Identifier
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00252: Permutations restrictionPermutations
Mp00130: Permutations descent topsBinary 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 [[.,.],[.,.]]=>[1,3,2]=>[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 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[2,3,1]=>01 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,1]=>11 [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,1]=>01 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,3,2]=>01 [[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,3,2]=>01 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,3]=>10 [[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,3]=>00 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1]=>11 [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1]=>01 [[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2]=>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 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[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 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[2,4,3,1]=>011 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[2,4,3,1]=>011 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[3,2,4,1]=>011 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[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 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[2,4,3,1]=>011 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,1]=>011 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,1]=>001 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,4,3,2]=>011 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,4,3,2]=>011 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,3,4,2]=>001 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,4,3,2]=>011 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,3,4,2]=>001 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,4,3]=>101 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,4,3]=>101 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,4,3]=>001 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,4,3]=>001 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,2,1,4]=>110 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[2,3,1,4]=>010 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,4]=>010 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,4]=>100 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[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 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[2,4,3,1]=>011 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1]=>011 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1]=>001 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,3,2]=>011 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,3,4,2]=>001 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3]=>101 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3]=>001 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4]=>110 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4]=>010 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4]=>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 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[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 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[3,5,4,2,1]=>1011 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[3,5,4,2,1]=>1011 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[4,3,5,2,1]=>1011 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[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 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[3,5,4,2,1]=>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 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[2,5,4,3,1]=>0111 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[2,5,4,3,1]=>0111 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[2,4,5,3,1]=>0101 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[2,5,4,3,1]=>0111 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[2,4,5,3,1]=>0101 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[3,2,5,4,1]=>0111 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[3,2,5,4,1]=>0111 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[2,3,5,4,1]=>0011 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[2,3,5,4,1]=>0011 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[4,3,2,5,1]=>0111 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[3,4,2,5,1]=>0011 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[2,4,3,5,1]=>0011 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[3,2,4,5,1]=>0101 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[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 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[3,5,4,2,1]=>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 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[2,5,4,3,1]=>0111 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[2,4,5,3,1]=>0101 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[3,2,5,4,1]=>0111 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[2,3,5,4,1]=>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 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[2,4,3,5,1]=>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 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,5,4,3,2]=>0111 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,5,4,3,2]=>0111 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,4,5,3,2]=>0101 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,5,4,3,2]=>0111 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,4,5,3,2]=>0101 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,3,5,4,2]=>0011 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,3,5,4,2]=>0011 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,4,3,5,2]=>0011 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,3,4,5,2]=>0001 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,5,4,3,2]=>0111 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,4,5,3,2]=>0101 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,3,5,4,2]=>0011 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,4,3,5,2]=>0011 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,3,4,5,2]=>0001 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,5,4,3]=>1011 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,5,4,3]=>1011 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,4,5,3]=>1001 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,5,4,3]=>1011 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,4,5,3]=>1001 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,5,4,3]=>0011 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,5,4,3]=>0011 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,4,5,3]=>0001 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,5,4,3]=>0011 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,4,5,3]=>0001 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,2,1,5,4]=>1101 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,1,5,4]=>1101 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[2,3,1,5,4]=>0101 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[2,3,1,5,4]=>0101 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,5,4]=>0101 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,5,4]=>0101 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,5,4]=>1001 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,5,4]=>1001 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,5,4]=>0001 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,5,4]=>0001 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,3,2,1,5]=>1110 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[3,4,2,1,5]=>1010 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[2,4,3,1,5]=>0110 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[3,2,4,1,5]=>0110 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[2,3,4,1,5]=>0010 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,3,2,5]=>0110 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,3,4,2,5]=>0010 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,5]=>1010 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,5]=>0010 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,2,1,4,5]=>1100 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[2,3,1,4,5]=>0100 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,5]=>0100 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,5]=>1000 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[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 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[3,5,4,2,1]=>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 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[2,5,4,3,1]=>0111 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[2,4,5,3,1]=>0101 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[3,2,5,4,1]=>0111 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[2,3,5,4,1]=>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 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[2,4,3,5,1]=>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 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,5,4,3,2]=>0111 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,4,5,3,2]=>0101 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,3,5,4,2]=>0011 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,4,3,5,2]=>0011 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,3,4,5,2]=>0001 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,5,4,3]=>1011 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,4,5,3]=>1001 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,5,4,3]=>0011 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,4,5,3]=>0001 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,2,1,5,4]=>1101 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[2,3,1,5,4]=>0101 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4]=>0101 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4]=>1001 