]=>[8,2,3,4,7,6,5,1]=>1000111
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>1111011
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[3,4,5,2,7,6,8,1]=>[8,5,3,4,2,7,6,1]=>1101011
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[8,2,5,3,4,7,6,1]=>1010011
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[2,4,5,3,7,6,8,1]=>[8,2,5,4,3,7,6,1]=>1011011
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>1101011
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[8,2,3,5,4,7,6,1]=>1001011
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>[8,4,2,3,5,7,6,1]=>1100011
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[3,4,2,5,7,6,8,1]=>[8,4,3,2,5,7,6,1]=>1110011
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,7,6,1]=>1000011
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,6,2,3,4,5,7,1]=>1100001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,6,2,5,4,3,7,1]=>1101101
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,6,2,4,5,3,7,1]=>1100101
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>[8,6,3,2,5,4,7,1]=>1110101
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[4,3,6,5,2,7,8,1]=>[8,6,4,3,2,5,7,1]=>1111001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,6,5,3,4,2,7,1]=>1110101
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>1111101
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[3,5,4,6,2,7,8,1]=>[8,6,3,5,4,2,7,1]=>1101101
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>1110101
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>1100101
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[8,2,6,3,4,5,7,1]=>1010001
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>1011101
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[2,4,5,6,3,7,8,1]=>[8,2,6,4,5,3,7,1]=>1010101
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>[8,2,3,6,5,4,7,1]=>1001101
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>[8,4,2,3,6,5,7,1]=>1100101
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]=>1110101
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>1010101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,5,2,3,4,6,7,1]=>1100001
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>1111001
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>1101001
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[8,2,5,4,3,6,7,1]=>1011001
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>[8,2,3,5,4,6,7,1]=>1001001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,4,2,3,5,6,7,1]=>1100001
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>1110001
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>1100001
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>1000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>0100000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,8,2,3,4,5,7,6]=>0100001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[1,8,2,3,4,6,5,7]=>0100010
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[1,8,2,3,4,7,6,5]=>0100011
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[1,8,2,3,4,6,7,5]=>0100001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[1,8,2,3,5,4,6,7]=>0100100
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,6,5,8,7,4,3,2]=>[1,8,2,3,6,5,4,7]=>0100110
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[1,8,2,3,5,6,4,7]=>0100010
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[1,8,2,3,7,5,6,4]=>0100101
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[1,8,2,3,7,6,5,4]=>0100111
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[1,8,2,3,6,5,7,4]=>0100101
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[1,8,2,3,5,6,7,4]=>0100001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[1,8,2,4,3,5,6,7]=>0101000
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>[1,8,2,4,3,6,5,7]=>0101010
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[1,4,7,6,8,5,3,2]=>[1,8,2,4,3,7,6,5]=>0101011
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[1,8,2,4,6,5,3,7]=>0100110
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[1,8,2,7,4,5,6,3]=>0101001
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[1,6,7,5,4,8,3,2]=>[1,8,2,7,4,6,5,3]=>0101011
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[1,6,5,7,4,8,3,2]=>[1,8,2,7,6,5,4,3]=>0101111
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[1,8,2,4,7,5,6,3]=>0100101
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[1,4,6,7,5,8,3,2]=>[1,8,2,4,7,6,5,3]=>0100111
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[1,5,4,7,6,8,3,2]=>[1,8,2,5,4,7,6,3]=>0101011
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[1,4,5,7,6,8,3,2]=>[1,8,2,4,5,7,6,3]=>0100011
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>[1,8,2,5,4,6,7,3]=>0101001
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[1,8,2,4,5,6,7,3]=>0100001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>[1,8,3,2,4,5,6,7]=>0110000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[1,3,7,8,6,5,4,2]=>[1,8,3,2,4,5,7,6]=>0110001
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[1,8,3,2,4,6,7,5]=>0110001
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[1,8,3,2,5,4,6,7]=>0110100
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,8,3,2,5,4,7,6]=>0110101
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[1,3,5,6,8,7,4,2]=>[1,8,3,2,5,6,4,7]=>0110010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[1,3,7,6,5,8,4,2]=>[1,8,3,2,7,5,6,4]=>0110101
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[1,8,3,2,7,6,5,4]=>0110111
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[1,8,3,2,5,6,7,4]=>0110001
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,8,4,3,2,5,6,7]=>0111000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[1,8,4,3,2,5,7,6]=>0111001
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[1,8,4,3,2,7,6,5]=>0111011
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[1,8,4,3,2,6,7,5]=>0111001
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[1,8,3,4,2,5,6,7]=>0101000
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[1,8,3,4,2,7,6,5]=>0101011
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[1,8,3,4,2,6,7,5]=>0101001
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[1,4,5,3,8,7,6,2]=>[1,8,5,4,3,2,6,7]=>0111100
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[1,4,5,3,7,8,6,2]=>[1,8,5,4,3,2,7,6]=>0111101
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[1,8,3,5,4,2,7,6]=>0101101
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>[1,8,4,3,5,2,7,6]=>0110101
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>[1,8,3,4,5,2,6,7]=>0100100
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>[1,8,3,4,5,2,7,6]=>0100101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[1,8,6,3,4,5,2,7]=>0110010
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[1,8,6,3,5,4,2,7]=>0110110
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[1,5,4,6,3,8,7,2]=>[1,8,6,5,4,3,2,7]=>0111110
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>[1,8,3,6,4,5,2,7]=>0101010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[1,8,4,3,6,5,2,7]=>0110110
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>[1,8,5,3,4,6,2,7]=>0110010
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[1,8,5,4,3,6,2,7]=>0111010
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[1,8,3,4,5,6,2,7]=>0100010
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[1,8,7,3,4,5,6,2]=>0110001
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[1,8,7,3,4,6,5,2]=>0110011
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[1,6,5,7,4,3,8,2]=>[1,8,7,3,6,5,4,2]=>0110111
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[1,8,7,4,3,5,6,2]=>0111001
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[1,8,7,4,3,6,5,2]=>0111011
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[1,5,4,7,6,3,8,2]=>[1,8,7,5,4,3,6,2]=>0111101
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[1,4,5,7,6,3,8,2]=>[1,8,7,4,5,3,6,2]=>0110101
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]=>0111111
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[1,8,7,5,4,6,3,2]=>0111011
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[1,8,7,4,5,6,3,2]=>0110011
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[1,3,6,5,7,4,8,2]=>[1,8,3,7,6,5,4,2]=>0101111
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[1,3,5,6,7,4,8,2]=>[1,8,3,7,5,6,4,2]=>0101011
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[1,5,4,3,7,6,8,2]=>[1,8,5,3,4,7,6,2]=>0110011
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[1,8,3,5,4,7,6,2]=>0101011
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[1,4,3,5,7,6,8,2]=>[1,8,4,3,5,7,6,2]=>0110011
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[1,4,6,5,3,7,8,2]=>[1,8,6,4,3,5,7,2]=>0111001
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[1,5,4,6,3,7,8,2]=>[1,8,6,5,4,3,7,2]=>0111101
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[1,4,5,6,3,7,8,2]=>[1,8,6,4,5,3,7,2]=>0110101
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>[1,8,3,6,5,4,7,2]=>0101101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]=>0110101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[1,8,5,3,4,6,7,2]=>0110001
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>0111001
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[1,8,3,5,4,6,7,2]=>0101001
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>0110001
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>0100001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,8,3,4,5,6,7]=>1010000
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[2,1,8,3,4,7,6,5]=>1010011
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,8,3,4,6,7,5]=>1010001
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[2,1,8,3,5,4,7,6]=>1010101
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[2,1,8,3,7,5,6,4]=>1010101
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,8,3,7,6,5,4]=>1010111
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[2,1,8,3,5,7,6,4]=>1010011
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[2,1,8,3,6,5,7,4]=>1010101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[2,1,8,3,5,6,7,4]=>1010001
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[2,1,8,4,3,5,7,6]=>1011001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[2,1,8,4,3,6,5,7]=>1011010
