Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00252: Permutations —restriction⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[]=>
[.,[.,.]]=>[2,1]=>[1]=>
[[.,.],.]=>[1,2]=>[1]=>
[.,[.,[.,.]]]=>[3,2,1]=>[2,1]=>1
[.,[[.,.],.]]=>[2,3,1]=>[2,1]=>1
[[.,.],[.,.]]=>[3,1,2]=>[1,2]=>0
[[.,[.,.]],.]=>[2,1,3]=>[2,1]=>1
[[[.,.],.],.]=>[1,2,3]=>[1,2]=>0
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[3,2,1]=>11
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,2,1]=>11
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[2,3,1]=>01
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,1]=>11
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,1]=>01
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,2]=>01
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[3,1,2]=>01
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,1,3]=>10
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,2,3]=>00
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1]=>11
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1]=>01
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2]=>01
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3]=>10
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3]=>00
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[4,3,2,1]=>111
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,3,2,1]=>111
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[3,4,2,1]=>101
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,2,1]=>111
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,2,1]=>101
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[4,2,3,1]=>011
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[4,2,3,1]=>011
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[3,2,4,1]=>011
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[2,3,4,1]=>001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,1]=>111
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,1]=>101
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[4,2,3,1]=>011
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,1]=>011
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,1]=>001
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[4,3,1,2]=>011
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[4,3,1,2]=>011
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[3,4,1,2]=>001
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[4,3,1,2]=>011
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,4,1,2]=>001
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,2,1,3]=>101
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,2,1,3]=>101
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,3]=>001
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[4,1,2,3]=>001
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[3,2,1,4]=>110
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[2,3,1,4]=>010
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,2,4]=>010
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,1,3,4]=>100
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,2,3,4]=>000
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1]=>111
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1]=>101
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,2,3,1]=>011
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1]=>011
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1]=>001
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[4,3,1,2]=>011
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,4,1,2]=>001
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[4,2,1,3]=>101
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3]=>001
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4]=>110
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4]=>010
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4]=>010
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4]=>100
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4]=>000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>1111
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,4,3,2,1]=>1111
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[4,5,3,2,1]=>1101
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,3,2,1]=>1111
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,3,2,1]=>1101
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[5,3,4,2,1]=>1011
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[5,3,4,2,1]=>1011
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[4,3,5,2,1]=>1011
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[3,4,5,2,1]=>1001
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,2,1]=>1111
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,2,1]=>1101
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[5,3,4,2,1]=>1011
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,2,1]=>1011
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,2,1]=>1001
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[5,4,2,3,1]=>0111
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[5,4,2,3,1]=>0111
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[4,5,2,3,1]=>0101
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[5,4,2,3,1]=>0111
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[4,5,2,3,1]=>0101
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[5,3,2,4,1]=>0111
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[5,3,2,4,1]=>0111
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[5,2,3,4,1]=>0011
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[5,2,3,4,1]=>0011
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[4,3,2,5,1]=>0111
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[3,4,2,5,1]=>0011
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[4,2,3,5,1]=>0011
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[3,2,4,5,1]=>0101
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[2,3,4,5,1]=>0001
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,1]=>1111
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,1]=>1101
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[5,3,4,2,1]=>1011
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,1]=>1011
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,1]=>1001
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[5,4,2,3,1]=>0111
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[4,5,2,3,1]=>0101
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[5,3,2,4,1]=>0111
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[5,2,3,4,1]=>0011
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,1]=>0111
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,1]=>0011
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[4,2,3,5,1]=>0011
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,1]=>0101
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,1]=>0001
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[5,4,3,1,2]=>0111
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[5,4,3,1,2]=>0111
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[4,5,3,1,2]=>0101
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[5,4,3,1,2]=>0111
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[4,5,3,1,2]=>0101
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[5,3,4,1,2]=>0011
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[5,3,4,1,2]=>0011
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[4,3,5,1,2]=>0011
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[3,4,5,1,2]=>0001
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[5,4,3,1,2]=>0111
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[4,5,3,1,2]=>0101
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[5,3,4,1,2]=>0011
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[4,3,5,1,2]=>0011
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[3,4,5,1,2]=>0001
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,4,2,1,3]=>1011
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,4,2,1,3]=>1011
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[4,5,2,1,3]=>1001
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,4,2,1,3]=>1011
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[4,5,2,1,3]=>1001
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[5,4,1,2,3]=>0011
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[5,4,1,2,3]=>0011
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[4,5,1,2,3]=>0001
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[5,4,1,2,3]=>0011
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[4,5,1,2,3]=>0001
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,3,2,1,4]=>1101
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,3,2,1,4]=>1101
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,2,3,1,4]=>0101
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,2,3,1,4]=>0101
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[5,3,1,2,4]=>0101
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[5,3,1,2,4]=>0101
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[5,2,1,3,4]=>1001
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[5,2,1,3,4]=>1001
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,4]=>0001
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[5,1,2,3,4]=>0001
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[4,3,2,1,5]=>1110
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[3,4,2,1,5]=>1010
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[4,2,3,1,5]=>0110
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[3,2,4,1,5]=>0110
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[2,3,4,1,5]=>0010
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[4,3,1,2,5]=>0110
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[3,4,1,2,5]=>0010
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,2,1,3,5]=>1010
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,3,5]=>0010
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[3,2,1,4,5]=>1100
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[2,3,1,4,5]=>0100
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,2,4,5]=>0100
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,1,3,4,5]=>1000
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,2,3,4,5]=>0000
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1]=>1111
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1]=>1101
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,3,4,2,1]=>1011
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1]=>1011
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1]=>1001
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,4,2,3,1]=>0111
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[4,5,2,3,1]=>0101
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,2,4,1]=>0111
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,2,3,4,1]=>0011
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1]=>0111
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1]=>0011
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[4,2,3,5,1]=>0011
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1]=>0101
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1]=>0001
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[5,4,3,1,2]=>0111
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[4,5,3,1,2]=>0101
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[5,3,4,1,2]=>0011
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[4,3,5,1,2]=>0011
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,4,5,1,2]=>0001
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[5,4,2,1,3]=>1011
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,5,2,1,3]=>1001
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[5,4,1,2,3]=>0011
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[4,5,1,2,3]=>0001
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[5,3,2,1,4]=>1101
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[5,2,3,1,4]=>0101
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[5,3,1,2,4]=>0101
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[5,2,1,3,4]=>1001
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4]=>0001
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5]=>1110
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5]=>1010
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,2,3,1,5]=>0110
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5]=>0110
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5]=>0010
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[4,3,1,2,5]=>0110
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[3,4,1,2,5]=>0010
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[4,2,1,3,5]=>1010
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5]=>0010
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5]=>1100
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5]=>0100
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5]=>0100
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5]=>1000
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5]=>0000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[5,6,4,3,2,1]=>11101
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,4,3,2,1]=>11101
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[6,4,5,3,2,1]=>11011
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[6,4,5,3,2,1]=>11011
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[5,4,6,3,2,1]=>11011
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[4,5,6,3,2,1]=>11001
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,3,2,1]=>11101
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[6,4,5,3,2,1]=>11011
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,3,2,1]=>11011
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,3,2,1]=>11001
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[6,5,3,4,2,1]=>10111
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[6,5,3,4,2,1]=>10111
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[5,6,3,4,2,1]=>10101
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[6,5,3,4,2,1]=>10111
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[5,6,3,4,2,1]=>10101
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[6,4,3,5,2,1]=>10111
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[6,4,3,5,2,1]=>10111
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[6,3,4,5,2,1]=>10011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[6,3,4,5,2,1]=>10011
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[5,4,3,6,2,1]=>10111
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[4,5,3,6,2,1]=>10011
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[5,3,4,6,2,1]=>10011
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[4,3,5,6,2,1]=>10101
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[3,4,5,6,2,1]=>10001
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,2,1]=>11101
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[6,4,5,3,2,1]=>11011
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,2,1]=>11011
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,2,1]=>11001
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[6,5,3,4,2,1]=>10111
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[5,6,3,4,2,1]=>10101
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[6,4,3,5,2,1]=>10111
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[6,3,4,5,2,1]=>10011
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,2,1]=>10111
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,2,1]=>10011
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[5,3,4,6,2,1]=>10011
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,2,1]=>10101
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,2,1]=>10001
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[6,5,4,2,3,1]=>01111
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[6,5,4,2,3,1]=>01111
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[5,6,4,2,3,1]=>01101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[6,5,4,2,3,1]=>01111
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[5,6,4,2,3,1]=>01101
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[6,4,5,2,3,1]=>01011
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[6,4,5,2,3,1]=>01011
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[5,4,6,2,3,1]=>01011
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[4,5,6,2,3,1]=>01001
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[6,5,4,2,3,1]=>01111
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[5,6,4,2,3,1]=>01101
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[6,4,5,2,3,1]=>01011
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[5,4,6,2,3,1]=>01011
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,5,6,2,3,1]=>01001
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[6,5,3,2,4,1]=>01111
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[6,5,3,2,4,1]=>01111
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[5,6,3,2,4,1]=>01101
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[6,5,3,2,4,1]=>01111
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[5,6,3,2,4,1]=>01101
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[6,5,2,3,4,1]=>00111
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[6,5,2,3,4,1]=>00111
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[5,6,2,3,4,1]=>00101
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[6,5,2,3,4,1]=>00111
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[5,6,2,3,4,1]=>00101
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[6,4,3,2,5,1]=>01111
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[6,4,3,2,5,1]=>01111
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[6,3,4,2,5,1]=>00111
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[6,3,4,2,5,1]=>00111