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[2,1,4,7,6,8,5,3]=>[2,1,8,4,3,7,6,5]=>1011011
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[2,1,5,4,8,7,6,3]=>[2,1,8,5,4,3,6,7]=>1011100
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[2,1,5,4,7,8,6,3]=>[2,1,8,5,4,3,7,6]=>1011101
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[2,1,8,4,5,3,7,6]=>1010101
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[2,1,5,6,4,8,7,3]=>[2,1,8,6,5,4,3,7]=>1011110
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[2,1,8,4,6,5,3,7]=>1010110
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[2,1,5,4,6,8,7,3]=>[2,1,8,5,4,6,3,7]=>1011010
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[2,1,6,7,5,4,8,3]=>[2,1,8,7,4,6,5,3]=>1011011
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[2,1,8,7,5,4,6,3]=>1011101
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>1011111
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>1011011
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[2,1,8,4,7,5,6,3]=>1010101
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]=>1010111
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>1011011
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[2,1,4,5,7,6,8,3]=>[2,1,8,4,5,7,6,3]=>1010011
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[2,1,6,5,4,7,8,3]=>[2,1,8,6,4,5,7,3]=>1011001
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]=>1011101
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[2,1,4,6,5,7,8,3]=>[2,1,8,4,6,5,7,3]=>1010101
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[2,1,8,5,4,6,7,3]=>1011001
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>1010001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>[1,2,8,3,4,5,6,7]=>0010000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[1,2,7,8,6,5,4,3]=>[1,2,8,3,4,5,7,6]=>0010001
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[1,2,6,8,7,5,4,3]=>[1,2,8,3,4,6,5,7]=>0010010
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[1,2,7,6,8,5,4,3]=>[1,2,8,3,4,7,6,5]=>0010011
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,8,3,4,6,7,5]=>0010001
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[1,2,5,8,7,6,4,3]=>[1,2,8,3,5,4,6,7]=>0010100
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[1,2,8,3,5,4,7,6]=>0010101
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[1,2,8,3,6,5,4,7]=>0010110
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[1,2,8,3,5,6,4,7]=>0010010
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[1,2,8,3,7,6,5,4]=>0010111
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[1,2,8,3,5,7,6,4]=>0010011
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[1,2,8,3,6,5,7,4]=>0010101
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,8,3,5,6,7,4]=>0010001
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[1,2,8,4,3,5,6,7]=>0011000
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[1,2,8,4,3,5,7,6]=>0011001
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>[1,2,8,4,3,6,5,7]=>0011010
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[1,2,4,7,6,8,5,3]=>[1,2,8,4,3,7,6,5]=>0011011
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[1,2,8,4,3,6,7,5]=>0011001
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>[1,2,8,5,4,3,6,7]=>0011100
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[1,2,8,4,5,3,6,7]=>0010100
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[1,2,8,4,5,3,7,6]=>0010101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>[1,2,8,6,4,5,3,7]=>0011010
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[1,2,5,6,4,8,7,3]=>[1,2,8,6,5,4,3,7]=>0011110
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>[1,2,8,5,4,6,3,7]=>0011010
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[1,2,4,5,6,8,7,3]=>[1,2,8,4,5,6,3,7]=>0010010
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[1,2,7,6,5,4,8,3]=>[1,2,8,7,4,5,6,3]=>0011001
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[1,2,6,7,5,4,8,3]=>[1,2,8,7,4,6,5,3]=>0011011
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[1,2,8,7,5,4,6,3]=>0011101
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[1,2,6,5,7,4,8,3]=>[1,2,8,7,6,5,4,3]=>0011111
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>0011011
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[1,2,8,4,7,6,5,3]=>0010111
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[1,2,5,4,7,6,8,3]=>[1,2,8,5,4,7,6,3]=>0011011
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[1,2,8,6,4,5,7,3]=>0011001
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[1,2,8,6,5,4,7,3]=>0011101
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>0011001
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>0010001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[3,1,2,8,4,5,6,7]=>1001000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[3,1,2,8,4,5,7,6]=>1001001
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[3,1,2,8,4,6,7,5]=>1001001
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[3,1,2,8,5,4,7,6]=>1001101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[3,1,2,8,6,5,4,7]=>1001110
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[3,1,2,8,5,6,4,7]=>1001010
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[3,1,2,8,7,5,6,4]=>1001101
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[3,1,2,8,7,6,5,4]=>1001111
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[3,1,2,8,6,5,7,4]=>1001101
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[3,1,2,8,5,6,7,4]=>1001001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[3,2,1,8,4,5,6,7]=>1101000
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[3,2,1,8,4,5,7,6]=>1101001
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[3,2,1,8,4,6,5,7]=>1101010
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[3,2,1,8,4,7,6,5]=>1101011
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[3,2,1,8,4,6,7,5]=>1101001
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[3,2,1,8,5,4,6,7]=>1101100
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[3,2,1,8,5,4,7,6]=>1101101
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[3,2,1,8,6,5,4,7]=>1101110
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[3,2,1,8,5,6,4,7]=>1101010
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,7,5,6,4]=>1101101
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>1101111
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>1101011
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[3,2,1,8,6,5,7,4]=>1101101
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>1101001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,4,5,6,7]=>0101000
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,3,2,7,8,6,5,4]=>[1,3,2,8,4,5,7,6]=>0101001
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>[1,3,2,8,4,6,5,7]=>0101010
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[1,3,2,6,7,8,5,4]=>[1,3,2,8,4,6,7,5]=>0101001
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[1,3,2,8,5,4,6,7]=>0101100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,7,8,6,4]=>[1,3,2,8,5,4,7,6]=>0101101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[1,3,2,8,6,5,4,7]=>0101110
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[1,3,2,5,6,8,7,4]=>[1,3,2,8,5,6,4,7]=>0101010
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>0101111
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]=>0101011
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>0101101
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,4,5,6,7]=>1001000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[2,1,3,8,4,5,7,6]=>1001001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>[2,1,3,8,4,6,5,7]=>1001010
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[2,1,3,7,6,8,5,4]=>[2,1,3,8,4,7,6,5]=>1001011
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[2,1,3,8,4,6,7,5]=>1001001
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[2,1,3,5,8,7,6,4]=>[2,1,3,8,5,4,6,7]=>1001100
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[2,1,3,5,7,8,6,4]=>[2,1,3,8,5,4,7,6]=>1001101
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[2,1,3,6,5,8,7,4]=>[2,1,3,8,6,5,4,7]=>1001110
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[2,1,3,7,6,5,8,4]=>[2,1,3,8,7,5,6,4]=>1001101
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>1001111
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]=>1001011
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[2,1,3,6,5,7,8,4]=>[2,1,3,8,6,5,7,4]=>1001101
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>1001001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,4,5,6,7]=>0001000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,4,5,7,6]=>0001001
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,4,6,5,7]=>0001010
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,4,7,6,5]=>0001011
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,4,6,7,5]=>0001001
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,5,4,6,7]=>0001100
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,5,4,7,6]=>0001101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,6,5,4,7]=>0001110
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,5,6,4,7]=>0001010
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,7,5,6,4]=>0001101
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>0001111
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>0001011
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>0001101
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>0001001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,1,2,3,8,5,6,7]=>1000100
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[4,1,2,3,8,5,7,6]=>1000101
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,1,2,3,8,6,5,7]=>1000110
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>1000111
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>1000101
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[4,1,3,2,8,5,6,7]=>1010100
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[4,1,3,2,8,5,7,6]=>1010101
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[4,1,3,2,8,6,5,7]=>1010110
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[4,1,3,2,8,7,6,5]=>1010111
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>1010101