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[6,4,2,3,5,1]=>00111
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[6,4,2,3,5,1]=>00111
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[6,3,2,4,5,1]=>01011
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[6,3,2,4,5,1]=>01011
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[6,2,3,4,5,1]=>00011
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[6,2,3,4,5,1]=>00011
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[5,4,3,2,6,1]=>01111
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[4,5,3,2,6,1]=>01011
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[5,3,4,2,6,1]=>00111
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[4,3,5,2,6,1]=>00111
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[3,4,5,2,6,1]=>00011
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[5,4,2,3,6,1]=>00111
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[4,5,2,3,6,1]=>00011
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[5,3,2,4,6,1]=>01011
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[5,2,3,4,6,1]=>00011
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[4,3,2,5,6,1]=>01101
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[3,4,2,5,6,1]=>00101
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[4,2,3,5,6,1]=>00101
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,1]=>01001
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,1]=>00001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,1]=>11111
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,1]=>11101
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[6,4,5,3,2,1]=>11011
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,1]=>11011
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,1]=>11001
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[6,5,3,4,2,1]=>10111
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[5,6,3,4,2,1]=>10101
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[6,4,3,5,2,1]=>10111
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[6,3,4,5,2,1]=>10011
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,1]=>10111
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,1]=>10011
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[5,3,4,6,2,1]=>10011
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,1]=>10101
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,1]=>10001
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[6,5,4,2,3,1]=>01111
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[5,6,4,2,3,1]=>01101
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[6,4,5,2,3,1]=>01011
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[5,4,6,2,3,1]=>01011
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[4,5,6,2,3,1]=>01001
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[6,5,3,2,4,1]=>01111
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[5,6,3,2,4,1]=>01101
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[6,5,2,3,4,1]=>00111
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[5,6,2,3,4,1]=>00101
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[6,4,3,2,5,1]=>01111
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[6,3,4,2,5,1]=>00111
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[6,4,2,3,5,1]=>00111
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[6,3,2,4,5,1]=>01011
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[6,2,3,4,5,1]=>00011
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,1]=>01111
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,1]=>01011
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[5,3,4,2,6,1]=>00111
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,1]=>00111
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,1]=>00011
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[5,4,2,3,6,1]=>00111
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[4,5,2,3,6,1]=>00011
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[5,3,2,4,6,1]=>01011
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[5,2,3,4,6,1]=>00011
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,1]=>01101
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,1]=>00101
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[4,2,3,5,6,1]=>00101
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,1]=>01001
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,1]=>00001
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[6,5,4,3,1,2]=>01111
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[6,5,4,3,1,2]=>01111
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[5,6,4,3,1,2]=>01101
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[6,5,4,3,1,2]=>01111
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[5,6,4,3,1,2]=>01101
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[6,4,5,3,1,2]=>01011
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[6,4,5,3,1,2]=>01011
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[5,4,6,3,1,2]=>01011
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[4,5,6,3,1,2]=>01001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[6,5,4,3,1,2]=>01111
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[5,6,4,3,1,2]=>01101
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[6,4,5,3,1,2]=>01011
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[5,4,6,3,1,2]=>01011
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,5,6,3,1,2]=>01001
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[6,5,3,4,1,2]=>00111
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[6,5,3,4,1,2]=>00111
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[5,6,3,4,1,2]=>00101
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[6,5,3,4,1,2]=>00111
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[5,6,3,4,1,2]=>00101
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[6,4,3,5,1,2]=>00111
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[6,4,3,5,1,2]=>00111
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[6,3,4,5,1,2]=>00011
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[6,3,4,5,1,2]=>00011
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[5,4,3,6,1,2]=>00111
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[4,5,3,6,1,2]=>00011
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[5,3,4,6,1,2]=>00011
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[4,3,5,6,1,2]=>00101
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[3,4,5,6,1,2]=>00001
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[6,5,4,3,1,2]=>01111
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[5,6,4,3,1,2]=>01101
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[6,4,5,3,1,2]=>01011
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[5,4,6,3,1,2]=>01011
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[4,5,6,3,1,2]=>01001
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[6,5,3,4,1,2]=>00111
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[5,6,3,4,1,2]=>00101
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[6,4,3,5,1,2]=>00111
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[6,3,4,5,1,2]=>00011
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[5,4,3,6,1,2]=>00111
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[4,5,3,6,1,2]=>00011
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[5,3,4,6,1,2]=>00011
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[4,3,5,6,1,2]=>00101
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[3,4,5,6,1,2]=>00001
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,5,4,2,1,3]=>10111
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,5,4,2,1,3]=>10111
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[5,6,4,2,1,3]=>10101
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,5,4,2,1,3]=>10111
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[5,6,4,2,1,3]=>10101
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,4,5,2,1,3]=>10011
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,4,5,2,1,3]=>10011
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[5,4,6,2,1,3]=>10011
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[4,5,6,2,1,3]=>10001
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,5,4,2,1,3]=>10111
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[5,6,4,2,1,3]=>10101
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,4,5,2,1,3]=>10011
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[5,4,6,2,1,3]=>10011
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,5,6,2,1,3]=>10001
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[6,5,4,1,2,3]=>00111
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[6,5,4,1,2,3]=>00111
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[5,6,4,1,2,3]=>00101
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[6,5,4,1,2,3]=>00111
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[5,6,4,1,2,3]=>00101
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[6,4,5,1,2,3]=>00011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[6,4,5,1,2,3]=>00011
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[5,4,6,1,2,3]=>00011
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[4,5,6,1,2,3]=>00001
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[6,5,4,1,2,3]=>00111
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[5,6,4,1,2,3]=>00101
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[6,4,5,1,2,3]=>00011
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[5,4,6,1,2,3]=>00011
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,5,6,1,2,3]=>00001
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,3,2,1,4]=>11011
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,3,2,1,4]=>11011
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[5,6,3,2,1,4]=>11001
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,3,2,1,4]=>11011
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[5,6,3,2,1,4]=>11001
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,5,2,3,1,4]=>01011
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,5,2,3,1,4]=>01011
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[5,6,2,3,1,4]=>01001
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,5,2,3,1,4]=>01011
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[5,6,2,3,1,4]=>01001
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[6,5,3,1,2,4]=>01011
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[6,5,3,1,2,4]=>01011
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[5,6,3,1,2,4]=>01001
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[6,5,3,1,2,4]=>01011
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[5,6,3,1,2,4]=>01001
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[6,5,2,1,3,4]=>10011
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[6,5,2,1,3,4]=>10011
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,6,2,1,3,4]=>10001
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[6,5,2,1,3,4]=>10011
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,6,2,1,3,4]=>10001
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[6,5,1,2,3,4]=>00011
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[6,5,1,2,3,4]=>00011
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[5,6,1,2,3,4]=>00001
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[6,5,1,2,3,4]=>00011
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[5,6,1,2,3,4]=>00001
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,4,3,2,1,5]=>11101
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,4,3,2,1,5]=>11101
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,3,4,2,1,5]=>10101
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,3,4,2,1,5]=>10101
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,4,2,3,1,5]=>01101
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,4,2,3,1,5]=>01101
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,3,2,4,1,5]=>01101
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,3,2,4,1,5]=>01101
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,2,3,4,1,5]=>00101
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,2,3,4,1,5]=>00101
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[6,4,3,1,2,5]=>01101
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[6,4,3,1,2,5]=>01101
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[6,3,4,1,2,5]=>00101
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[6,3,4,1,2,5]=>00101
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[6,4,2,1,3,5]=>10101
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[6,4,2,1,3,5]=>10101
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[6,4,1,2,3,5]=>00101
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[6,4,1,2,3,5]=>00101
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[6,3,2,1,4,5]=>11001
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[6,3,2,1,4,5]=>11001
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[6,2,3,1,4,5]=>01001
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[6,2,3,1,4,5]=>01001
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[6,3,1,2,4,5]=>01001
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[6,3,1,2,4,5]=>01001
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[6,2,1,3,4,5]=>10001
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[6,2,1,3,4,5]=>10001
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,5]=>00001
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[6,1,2,3,4,5]=>00001
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[4,5,3,2,1,6]=>11010
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[5,3,4,2,1,6]=>10110
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[4,3,5,2,1,6]=>10110
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[3,4,5,2,1,6]=>10010
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[5,4,2,3,1,6]=>01110
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[4,5,2,3,1,6]=>01010
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[5,3,2,4,1,6]=>01110
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[5,2,3,4,1,6]=>00110
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[4,3,2,5,1,6]=>01110
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[3,4,2,5,1,6]=>00110
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[4,2,3,5,1,6]=>00110
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[3,2,4,5,1,6]=>01010
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[2,3,4,5,1,6]=>00010
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[5,4,3,1,2,6]=>01110
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[4,5,3,1,2,6]=>01010
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[5,3,4,1,2,6]=>00110
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[4,3,5,1,2,6]=>00110
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[3,4,5,1,2,6]=>00010
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,4,2,1,3,6]=>10110
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[4,5,2,1,3,6]=>10010
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[5,4,1,2,3,6]=>00110
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[4,5,1,2,3,6]=>00010
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,3,2,1,4,6]=>11010
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,2,3,1,4,6]=>01010
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[5,3,1,2,4,6]=>01010
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[5,2,1,3,4,6]=>10010
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,4,6]=>00010
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[3,4,2,1,5,6]=>10100
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[4,2,3,1,5,6]=>01100
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[3,2,4,1,5,6]=>01100
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[2,3,4,1,5,6]=>00100
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,3,1,2,5,6]=>01100
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[3,4,1,2,5,6]=>00100
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,2,1,3,5,6]=>10100
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,3,5,6]=>00100
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[2,3,1,4,5,6]=>01000
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,2,4,5,6]=>01000
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1]=>11111
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1]=>11101
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,4,5,3,2,1]=>11011
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1]=>11011
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1]=>11001
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1]=>10111
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[5,6,3,4,2,1]=>10101
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,4,3,5,2,1]=>10111
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,3,4,5,2,1]=>10011
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1]=>10111
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1]=>10011
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[5,3,4,6,2,1]=>10011
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1]=>10101
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1]=>10001
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,5,4,2,3,1]=>01111
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[5,6,4,2,3,1]=>01101
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1]=>01011
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[5,4,6,2,3,1]=>01011
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[4,5,6,2,3,1]=>01001
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,5,3,2,4,1]=>01111
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[5,6,3,2,4,1]=>01101
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,5,2,3,4,1]=>00111
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[5,6,2,3,4,1]=>00101