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[4,2,1,3,8,5,6,7]=>1100100
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[4,2,1,3,8,5,7,6]=>1100101
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[4,2,1,3,8,6,5,7]=>1100110
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[4,2,1,3,8,7,6,5]=>1100111
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[4,2,1,3,8,6,7,5]=>1100101
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,8,5,6,7]=>1110100
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,8,5,7,6]=>1110101
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,8,6,5,7]=>1110110
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>1110111
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>1110101
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,8,5,6,7]=>1010100
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,8,5,7,6]=>1010101
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,8,6,5,7]=>1010110
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>1010111
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>1010101
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,4,2,3,8,5,6,7]=>0100100
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[1,4,3,2,7,8,6,5]=>[1,4,2,3,8,5,7,6]=>0100101
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[1,4,2,3,8,6,5,7]=>0100110
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,4,2,3,8,7,6,5]=>0100111
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,8,5,6,7]=>0110100
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,8,6,5,7]=>0110110
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>0110111
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,5,6,7]=>1010100
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,5,7,6]=>1010101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,6,5,7]=>1010110
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>1010111
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>1010101
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,5,6,7]=>0010100
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,8,5,7,6]=>0010101
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,8,6,5,7]=>0010110
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>0010111
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,1,2,4,8,5,6,7]=>1000100
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[3,1,2,4,8,5,7,6]=>1000101
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[3,1,2,4,8,6,5,7]=>1000110
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]=>1000111
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>1000101
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,8,5,6,7]=>1100100
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,8,5,7,6]=>1100101
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[2,3,1,4,6,8,7,5]=>[3,2,1,4,8,6,5,7]=>1100110
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>1100111
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>1100101
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,5,6,7]=>0100100
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[1,3,2,4,7,8,6,5]=>[1,3,2,4,8,5,7,6]=>0100101
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,8,6,5,7]=>0100110
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>0100111
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>0100101
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,5,6,7]=>1000100
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,5,7,6]=>1000101
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[2,1,3,4,6,8,7,5]=>[2,1,3,4,8,6,5,7]=>1000110
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>1000111
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>1000101
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,5,6,7]=>0000100
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,5,7,6]=>0000101
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,8,6,5,7]=>0000110
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>0000111
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>0000101
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[5,1,2,3,4,8,6,7]=>1000010
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[5,1,2,3,4,8,7,6]=>1000011
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[4,5,3,2,1,7,8,6]=>[5,1,2,4,3,8,7,6]=>1001011
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[5,1,3,2,4,8,6,7]=>1010010
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>[5,1,3,2,4,8,7,6]=>1010011
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[4,3,5,2,1,7,8,6]=>[5,1,4,3,2,8,7,6]=>1011011
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[5,1,3,4,2,8,6,7]=>1001010
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[3,4,5,2,1,7,8,6]=>[5,1,3,4,2,8,7,6]=>1001011
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[5,2,1,3,4,8,7,6]=>1100011
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[5,2,1,4,3,8,6,7]=>1101010
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[2,4,5,3,1,7,8,6]=>[5,2,1,4,3,8,7,6]=>1101011
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[5,3,2,1,4,8,6,7]=>1110010
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[5,3,2,1,4,8,7,6]=>1110011
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[5,2,3,1,4,8,6,7]=>1010010
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[2,3,5,4,1,7,8,6]=>[5,2,3,1,4,8,7,6]=>1010011
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,4,2,3,1,8,6,7]=>1101010
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[5,4,2,3,1,8,7,6]=>1101011
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,8,6,7]=>1111010
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>1111011
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>1011011
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>1101011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,8,6,7]=>1001010
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>1001011
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]=>[1,5,2,3,4,8,6,7]=>0100010
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[1,5,4,3,2,7,8,6]=>[1,5,2,3,4,8,7,6]=>0100011
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[1,4,5,3,2,8,7,6]=>[1,5,2,4,3,8,6,7]=>0101010
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[1,4,5,3,2,7,8,6]=>[1,5,2,4,3,8,7,6]=>0101011
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[1,3,5,4,2,8,7,6]=>[1,5,3,2,4,8,6,7]=>0110010
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[1,3,5,4,2,7,8,6]=>[1,5,3,2,4,8,7,6]=>0110011
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>0111011
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>0101011
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>1011011
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]=>[1,2,5,3,4,8,6,7]=>0010010
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[1,2,5,3,4,8,7,6]=>0010011
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,8,6,7]=>0011010
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>0011011
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,8,6,7]=>0101010
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>0101011
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>1001011
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,8,6,7]=>0001010
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>0001011
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[4,1,2,3,5,8,6,7]=>1000010
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>1000011
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[2,4,3,1,5,8,7,6]=>[4,2,1,3,5,8,6,7]=>1100010
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[4,2,1,3,5,8,7,6]=>1100011
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,8,6,7]=>1110010
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>1110011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,8,6,7]=>1010010
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[1,4,2,3,5,8,6,7]=>0100010
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>0100011
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,8,6,7]=>0110010
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>0110011
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,8,6,7]=>1010010
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>1010011
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,8,6,7]=>0010010
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>0010011
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,1,2,4,5,8,6,7]=>1000010
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[2,3,1,4,5,8,7,6]=>[3,2,1,4,5,8,6,7]=>1100010
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>1100011
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,8,6,7]=>0100010
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>0100011
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,8,6,7]=>1000010
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>1000011
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,6,7]=>0000010
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>0000011
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[6,1,2,3,4,5,8,7]=>1000001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[6,1,2,4,3,5,8,7]=>1001001
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[6,1,2,5,4,3,8,7]=>1001101
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[6,1,2,4,5,3,8,7]=>1000101
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[6,1,3,2,4,5,8,7]=>1010001
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[6,1,3,2,5,4,8,7]=>1010101
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[3,4,6,5,2,1,8,7]=>[6,1,3,4,2,5,8,7]=>1001001
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[6,1,5,3,4,2,8,7]=>1010101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[6,1,5,4,3,2,8,7]=>1011101
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[3,5,4,6,2,1,8,7]=>[6,1,3,5,4,2,8,7]=>1001101
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[6,1,4,3,5,2,8,7]=>1010101
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[6,2,1,4,3,5,8,7]=>1101001
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[2,5,4,6,3,1,8,7]=>[6,2,1,5,4,3,8,7]=>1101101
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[3,2,6,5,4,1,8,7]=>[6,3,2,1,4,5,8,7]=>1110001
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[3,2,5,6,4,1,8,7]=>[6,3,2,1,5,4,8,7]=>1110101