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1]=>01111
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,3,4,2,5,1]=>00111
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,4,2,3,5,1]=>00111
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1]=>01011
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1]=>00011
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1]=>01111
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1]=>01011
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[5,3,4,2,6,1]=>00111
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1]=>00111
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1]=>00011
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[5,4,2,3,6,1]=>00111
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[4,5,2,3,6,1]=>00011
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[5,3,2,4,6,1]=>01011
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[5,2,3,4,6,1]=>00011
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1]=>01101
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1]=>00101
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[4,2,3,5,6,1]=>00101
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1]=>01001
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1]=>00001
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[6,5,4,3,1,2]=>01111
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[5,6,4,3,1,2]=>01101
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[6,4,5,3,1,2]=>01011
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[5,4,6,3,1,2]=>01011
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[4,5,6,3,1,2]=>01001
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[6,5,3,4,1,2]=>00111
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2]=>00101
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[6,4,3,5,1,2]=>00111
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[6,3,4,5,1,2]=>00011
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[5,4,3,6,1,2]=>00111
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[4,5,3,6,1,2]=>00011
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[5,3,4,6,1,2]=>00011
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[4,3,5,6,1,2]=>00101
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[3,4,5,6,1,2]=>00001
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[6,5,4,2,1,3]=>10111
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,6,4,2,1,3]=>10101
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[6,4,5,2,1,3]=>10011
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3]=>10011
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[4,5,6,2,1,3]=>10001
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[6,5,4,1,2,3]=>00111
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[5,6,4,1,2,3]=>00101
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[6,4,5,1,2,3]=>00011
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[5,4,6,1,2,3]=>00011
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3]=>00001
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[6,5,3,2,1,4]=>11011
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,6,3,2,1,4]=>11001
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[6,5,2,3,1,4]=>01011
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,6,2,3,1,4]=>01001
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[6,5,3,1,2,4]=>01011
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[5,6,3,1,2,4]=>01001
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[6,5,2,1,3,4]=>10011
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[5,6,2,1,3,4]=>10001
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[6,5,1,2,3,4]=>00011
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[5,6,1,2,3,4]=>00001
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[6,4,3,2,1,5]=>11101
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[6,3,4,2,1,5]=>10101
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[6,4,2,3,1,5]=>01101
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[6,3,2,4,1,5]=>01101
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[6,2,3,4,1,5]=>00101
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[6,4,3,1,2,5]=>01101
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[6,3,4,1,2,5]=>00101
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[6,4,2,1,3,5]=>10101
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[6,4,1,2,3,5]=>00101
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[6,3,2,1,4,5]=>11001
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[6,2,3,1,4,5]=>01001
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[6,3,1,2,4,5]=>01001
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[6,2,1,3,4,5]=>10001
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5]=>00001
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6]=>11110
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6]=>11010
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,3,4,2,1,6]=>10110
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6]=>10110
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6]=>10010
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,4,2,3,1,6]=>01110
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[4,5,2,3,1,6]=>01010
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6]=>01110
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6]=>00110
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6]=>01110
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6]=>00110
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[4,2,3,5,1,6]=>00110
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6]=>01010
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6]=>00010
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[5,4,3,1,2,6]=>01110
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6]=>01010
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[5,3,4,1,2,6]=>00110
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,3,5,1,2,6]=>00110
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[3,4,5,1,2,6]=>00010
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[5,4,2,1,3,6]=>10110
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,5,2,1,3,6]=>10010
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[5,4,1,2,3,6]=>00110
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[4,5,1,2,3,6]=>00010
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[5,3,2,1,4,6]=>11010
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[5,2,3,1,4,6]=>01010
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[5,3,1,2,4,6]=>01010
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[5,2,1,3,4,6]=>10010
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6]=>00010
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6]=>11100
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6]=>10100
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6]=>01100
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6]=>01100
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6]=>00100
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[4,3,1,2,5,6]=>01100
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6]=>00100
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[4,2,1,3,5,6]=>10100
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6]=>00100
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6]=>11000
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6]=>01000
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6]=>01000
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6]=>10000
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>111101
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>111011
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[7,5,6,4,3,2,1]=>111011
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[6,5,7,4,3,2,1]=>111011
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,4,3,2,1]=>111001
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[7,6,4,5,3,2,1]=>110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[7,6,4,5,3,2,1]=>110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[6,7,4,5,3,2,1]=>110101
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,3,2,1]=>111011
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[7,6,4,5,3,2,1]=>110111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[7,5,4,6,3,2,1]=>110111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[7,4,5,6,3,2,1]=>110011
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,3,2,1]=>110001
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[7,6,5,3,4,2,1]=>101111
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[7,6,5,3,4,2,1]=>101111
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[6,7,5,3,4,2,1]=>101101
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[7,5,6,3,4,2,1]=>101011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[5,6,7,3,4,2,1]=>101001