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[6,2,3,1,4,5,8,7]=>1010001
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[6,4,3,2,1,5,8,7]=>1111001
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[6,2,4,3,1,5,8,7]=>1011001
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>[6,5,3,2,4,1,8,7]=>1110101
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>1111101
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>1101101
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>[6,2,5,3,4,1,8,7]=>1010101
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]=>1011101
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>1101101
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[6,4,2,3,5,1,8,7]=>1100101
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>1110101
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[2,4,3,5,6,1,8,7]=>[6,2,4,3,5,1,8,7]=>1010101
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>1000101
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]=>[1,6,2,3,4,5,8,7]=>0100001
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[1,3,4,6,5,2,8,7]=>[1,6,3,4,2,5,8,7]=>0101001
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,6,3,4,5,8,7]=>1010001
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,6,3,5,4,8,7]=>1010101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,6,4,3,5,8,7]=>1011001
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>1011101
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>1010101
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[1,2,6,3,4,5,8,7]=>0010001
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[3,1,2,6,4,5,8,7]=>1001001
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]=>1101101
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>0101101
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>[2,1,3,6,4,5,8,7]=>1001001
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[1,2,3,6,4,5,8,7]=>0001001
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>0001101
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>1000101
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>1010101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>1100101
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>1110101
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>1010101
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>0100101
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>0010101
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>1000101
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>0100101
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>1000101
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>0000101
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[5,1,2,3,4,6,8,7]=>1000001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[5,1,2,4,3,6,8,7]=>1001001
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[5,1,3,2,4,6,8,7]=>1010001
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[4,3,5,2,1,6,8,7]=>[5,1,4,3,2,6,8,7]=>1011001
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[3,4,5,2,1,6,8,7]=>[5,1,3,4,2,6,8,7]=>1001001
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[5,2,1,4,3,6,8,7]=>1101001
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[5,3,2,1,4,6,8,7]=>1110001
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[2,3,5,4,1,6,8,7]=>[5,2,3,1,4,6,8,7]=>1010001
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[4,3,2,5,1,6,8,7]=>[5,4,2,3,1,6,8,7]=>1101001
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>1111001
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[2,4,3,5,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>1011001
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>1001001
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]=>[1,5,2,3,4,6,8,7]=>0100001
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[1,4,5,3,2,6,8,7]=>[1,5,2,4,3,6,8,7]=>0101001
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>[1,5,3,2,4,6,8,7]=>0110001
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[2,1,5,3,4,6,8,7]=>1010001
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[1,2,5,3,4,6,8,7]=>0010001
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>0011001
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>1001001
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>1001001
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>0001001
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>1000001
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[2,4,3,1,5,6,8,7]=>[4,2,1,3,5,6,8,7]=>1100001
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>1110001
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>0100001
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>0110001
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>1010001
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>0010001
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>1000001
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>1100001
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>0100001
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>1000001
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>0000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,1,2,3,4,5,6,8]=>1000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,1,2,3,4,6,5,8]=>1000010
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,1,2,3,5,4,6,8]=>1000100
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,1,2,3,6,5,4,8]=>1000110
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,1,2,3,5,6,4,8]=>1000010
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,1,2,4,3,5,6,8]=>1001000
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,1,2,6,4,5,3,8]=>1001010
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[7,1,2,6,5,4,3,8]=>1001110
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,1,2,5,4,6,3,8]=>1001010
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,1,2,4,5,6,3,8]=>1000010
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[3,7,6,5,4,2,1,8]=>[7,1,3,2,4,5,6,8]=>1010000
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[7,1,3,2,5,4,6,8]=>1010100
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[7,1,3,2,5,6,4,8]=>1010010
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[4,3,7,6,5,2,1,8]=>[7,1,4,3,2,5,6,8]=>1011000
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[7,1,6,3,5,4,2,8]=>1010110
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,1,6,5,4,3,2,8]=>1011110
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[3,6,5,4,7,2,1,8]=>[7,1,3,6,4,5,2,8]=>1001010
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[7,1,3,6,5,4,2,8]=>1001110
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[7,1,3,4,5,6,2,8]=>1000010
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[2,7,6,5,4,3,1,8]=>[7,2,1,3,4,5,6,8]=>1100000
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[2,5,7,6,4,3,1,8]=>[7,2,1,3,5,4,6,8]=>1100100
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[7,2,1,4,3,5,6,8]=>1101000
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[7,2,1,4,3,6,5,8]=>1101010
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[2,5,4,7,6,3,1,8]=>[7,2,1,5,4,3,6,8]=>1101100
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[7,2,1,4,5,3,6,8]=>1100100
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[2,5,6,4,7,3,1,8]=>[7,2,1,6,5,4,3,8]=>1101110
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[2,5,4,6,7,3,1,8]=>[7,2,1,5,4,6,3,8]=>1101010
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[2,4,5,6,7,3,1,8]=>[7,2,1,4,5,6,3,8]=>1100010
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,3,2,1,4,5,6,8]=>1110000
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[7,3,2,1,4,6,5,8]=>1110010
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>[7,3,2,1,5,4,6,8]=>1110100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[3,2,5,6,7,4,1,8]=>[7,3,2,1,5,6,4,8]=>1110010
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,2,3,1,4,5,6,8]=>1010000
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>[7,2,3,1,4,6,5,8]=>1010010
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>[7,2,3,1,5,6,4,8]=>1010010
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[7,4,3,2,1,5,6,8]=>1111000
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[7,4,3,2,1,6,5,8]=>1111010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[2,4,3,7,6,5,1,8]=>[7,2,4,3,1,5,6,8]=>1011000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,2,3,4,1,5,6,8]=>1001000
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[2,3,4,6,7,5,1,8]=>[7,2,3,4,1,6,5,8]=>1001010
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[7,5,2,3,4,1,6,8]=>1100100
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[7,5,2,4,3,1,6,8]=>1101100
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[7,5,3,2,4,1,6,8]=>1110100
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[4,3,5,2,7,6,1,8]=>[7,5,4,3,2,1,6,8]=>1111100
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,3,2,5,4,1,6,8]=>1101100
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[2,3,5,4,7,6,1,8]=>[7,2,3,5,4,1,6,8]=>1001100
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>[7,4,2,3,5,1,6,8]=>1100100
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[7,2,3,4,5,1,6,8]=>1000100
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,6,2,3,4,5,1,8]=>1100010
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[7,6,2,3,5,4,1,8]=>1100110
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,6,2,5,4,3,1,8]=>1101110
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[7,6,3,2,4,5,1,8]=>1110010
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[3,5,6,4,2,7,1,8]=>[7,6,3,2,5,4,1,8]=>1110110
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[4,3,6,5,2,7,1,8]=>[7,6,4,3,2,5,1,8]=>1111010
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>1110110
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>1101110
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>1110110
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>1100110
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[2,6,5,4,3,7,1,8]=>[7,2,6,3,4,5,1,8]=>1010010
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[7,2,6,5,4,3,1,8]=>1011110
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[2,4,5,6,3,7,1,8]=>[7,2,6,4,5,3,1,8]=>1010110
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>1001110
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[4,3,2,6,5,7,1,8]=>[7,4,2,3,6,5,1,8]=>1100110
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>[7,4,3,2,6,5,1,8]=>1110110
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>[7,2,4,3,6,5,1,8]=>1010110
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,6,5,1,8]=>1000110
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[7,5,3,2,4,6,1,8]=>1110010
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>1111010
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>1101010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[7,2,5,3,4,6,1,8]=>1010010
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[2,4,5,3,6,7,1,8]=>[7,2,5,4,3,6,1,8]=>1011010
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[3,2,5,4,6,7,1,8]=>[7,3,2,5,4,6,1,8]=>1101010
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[2,3,5,4,6,7,1,8]=>[7,2,3,5,4,6,1,8]=>1001010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>1100010
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>1000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]=>[1,7,2,3,4,5,6,8]=>0100000
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[1,6,7,5,4,3,2,8]=>[1,7,2,3,4,6,5,8]=>0100010
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[1,5,7,6,4,3,2,8]=>[1,7,2,3,5,4,6,8]=>0100100
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[1,4,7,6,5,3,2,8]=>[1,7,2,4,3,5,6,8]=>0101000
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[1,5,4,7,6,3,2,8]=>[1,7,2,5,4,3,6,8]=>0101100
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[1,4,5,7,6,3,2,8]=>[1,7,2,4,5,3,6,8]=>0100100
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[1,5,6,4,7,3,2,8]=>[1,7,2,6,5,4,3,8]=>0101110
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>[1,7,2,4,6,5,3,8]=>0100110
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[1,5,4,6,7,3,2,8]=>[1,7,2,5,4,6,3,8]=>0101010
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[1,7,2,4,5,6,3,8]=>0100010
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[1,3,7,6,5,4,2,8]=>[1,7,3,2,4,5,6,8]=>0110000
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[1,7,3,2,4,6,5,8]=>0110010
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[1,7,3,2,5,4,6,8]=>0110100
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>[1,7,3,2,5,6,4,8]=>0110010
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[1,4,3,7,6,5,2,8]=>[1,7,4,3,2,5,6,8]=>0111000
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[1,7,3,4,2,6,5,8]=>0101010
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[1,4,5,3,7,6,2,8]=>[1,7,5,4,3,2,6,8]=>0111100
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>[1,7,3,5,4,2,6,8]=>0101100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[1,6,5,4,3,7,2,8]=>[1,7,6,3,4,5,2,8]=>0110010
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[1,5,6,4,3,7,2,8]=>[1,7,6,3,5,4,2,8]=>0110110
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[1,7,6,5,4,3,2,8]=>0111110
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[1,4,5,6,3,7,2,8]=>[1,7,6,4,5,3,2,8]=>0110110
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[1,3,5,6,4,7,2,8]=>[1,7,3,6,5,4,2,8]=>0101110
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[1,4,5,3,6,7,2,8]=>[1,7,5,4,3,6,2,8]=>0111010
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[1,3,5,4,6,7,2,8]=>[1,7,3,5,4,6,2,8]=>0101010
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>0100010
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]=>[2,1,7,3,4,5,6,8]=>1010000
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[2,1,5,6,4,7,3,8]=>[2,1,7,6,5,4,3,8]=>1011110
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[1,2,7,3,4,5,6,8]=>0010000
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[1,2,6,7,5,4,3,8]=>[1,2,7,3,4,6,5,8]=>0010010
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>[1,2,7,3,5,4,6,8]=>0010100
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,2,4,7,6,5,3,8]=>[1,2,7,4,3,5,6,8]=>0011000
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]=>0011110
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[1,2,7,5,4,6,3,8]=>0011010
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[3,1,2,7,5,4,6,8]=>1001100
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[3,2,1,7,4,6,5,8]=>1101010
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]=>1101110
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]=>[1,3,2,7,4,5,6,8]=>0101000
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[1,3,2,6,7,5,4,8]=>[1,3,2,7,4,6,5,8]=>0101010
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[1,3,2,7,5,4,6,8]=>0101100
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]=>0101110
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[1,2,3,7,4,5,6,8]=>0001000
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[1,2,3,7,4,6,5,8]=>0001010
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[1,2,3,7,5,4,6,8]=>0001100
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>0001110
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>0001010
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[4,1,2,3,7,5,6,8]=>1000100
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>1000110
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,7,5,6,8]=>1110100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>1110110
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,4,2,3,7,5,6,8]=>0100100
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>0110110
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,7,5,6,8]=>0010100
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[3,1,2,4,7,5,6,8]=>1000100
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>1100110
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>0100110
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,7,5,6,8]=>0000100
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>0000110
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[5,1,2,4,3,7,6,8]=>1001010
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[5,1,3,2,4,7,6,8]=>1010010
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8]=>[5,1,3,4,2,7,6,8]=>1001010
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[5,2,1,4,3,7,6,8]=>1101010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[5,3,2,1,4,7,6,8]=>1110010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>1111010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>1011010
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[3,2,4,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>1101010
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[1,5,2,3,4,7,6,8]=>0100010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[1,4,5,3,2,7,6,8]=>[1,5,2,4,3,7,6,8]=>0101010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[1,5,3,2,4,7,6,8]=>0110010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>0111010
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]=>[1,2,5,3,4,7,6,8]=>0010010
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>1001010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>1101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>0101010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>0001010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>1000010
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[3,4,2,1,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>1010010
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[2,4,3,1,5,7,6,8]=>[4,2,1,3,5,7,6,8]=>1100010
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>1110010
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>1010010
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>0100010
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>0110010
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>0010010
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>1000010
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>0100010
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>1000010
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,1,2,3,4,5,7,8]=>1000000
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,1,2,3,5,4,7,8]=>1000100
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[6,1,2,4,5,3,7,8]=>1000100
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[3,5,4,6,2,1,7,8]=>[6,1,3,5,4,2,7,8]=>1001100
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[6,1,3,4,5,2,7,8]=>1000100
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[6,2,1,4,3,5,7,8]=>1101000
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[6,2,1,5,4,3,7,8]=>1101100
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>[6,2,1,4,5,3,7,8]=>1100100
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[2,3,6,5,4,1,7,8]=>[6,2,3,1,4,5,7,8]=>1010000
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[2,3,5,6,4,1,7,8]=>[6,2,3,1,5,4,7,8]=>1010100
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[6,4,3,2,1,5,7,8]=>1111000
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[2,4,3,6,5,1,7,8]=>[6,2,4,3,1,5,7,8]=>1011000
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>1100100
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>1101100
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[3,2,5,4,6,1,7,8]=>[6,3,2,5,4,1,7,8]=>1101100
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>1001100
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>1110100
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>1000100
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]=>[1,6,2,3,4,5,7,8]=>0100000
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>[1,6,2,4,3,5,7,8]=>0101000
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>[1,6,2,4,5,3,7,8]=>0100100
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[1,6,3,2,4,5,7,8]=>0110000
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[1,6,3,2,5,4,7,8]=>0110100
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[1,6,4,3,2,5,7,8]=>0111000
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[1,3,4,6,5,2,7,8]=>[1,6,3,4,2,5,7,8]=>0101000
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[1,4,5,3,6,2,7,8]=>[1,6,5,4,3,2,7,8]=>0111100
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[1,3,5,4,6,2,7,8]=>[1,6,3,5,4,2,7,8]=>0101100
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[1,4,3,5,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>0110100