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[6,7,3,4,5,2,1]=>100101
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[7,5,4,3,6,2,1]=>101111
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[6,4,5,7,3,2,1]=>110011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,2,1]=>110101
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[7,6,5,3,4,2,1]=>101111
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[7,6,4,3,5,2,1]=>101111
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[7,6,3,4,5,2,1]=>100111
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[6,3,4,5,7,2,1]=>100011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[4,3,5,6,7,2,1]=>101001
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[7,6,5,4,2,3,1]=>011111
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[7,6,5,4,2,3,1]=>011111
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[6,7,5,4,2,3,1]=>011101
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>011011
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[5,6,7,4,2,3,1]=>011001
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[7,6,4,5,2,3,1]=>010111
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[6,7,4,5,2,3,1]=>010101
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[4,5,6,7,2,3,1]=>010001
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[7,6,5,3,2,4,1]=>011111
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[6,5,7,3,2,4,1]=>011011
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[5,6,7,3,2,4,1]=>011001
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[7,6,5,2,3,4,1]=>001111
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[6,7,5,2,3,4,1]=>001101
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[5,6,7,2,3,4,1]=>001001
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[5,6,7,2,3,4,1]=>001001
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[7,3,2,4,5,6,1]=>010011
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,1]=>111111
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[6,7,5,4,3,2,1]=>111101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[6,5,7,4,3,2,1]=>111011
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[6,4,5,7,3,2,1]=>110011
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,1]=>101111
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,1]=>100111
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[6,5,3,4,7,2,1]=>100111
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[7,6,5,4,2,3,1]=>011111
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[6,7,4,5,2,3,1]=>010101
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[6,4,5,7,2,3,1]=>010011
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[4,5,6,7,2,3,1]=>010001
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[7,6,5,3,2,4,1]=>011111
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[7,6,5,2,3,4,1]=>001111
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[6,7,2,3,4,5,1]=>000101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,1]=>011101
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,5,2,6,7,1]=>000101
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[5,2,3,4,6,7,1]=>000101
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[4,3,2,5,6,7,1]=>011001
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[3,4,2,5,6,7,1]=>001001
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[4,2,3,5,6,7,1]=>001001
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,1]=>010001
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,1]=>000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[7,6,5,4,3,1,2]=>011111
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[7,6,5,4,3,1,2]=>011111
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>011101
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[7,5,6,4,3,1,2]=>011011
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[6,5,7,4,3,1,2]=>011011
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[5,6,7,4,3,1,2]=>011001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[7,6,4,5,3,1,2]=>010111
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[7,6,4,5,3,1,2]=>010111
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[4,5,6,7,3,1,2]=>010001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[7,6,5,3,4,1,2]=>001111
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[7,5,6,3,4,1,2]=>001011
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[7,5,6,3,4,1,2]=>001011
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[7,6,5,3,4,1,2]=>001111
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[6,7,5,3,4,1,2]=>001101
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[7,5,6,3,4,1,2]=>001011
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[6,5,7,3,4,1,2]=>001011
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[5,6,7,3,4,1,2]=>001001
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[7,5,4,3,6,1,2]=>001111
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[7,4,5,3,6,1,2]=>000111
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[7,5,3,4,6,1,2]=>000111
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[7,4,3,5,6,1,2]=>001011
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[7,3,4,5,6,1,2]=>000011
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[4,3,5,6,7,1,2]=>001001
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[3,4,5,6,7,1,2]=>000001
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[7,6,5,4,3,1,2]=>011111
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[6,5,7,4,3,1,2]=>011011
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[5,6,7,4,3,1,2]=>011001
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[6,7,4,5,3,1,2]=>010101
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[5,6,4,7,3,1,2]=>010011
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[5,4,6,7,3,1,2]=>010101
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[5,4,6,3,7,1,2]=>000111
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[5,6,3,4,7,1,2]=>000011
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[6,4,3,5,7,1,2]=>001011
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[6,3,4,5,7,1,2]=>000011
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[5,4,3,6,7,1,2]=>001101
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[4,5,3,6,7,1,2]=>000101
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[4,3,5,6,7,1,2]=>001001
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[3,4,5,6,7,1,2]=>000001
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,6,5,4,2,1,3]=>101111
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,6,5,4,2,1,3]=>101111
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[5,6,7,4,2,1,3]=>101001
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[4,5,6,7,2,1,3]=>100001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[7,6,5,4,1,2,3]=>001111
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[6,7,5,4,1,2,3]=>001101
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[5,6,7,4,1,2,3]=>001001
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[6,5,7,4,1,2,3]=>001011
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[5,6,7,4,1,2,3]=>001001
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[7,6,4,5,1,2,3]=>000111
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[6,7,4,5,1,2,3]=>000101
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[7,4,5,6,1,2,3]=>000011
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[7,4,5,6,1,2,3]=>000011
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[6,7,4,5,1,2,3]=>000101
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[6,5,4,7,1,2,3]=>000111
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[4,5,6,7,1,2,3]=>000001
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,5,3,2,1,4]=>110111
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,5,6,3,2,1,4]=>110011
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,5,3,2,1,4]=>110111
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[5,6,7,3,2,1,4]=>110001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,6,5,2,3,1,4]=>010111
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,5,6,2,3,1,4]=>010011
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[6,7,5,2,3,1,4]=>010101
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,5,6,2,3,1,4]=>010011
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[5,6,7,2,3,1,4]=>010001
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[7,6,5,3,1,2,4]=>010111
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[7,5,6,3,1,2,4]=>010011
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[6,7,5,3,1,2,4]=>010101
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[7,5,6,3,1,2,4]=>010011
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[5,6,7,3,1,2,4]=>010001
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[7,6,5,2,1,3,4]=>100111
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[7,6,5,2,1,3,4]=>100111