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>0100100
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[2,1,6,4,3,5,7,8]=>1011000
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[1,2,6,3,4,5,7,8]=>0010000
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[1,2,6,3,5,4,7,8]=>0010100
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[1,2,6,4,3,5,7,8]=>0011000
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[1,2,5,4,6,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>0010100
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>1101100
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]=>[1,3,2,6,4,5,7,8]=>0101000
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>0101100
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[2,1,3,6,5,4,7,8]=>[2,1,3,6,4,5,7,8]=>1001000
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]=>[1,2,3,6,4,5,7,8]=>0001000
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>1000100
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[2,4,3,1,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>1100100
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>0100100
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>1010100
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>0010100
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>0100100
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>1000100
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>1010000
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,1,3,4,2,6,7,8]=>1001000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>1100000
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[5,2,1,4,3,6,7,8]=>1101000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>1110000
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>1010000
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>1101000
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>1011000
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>1101000
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>1001000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>0100000
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[1,4,5,3,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>0101000
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[1,5,3,2,4,6,7,8]=>0110000
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[1,4,3,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>0101000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[2,1,5,3,4,6,7,8]=>1010000
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>1011000
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>0010000
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>1101000
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>0101000
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1100000
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>1010000
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0100000
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>1010000
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,1,2,3,4,5,6,7,8]=>10000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,1,2,3,4,5,6,8,7]=>10000001
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,1,2,3,4,5,7,8,6]=>10000001
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[9,1,2,3,4,6,7,8,5]=>10000001
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[9,1,3,4,5,6,7,8,2]=>10000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>10000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[7,9,8,6,5,4,3,2,1]=>[9,1,2,3,4,5,7,6,8]=>10000010
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,8,9,7]=>100000001
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[10,1,2,3,4,5,7,8,9,6]=>100000001
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,1,2,3,4,6,7,8,9,5]=>100000001
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[2,4,5,6,7,8,9,3,1]=>[9,2,1,4,5,6,7,8,3]=>11000001
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,1,3,4,5,6,7,8,9,2]=>100000001
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>01000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>100000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,1,2,3,4,5,8,7,6]=>10000011
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,1,2,3,4,8,6,7,5]=>10000101
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,1,2,3,8,5,6,7,4]=>10001001
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,1,2,8,4,5,6,7,3]=>10010001
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,1,8,3,4,5,6,7,2]=>10100001
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,8,2,3,4,5,6,7,1]=>11000001
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,6,7,9]=>10000000
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,9,8,7]=>100000011
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,1,2,3,4,5,9,7,8,6]=>100000101
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[10,1,2,3,4,9,6,7,8,5]=>100001001
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[10,1,2,3,9,5,6,7,8,4]=>100010001
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[10,1,2,9,4,5,6,7,8,3]=>100100001
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,1,9,3,4,5,6,7,8,2]=>101000001
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]=>[1,8,2,3,4,5,6,7,9]=>01000000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,9,2,3,4,5,6,7,8,1]=>110000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>[1,5,6,4,7,3,9,10,8,2]=>[1,10,7,6,5,4,3,2,9,8]=>011111101
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[1,6,7,5,8,4,9,3,10,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]=>[2,3,1,7,8,6,9,5,10,4]=>[3,2,1,10,9,8,7,6,5,4]=>110111111
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>[3,4,2,5,1,8,9,7,10,6]=>[5,4,3,2,1,10,9,8,7,6]=>111101111
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]=>[4,5,3,6,2,7,1,9,10,8]=>[7,6,5,4,3,2,1,10,9,8]=>111111011
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]=>[2,6,7,5,8,4,9,3,1,10]=>[9,2,1,8,7,6,5,4,3,10]=>110111110
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>[1,7,8,6,9,5,10,4,11,3,12,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>01111111111
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[2,3,1,8,9,7,10,6,11,5,12,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>11011111111
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]=>[3,4,2,5,1,9,10,8,11,7,12,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>11110111111
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]=>[4,5,3,6,2,7,1,10,11,9,12,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>11111101111
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]=>[5,6,4,7,3,8,2,9,1,11,12,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>11111111011
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>11111111110
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>101010101
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>10000001
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>11000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>100000001
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>01000001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>11100001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>110000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>1000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>00000011
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>00000101
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>00001001
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>00010001
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>00100001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,7,8]=>00000010
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,8,7,6]=>00000111
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>000000101
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,9,7,6,8,5]=>00001101
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>000001001
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,3,6,5,7,8,9,4]=>[1,2,3,9,6,5,7,8,4]=>00011001
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>000010001
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[1,2,5,4,6,7,8,9,3]=>[1,2,9,5,4,6,7,8,3]=>00110001
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>000100001
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>[1,9,4,3,5,6,7,8,2]=>01100001
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>001000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>010000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>01000000
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,8,7]=>01000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>1000000000
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,1,2,3,4,5,6,8,7,10]=>100000010
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[8,1,2,3,4,7,6,5,9]=>10000110
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>[1,9,2,3,4,5,8,7,6]=>01000011
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,9,8]=>010000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>0100000000
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,8,3,9,2,10,1]=>[10,9,8,5,4,7,6,3,2,1]=>111101111
[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,7,6,8,5,9,2,10,1]=>[10,9,4,3,8,7,6,5,2,1]=>111011111
[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,9,2,10,1]=>[10,9,6,5,4,3,8,7,2,1]=>111110111
[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,9,2,10,1]=>[10,9,4,3,6,5,8,7,2,1]=>111010111
[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,7,6,8,5,9,4,10,1]=>[10,3,2,9,8,7,6,5,4,1]=>110111111
[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,9,4,10,1]=>[10,3,2,9,6,5,8,7,4,1]=>110110111
[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,8,7,9,6,10,1]=>[10,5,4,3,2,9,8,7,6,1]=>111101111
[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,8,7,9,6,10,1]=>[10,3,2,5,4,9,8,7,6,1]=>110101111
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,10,1]=>[10,7,6,5,4,3,2,9,8,1]=>111111011
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,10,1]=>[10,7,4,3,6,5,2,9,8,1]=>111011011
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[3,2,6,5,7,4,9,8,10,1]=>[10,3,2,7,6,5,4,9,8,1]=>110111011
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[4,3,5,2,7,6,9,8,10,1]=>[10,5,4,3,2,7,6,9,8,1]=>111101011