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,7,5,2,1,3,4]=>100101
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[7,5,6,2,1,3,4]=>100011
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,5,7,2,1,3,4]=>100011
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[5,6,7,2,1,3,4]=>100001
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>000101
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>000101
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[7,5,6,1,2,3,4]=>000011
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[7,5,6,1,2,3,4]=>000011
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[6,5,7,1,2,3,4]=>000011
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[5,6,7,1,2,3,4]=>000001
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[7,6,5,1,2,3,4]=>000111
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[6,7,5,1,2,3,4]=>000101
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[7,5,6,1,2,3,4]=>000011
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[6,5,7,1,2,3,4]=>000011
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,1,2,3,4]=>000001
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,4,3,2,1,5]=>111011
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[6,7,4,3,2,1,5]=>111001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,3,4,2,1,5]=>101011
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[6,7,3,4,2,1,5]=>101001
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,6,4,2,3,1,5]=>011011
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[6,7,4,2,3,1,5]=>011001
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,6,3,2,4,1,5]=>011011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[6,7,3,2,4,1,5]=>011001
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,6,2,3,4,1,5]=>001011
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[6,7,2,3,4,1,5]=>001001
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[7,6,4,3,1,2,5]=>011011
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[6,7,4,3,1,2,5]=>011001
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[7,6,3,4,1,2,5]=>001011
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[6,7,3,4,1,2,5]=>001001
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[7,6,4,2,1,3,5]=>101011
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,7,4,2,1,3,5]=>101001
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[7,6,4,1,2,3,5]=>001011
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[6,7,4,1,2,3,5]=>001001
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[7,6,3,2,1,4,5]=>110011
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,7,3,2,1,4,5]=>110001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[7,6,2,3,1,4,5]=>010011
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,7,2,3,1,4,5]=>010001
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[7,6,3,1,2,4,5]=>010011
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[6,7,3,1,2,4,5]=>010001
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[7,6,2,1,3,4,5]=>100011
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[6,7,2,1,3,4,5]=>100001
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>000011
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>000011
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[6,7,1,2,3,4,5]=>000001
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>000011
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[6,7,1,2,3,4,5]=>000001
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,5,4,3,2,1,6]=>111101
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,4,5,2,3,1,6]=>010101
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[7,3,4,2,5,1,6]=>001101
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[7,5,4,2,1,3,6]=>101101
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[7,5,4,1,2,3,6]=>001101
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[7,4,5,1,2,3,6]=>000101
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[7,5,2,1,3,4,6]=>100101
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[7,5,2,1,3,4,6]=>100101
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[7,5,1,2,3,4,6]=>000101
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[7,5,1,2,3,4,6]=>000101
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[7,4,3,2,1,5,6]=>111001
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[7,4,3,2,1,5,6]=>111001
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[7,3,2,4,1,5,6]=>011001
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[7,2,3,4,1,5,6]=>001001
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[7,3,4,1,2,5,6]=>001001
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[7,4,2,1,3,5,6]=>101001
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[7,4,1,2,3,5,6]=>001001
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[7,3,2,1,4,5,6]=>110001
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[7,3,2,1,4,5,6]=>110001
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>100001
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>000001
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>110010
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[6,5,4,3,1,2,7]=>011110
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>001010
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[4,3,5,6,1,2,7]=>001010
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[3,4,5,6,1,2,7]=>000010
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[6,5,4,2,1,3,7]=>101110
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[6,4,5,1,2,3,7]=>000110
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,5,2,3,1,4,7]=>010110
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[5,6,2,3,1,4,7]=>010010
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,6,2,1,3,4,7]=>100010
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[6,5,1,2,3,4,7]=>000110
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[5,6,1,2,3,4,7]=>000010
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,4,3,2,1,5,7]=>111010
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,3,4,2,1,5,7]=>101010
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[6,4,2,1,3,5,7]=>101010
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>001000
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>001000
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>010000
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>010000
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1]=>111111
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[6,7,5,4,3,2,1]=>111101
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1]=>111011
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1]=>111001
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,6,4,5,3,2,1]=>110111
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,4,5,6,3,2,1]=>110011
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1]=>110111
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,5,6,3,4,2,1]=>101011
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[5,6,7,3,4,2,1]=>101001
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,5,2,1]=>101111
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,3,4,5,2,1]=>100111
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[7,5,4,3,6,2,1]=>101111
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[6,7,5,4,2,3,1]=>011101
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[5,6,7,4,2,3,1]=>011001
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,6,4,5,2,3,1]=>010111
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[6,7,4,5,2,3,1]=>010101
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,4,5,6,2,3,1]=>010011
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[5,6,4,7,2,3,1]=>010011
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[6,5,7,3,2,4,1]=>011011
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[5,6,7,3,2,4,1]=>011001
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,6,5,2,3,4,1]=>001111
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[6,7,5,2,3,4,1]=>001101
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,5,6,2,3,4,1]=>001011
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[6,5,7,2,3,4,1]=>001011
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[5,6,7,2,3,4,1]=>001001
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[6,7,3,4,2,5,1]=>001101
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,4,5,2,3,6,1]=>000111
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[5,6,3,4,2,7,1]=>001011
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[4,5,3,6,2,7,1]=>000111
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1]=>011101
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[3,2,4,5,6,7,1]=>010001
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,1]=>000001
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[7,6,5,4,3,1,2]=>011111
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[7,5,6,4,3,1,2]=>011011