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,10,1]=>[10,3,2,5,4,7,6,9,8,1]=>110101011
[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,7,6,8,5,9,4,10,3]=>[2,1,10,9,8,7,6,5,4,3]=>101111111
[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,6,5,8,7,9,4,10,3]=>[2,1,10,9,6,5,8,7,4,3]=>101110111
[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,5,4,8,7,9,6,10,3]=>[2,1,10,5,4,9,8,7,6,3]=>101101111
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,10,3]=>[2,1,10,7,6,5,4,9,8,3]=>101111011
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,10,3]=>[2,1,10,5,4,7,6,9,8,3]=>101101011
[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,8,7,9,6,10,5]=>[4,3,2,1,10,9,8,7,6,5]=>111011111
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,10,5]=>[4,3,2,1,10,7,6,9,8,5]=>111011011
[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,8,7,9,6,10,5]=>[2,1,4,3,10,9,8,7,6,5]=>101011111
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,10,5]=>[2,1,4,3,10,7,6,9,8,5]=>101011011
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,9,8,10,7]=>[6,5,4,3,2,1,10,9,8,7]=>111110111
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,9,8,10,7]=>[6,3,2,5,4,1,10,9,8,7]=>110110111
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,9,8,10,7]=>[2,1,6,5,4,3,10,9,8,7]=>101110111
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,9,8,10,7]=>[4,3,2,1,6,5,10,9,8,7]=>111010111
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,9,8,10,7]=>[2,1,4,3,6,5,10,9,8,7]=>101010111
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>111111101
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9]=>[8,7,4,3,6,5,2,1,10,9]=>111011101
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9]=>[8,3,2,7,6,5,4,1,10,9]=>110111101
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[4,3,5,2,7,6,8,1,10,9]=>[8,5,4,3,2,7,6,1,10,9]=>111101101
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,7,6,8,1,10,9]=>[8,3,2,5,4,7,6,1,10,9]=>110101101
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>101111101
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[2,1,5,4,7,6,8,3,10,9]=>[2,1,8,5,4,7,6,3,10,9]=>101101101
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,7,6,8,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>111011101
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,4,3,7,6,8,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>101011101
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,5,2,6,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>111110101
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,6,1,8,7,10,9]=>[6,3,2,5,4,1,8,7,10,9]=>110110101
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[2,1,5,4,6,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>101110101
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>111010101
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111
[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>11111011111
[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>11110111111
[.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>[12,11,10,7,6,5,4,9,8,3,2,1]=>11111101111
[.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>[12,11,10,5,4,7,6,9,8,3,2,1]=>11110101111
[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>11101111111
[.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>[12,11,4,3,10,7,6,9,8,5,2,1]=>11101101111
[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>11111011111
[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>[12,11,4,3,6,5,10,9,8,7,2,1]=>11101011111
[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>[12,11,8,7,6,5,4,3,10,9,2,1]=>11111110111
[.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>[12,11,8,5,4,7,6,3,10,9,2,1]=>11110110111
[.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>[12,11,4,3,8,7,6,5,10,9,2,1]=>11101110111
[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>[12,11,6,5,4,3,8,7,10,9,2,1]=>11111010111
[.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>[12,11,4,3,6,5,8,7,10,9,2,1]=>11101010111
[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>11011111111
[.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>[12,3,2,11,10,7,6,9,8,5,4,1]=>11011101111
[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>[12,3,2,11,6,5,10,9,8,7,4,1]=>11011011111
[.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>[12,3,2,11,8,7,6,5,10,9,4,1]=>11011110111
[.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>[12,3,2,11,6,5,8,7,10,9,4,1]=>11011010111
[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>[12,5,4,3,2,11,10,9,8,7,6,1]=>11110111111
[.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>[12,5,4,3,2,11,8,7,10,9,6,1]=>11110110111
[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>[12,3,2,5,4,11,10,9,8,7,6,1]=>11010111111
[.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>[12,3,2,5,4,11,8,7,10,9,6,1]=>11010110111
[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>[12,7,6,5,4,3,2,11,10,9,8,1]=>11111101111
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>[12,7,4,3,6,5,2,11,10,9,8,1]=>11101101111
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>[12,3,2,7,6,5,4,11,10,9,8,1]=>11011101111
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>[12,5,4,3,2,7,6,11,10,9,8,1]=>11110101111
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>[12,3,2,5,4,7,6,11,10,9,8,1]=>11010101111
[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>[12,9,8,7,6,5,4,3,2,11,10,1]=>11111111011
[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>[12,9,8,5,4,7,6,3,2,11,10,1]=>11110111011
[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>[12,9,4,3,8,7,6,5,2,11,10,1]=>11101111011
[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>[12,9,6,5,4,3,8,7,2,11,10,1]=>11111011011
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>[12,9,4,3,6,5,8,7,2,11,10,1]=>11101011011
[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>[12,3,2,9,8,7,6,5,4,11,10,1]=>11011111011
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>[12,3,2,9,6,5,8,7,4,11,10,1]=>11011011011
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>[12,5,4,3,2,9,8,7,6,11,10,1]=>11110111011
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>[12,3,2,5,4,9,8,7,6,11,10,1]=>11010111011
[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>[12,7,6,5,4,3,2,9,8,11,10,1]=>11111101011
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>[12,7,4,3,6,5,2,9,8,11,10,1]=>11101101011
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>[12,3,2,7,6,5,4,9,8,11,10,1]=>11011101011
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>[12,5,4,3,2,7,6,9,8,11,10,1]=>11110101011
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>11010101011
[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>10111111111
[[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>[2,1,12,11,10,7,6,9,8,5,4,3]=>10111101111
[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>[2,1,12,11,6,5,10,9,8,7,4,3]=>10111011111
[[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>[2,1,12,11,8,7,6,5,10,9,4,3]=>10111110111
[[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>[2,1,12,11,6,5,8,7,10,9,4,3]=>10111010111
[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>[2,1,12,5,4,11,10,9,8,7,6,3]=>10110111111
[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>[2,1,12,5,4,11,8,7,10,9,6,3]=>10110110111
[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>[2,1,12,7,6,5,4,11,10,9,8,3]=>10111101111
[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>[2,1,12,5,4,7,6,11,10,9,8,3]=>10110101111
[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>[2,1,12,9,8,7,6,5,4,11,10,3]=>10111111011
[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>[2,1,12,9,6,5,8,7,4,11,10,3]=>10111011011
[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>[2,1,12,5,4,9,8,7,6,11,10,3]=>10110111011
[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>[2,1,12,7,6,5,4,9,8,11,10,3]=>10111101011
[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>[2,1,12,5,4,7,6,9,8,11,10,3]=>10110101011
[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>11101111111
[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>[4,3,2,1,12,11,8,7,10,9,6,5]=>11101110111
[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>[4,3,2,1,12,7,6,11,10,9,8,5]=>11101101111
[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>[4,3,2,1,12,9,8,7,6,11,10,5]=>11101111011
[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>[4,3,2,1,12,7,6,9,8,11,10,5]=>11101101011
[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>10101111111
[[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>[2,1,4,3,12,11,8,7,10,9,6,5]=>10101110111
[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>[2,1,4,3,12,7,6,11,10,9,8,5]=>10101101111
[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>[2,1,4,3,12,9,8,7,6,11,10,5]=>10101111011
[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>[2,1,4,3,12,7,6,9,8,11,10,5]=>10101101011
[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>11111011111
[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>[6,5,4,3,2,1,12,9,8,11,10,7]=>11111011011
[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>[6,3,2,5,4,1,12,11,10,9,8,7]=>11011011111
[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>[6,3,2,5,4,1,12,9,8,11,10,7]=>11011011011
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>10111011111
[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>[2,1,6,5,4,3,12,9,8,11,10,7]=>10111011011
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>11101011111
[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>[4,3,2,1,6,5,12,9,8,11,10,7]=>11101011011
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>10101011111
[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>[2,1,4,3,6,5,12,9,8,11,10,7]=>10101011011
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>11111110111
[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>[8,7,4,3,6,5,2,1,12,11,10,9]=>11101110111
[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>[8,3,2,7,6,5,4,1,12,11,10,9]=>11011110111
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,7,6,8,1,11,10,12,9]=>[8,5,4,3,2,7,6,1,12,11,10,9]=>11110110111
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>[8,3,2,5,4,7,6,1,12,11,10,9]=>11010110111