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[7,4,5,6,3,1,2]=>010011
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[7,6,5,4,2,1,3]=>101111
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[6,5,7,4,2,1,3]=>101011
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[7,5,4,6,2,1,3]=>100111
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[7,4,5,6,2,1,3]=>100011
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[7,6,5,4,1,2,3]=>001111
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3]=>001001
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[7,4,5,6,1,2,3]=>000011
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[5,6,4,7,1,2,3]=>000011
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[5,4,6,7,1,2,3]=>000101
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[5,6,7,3,1,2,4]=>010001
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[5,6,7,2,1,3,4]=>100001
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[7,6,5,1,2,3,4]=>000111
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[6,7,5,1,2,3,4]=>000101
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[7,5,6,1,2,3,4]=>000011
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[6,5,7,1,2,3,4]=>000011
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[5,6,7,1,2,3,4]=>000001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[7,6,4,3,2,1,5]=>111011
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[7,6,4,3,1,2,5]=>011011
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[6,7,1,2,3,4,5]=>000001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[7,5,3,1,2,4,6]=>010101
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[7,5,1,2,3,4,6]=>000101
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[7,4,3,2,1,5,6]=>111001
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[7,3,1,2,4,5,6]=>010001
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[7,2,1,3,4,5,6]=>100001
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6]=>000001
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7]=>111110
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7]=>011110
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[4,5,3,2,6,1,7]=>010110
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[4,2,3,5,6,1,7]=>001010
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[2,3,4,5,6,1,7]=>000010
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[5,6,4,3,1,2,7]=>011010
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[5,4,6,3,1,2,7]=>010110
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7]=>001010
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[5,4,3,6,1,2,7]=>001110
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,6,4,2,1,3,7]=>101010
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7]=>100110
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[4,5,6,1,2,3,7]=>000010
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,6,3,2,1,4,7]=>110010
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[6,4,3,2,1,5,7]=>111010
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[6,4,3,1,2,5,7]=>011010
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[6,4,1,2,3,5,7]=>001010
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[6,2,3,1,4,5,7]=>010010
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7]=>000010
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7]=>111100
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[4,5,2,3,1,6,7]=>010100
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,2,3,4,1,6,7]=>001100
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7]=>000100
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[5,3,1,2,4,6,7]=>010100
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7]=>000100
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7]=>111000
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7]=>011000
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7]=>001000
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7]=>001000
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7]=>001000
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7]=>110000
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7]=>010000
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7]=>100000
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[7,8,6,5,4,3,2,1]=>1111101
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,1]=>0000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[6,7,8,9,5,4,3,2,1]=>11110001
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[3,4,5,6,7,8,1,2]=>0000001
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,1]=>00000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,1]=>1111111
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[8,6,7,5,4,3,2,1]=>1111011
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[8,7,5,6,4,3,2,1]=>1110111
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>[8,7,6,4,5,3,2,1]=>1101111
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>[8,7,6,5,3,4,2,1]=>1011111
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[8,7,6,5,4,2,3,1]=>0111111
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[8,7,6,5,4,3,1,2]=>0111111
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1]=>11111111
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[9,7,8,5,6,3,4,1,2]=>00101011
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,1]=>0100001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>0100000
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0100000
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[4,2,3,5,6,7,8,1]=>0010001
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[3,4,2,5,6,7,8,1]=>0010001
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[3,2,4,5,6,7,8,9,1]=>01000001
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0000001
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[7,8,1,2,3,4,5,6]=>0000001
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[6,7,8,1,2,3,4,5]=>0000001
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>0000001
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>00000001
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[8,9,1,2,3,4,5,6,7]=>00000001
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[7,8,9,1,2,3,4,5,6]=>00000001
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,1,2,3,4,5]=>00000001
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[3,4,5,6,7,8,9,1,2]=>00000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,1,2]=>0111111
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[7,8,6,5,4,3,2,1]=>1111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,1,2]=>01111111
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[8,9,7,6,5,4,3,2,1]=>11111101
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[7,6,8,5,4,3,2,1]=>1111011
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[8,7,6,5,4,1,2,3]=>0011111
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8]=>1111110
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8]=>1111100
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8]=>1100000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8]=>1000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9]=>11111110
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9]=>11111100
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9]=>11111000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9]=>11110000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9]=>11100000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[2,3,4,5,6,7,8,1]=>0000001
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[2,3,4,5,6,7,1,8]=>0000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[2,3,4,5,6,7,8,9,1]=>00000001
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8]=>0000010
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7]=>0000001
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8]=>00000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,1,2,3]=>00111111
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>00000001
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[8,7,1,2,3,4,5,6]=>0000011
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[8,7,6,1,2,3,4,5]=>0000111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[8,7,6,5,1,2,3,4]=>0001111
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[9,8,1,2,3,4,5,6,7]=>00000011
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[9,8,7,1,2,3,4,5,6]=>00000111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[9,8,7,6,1,2,3,4,5]=>00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[9,8,7,6,5,1,2,3,4]=>00011111
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8]=>0010000
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
This map is undefined for the empty permutation.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
searching the database
Sorry, this map was not found in the database.