[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>10111110111
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>[2,1,8,5,4,7,6,3,12,11,10,9]=>10110110111
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>11101110111
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>10101110111
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>11111010111
[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>[6,3,2,5,4,1,8,7,12,11,10,9]=>11011010111
[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>10111010111
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>11101010111
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>10101010111
[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>11111111101
[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>[10,9,8,5,4,7,6,3,2,1,12,11]=>11110111101
[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>[10,9,4,3,8,7,6,5,2,1,12,11]=>11101111101
[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>[10,9,6,5,4,3,8,7,2,1,12,11]=>11111011101
[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>[10,9,4,3,6,5,8,7,2,1,12,11]=>11101011101
[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>[10,3,2,9,8,7,6,5,4,1,12,11]=>11011111101
[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>[10,3,2,9,6,5,8,7,4,1,12,11]=>11011011101
[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>[10,5,4,3,2,9,8,7,6,1,12,11]=>11110111101
[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>[10,3,2,5,4,9,8,7,6,1,12,11]=>11010111101
[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>[10,7,6,5,4,3,2,9,8,1,12,11]=>11111101101
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>[4,3,6,5,7,2,9,8,10,1,12,11]=>[10,7,4,3,6,5,2,9,8,1,12,11]=>11101101101
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[3,2,6,5,7,4,9,8,10,1,12,11]=>[10,3,2,7,6,5,4,9,8,1,12,11]=>11011101101
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>[4,3,5,2,7,6,9,8,10,1,12,11]=>[10,5,4,3,2,7,6,9,8,1,12,11]=>11110101101
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>[10,3,2,5,4,7,6,9,8,1,12,11]=>11010101101
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>10111111101
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>[2,1,10,9,6,5,8,7,4,3,12,11]=>10111011101
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>[2,1,10,5,4,9,8,7,6,3,12,11]=>10110111101
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>[2,1,10,7,6,5,4,9,8,3,12,11]=>10111101101
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>[2,1,10,5,4,7,6,9,8,3,12,11]=>10110101101
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>11101111101
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>[4,3,2,1,10,7,6,9,8,5,12,11]=>11101101101
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>10101111101
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>[2,1,4,3,10,7,6,9,8,5,12,11]=>10101101101
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>11111011101
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>[6,3,2,5,4,1,10,9,8,7,12,11]=>11011011101
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>10111011101
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>11101011101
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>10101011101
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>11111110101
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>[8,7,4,3,6,5,2,1,10,9,12,11]=>11101110101
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>[8,3,2,7,6,5,4,1,10,9,12,11]=>11011110101
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>[4,3,5,2,7,6,8,1,10,9,12,11]=>[8,5,4,3,2,7,6,1,10,9,12,11]=>11110110101
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>[8,3,2,5,4,7,6,1,10,9,12,11]=>11010110101
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>10111110101
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>[2,1,8,5,4,7,6,3,10,9,12,11]=>10110110101
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>11101110101
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>10101110101
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>[4,3,5,2,6,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>11111010101
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>[6,3,2,5,4,1,8,7,10,9,12,11]=>11011010101
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>10111010101
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>11101010101
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,3,4,5,6,7,8]=>10100000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]=>[3,1,2,9,4,5,6,7,8]=>10010000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]=>[4,1,2,3,9,5,6,7,8]=>10001000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]=>[5,1,2,3,4,9,6,7,8]=>10000100
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]=>[6,1,2,3,4,5,9,7,8]=>10000010
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]=>[7,1,2,3,4,5,6,9,8]=>10000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]=>[1,2,9,3,4,5,6,7,8]=>00100000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,3,4,5,6,7,8,9]=>101000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]=>[3,1,2,10,4,5,6,7,8,9]=>100100000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[4,1,2,3,10,5,6,7,8,9]=>100010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]=>[5,1,2,3,4,10,6,7,8,9]=>100001000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[6,1,2,3,4,5,10,7,8,9]=>100000100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]=>[7,1,2,3,4,5,6,10,8,9]=>100000010
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[8,1,2,3,4,5,6,7,10,9]=>100000001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>10000000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>10000000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>10000000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>100000000
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>100000000
[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,7,6,5,4,3,2,8,9]=>[1,7,2,3,4,5,6,8,9]=>01000000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>100000000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>100000000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>100000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>01000000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>100000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>01000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[3,9,8,7,6,5,4,2,1]=>[9,1,3,2,4,5,6,7,8]=>10100000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1]=>[9,2,1,3,4,5,6,7,8]=>11000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[6,10,9,8,7,5,4,3,2,1]=>[10,1,2,3,4,6,5,7,8,9]=>100001000
[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7,10,9]=>[4,2,1,3,6,5,8,7,10,9]=>110010101
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,9,8,1]=>[9,2,3,4,5,6,7,1,8]=>10000010
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>10000010
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[2,3,4,5,6,8,9,7,1]=>[9,2,3,4,5,6,1,8,7]=>10000101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,7,8,10,9,1]=>[10,2,3,4,5,6,7,8,1,9]=>100000010
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>10100000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>10000010
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>10000100
[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>100000010
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>00100000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>00010000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>00001000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>00000100
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>00000010
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>001000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>000100000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>000010000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>000001000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>000000100
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>000000010
[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1]=>[9,4,2,3,5,6,7,8,1]=>11000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>[1,7,2,3,4,5,6,9,8]=>01000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7]=>[6,1,2,3,4,5,9,8,7]=>10000011
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]=>[1,2,10,3,4,5,6,7,8,9]=>001000000
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>[2,1,8,3,4,5,6,7,9]=>10100000
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[1,9,2,3,4,5,6,7,8,10]=>010000000
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>01010000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>10100001
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,10,8,9]=>000000010
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,9,6,7,8]=>00000100
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,9,5,6,7,8]=>00001000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]=>[1,2,3,9,4,5,6,7,8]=>00010000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>00000101
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,10,7,8,9]=>000000100
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,10,6,7,8,9]=>000001000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,10,5,6,7,8,9]=>000010000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]=>[1,2,3,10,4,5,6,7,8,9]=>000100000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>000000101
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000
[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9,10]=>[4,1,3,2,5,6,7,8,9,10]=>101000000
[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000
[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>11010000
[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[9,2,3,1,4,5,6,7,8]=>10100000
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[8,2,1,3,4,5,6,7,9]=>11000000
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>10000101
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>01100000
[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,4,5,6,7,8,3,9,2]=>[1,9,8,4,5,6,7,3,2]=>01100011
[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>0000000010
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
searching the database
Sorry, this map was not found in the database.