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4]=>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 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[2,4,3,1,5]=>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 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,4,3,2,5]=>0110 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,3,4,2,5]=>0010 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5]=>1010 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5]=>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 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5]=>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 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[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 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[4,6,5,3,2,1]=>11011 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[4,6,5,3,2,1]=>11011 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[5,4,6,3,2,1]=>11011 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[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 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[4,6,5,3,2,1]=>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 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[3,6,5,4,2,1]=>10111 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[3,6,5,4,2,1]=>10111 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[3,5,6,4,2,1]=>10101 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[3,6,5,4,2,1]=>10111 [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[3,5,6,4,2,1]=>10101 [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[4,3,6,5,2,1]=>10111 [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[4,3,6,5,2,1]=>10111 [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[3,4,6,5,2,1]=>10011 [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[3,4,6,5,2,1]=>10011 [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[5,4,3,6,2,1]=>10111 [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[4,5,3,6,2,1]=>10011 [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[3,5,4,6,2,1]=>10011 [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[4,3,5,6,2,1]=>10101 [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[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 [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[4,6,5,3,2,1]=>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 [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[3,6,5,4,2,1]=>10111 [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[3,5,6,4,2,1]=>10101 [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[4,3,6,5,2,1]=>10111 [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[3,4,6,5,2,1]=>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 [.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[3,5,4,6,2,1]=>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 [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[2,6,5,4,3,1]=>01111 [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[2,6,5,4,3,1]=>01111 [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[2,5,6,4,3,1]=>01101 [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[2,6,5,4,3,1]=>01111 [.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[2,5,6,4,3,1]=>01101 [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[2,4,6,5,3,1]=>01011 [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[2,4,6,5,3,1]=>01011 [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[2,5,4,6,3,1]=>01011 [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[2,4,5,6,3,1]=>01001 [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[2,6,5,4,3,1]=>01111 [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[2,5,6,4,3,1]=>01101 [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[2,4,6,5,3,1]=>01011 [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[2,5,4,6,3,1]=>01011 [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[2,4,5,6,3,1]=>01001 [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[3,2,6,5,4,1]=>01111 [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[3,2,6,5,4,1]=>01111 [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[3,2,5,6,4,1]=>01101 [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[3,2,6,5,4,1]=>01111 [.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[3,2,5,6,4,1]=>01101 [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[2,3,6,5,4,1]=>00111 [.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[2,3,6,5,4,1]=>00111 [.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[2,3,5,6,4,1]=>00101 [.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[2,3,6,5,4,1]=>00111 [.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[2,3,5,6,4,1]=>00101 [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[4,3,2,6,5,1]=>01111 [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[4,3,2,6,5,1]=>01111 [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[3,4,2,6,5,1]=>00111 [.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[3,4,2,6,5,1]=>00111 [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[2,4,3,6,5,1]=>00111 [.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[2,4,3,6,5,1]=>00111 [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[3,2,4,6,5,1]=>01011 [.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[3,2,4,6,5,1]=>01011 [.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[2,3,4,6,5,1]=>00011 [.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[2,3,4,6,5,1]=>00011 [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[5,4,3,2,6,1]=>01111 [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[4,5,3,2,6,1]=>01011 [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[3,5,4,2,6,1]=>00111 [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[4,3,5,2,6,1]=>00111 [.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[3,4,5,2,6,1]=>00011 [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[2,5,4,3,6,1]=>00111 [.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[2,4,5,3,6,1]=>00011 [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[3,2,5,4,6,1]=>01011 [.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[2,3,5,4,6,1]=>00011 [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[4,3,2,5,6,1]=>01101 [.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[3,4,2,5,6,1]=>00101 [.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[2,4,3,5,6,1]=>00101 [.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[3,2,4,5,6,1]=>01001 [.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[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 [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[4,6,5,3,2,1]=>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 [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[3,6,5,4,2,1]=>10111 [.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[3,5,6,4,2,1]=>10101 [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[4,3,6,5,2,1]=>10111 [.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[3,4,6,5,2,1]=>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 [.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[3,5,4,6,2,1]=>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 [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[2,6,5,4,3,1]=>01111 [.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[2,5,6,4,3,1]=>01101 [.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[2,4,6,5,3,1]=>01011 [.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[2,5,4,6,3,1]=>01011 [.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[2,4,5,6,3,1]=>01001 [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[3,2,6,5,4,1]=>01111 [.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[3,2,5,6,4,1]=>01101 [.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[2,3,6,5,4,1]=>00111 [.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[2,3,5,6,4,1]=>00101 [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[4,3,2,6,5,1]=>01111 [.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[3,4,2,6,5,1]=>00111 [.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[2,4,3,6,5,1]=>00111 [.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[3,2,4,6,5,1]=>01011 [.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[2,3,4,6,5,1]=>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 [.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[3,5,4,2,6,1]=>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 [.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[2,5,4,3,6,1]=>00111 [.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[2,4,5,3,6,1]=>00011 [.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[3,2,5,4,6,1]=>01011 [.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[2,3,5,4,6,1]=>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 [.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[2,4,3,5,6,1]=>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 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,6,5,4,3,2]=>01111 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,6,5,4,3,2]=>01111 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,5,6,4,3,2]=>01101 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,6,5,4,3,2]=>01111 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,5,6,4,3,2]=>01101 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,4,6,5,3,2]=>01011 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,4,6,5,3,2]=>01011 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,5,4,6,3,2]=>01011 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,4,5,6,3,2]=>01001 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,6,5,4,3,2]=>01111 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,5,6,4,3,2]=>01101 [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,4,6,5,3,2]=>01011 [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,5,4,6,3,2]=>01011 [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,4,5,6,3,2]=>01001 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,3,6,5,4,2]=>00111 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,3,6,5,4,2]=>00111 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,3,5,6,4,2]=>00101 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,3,6,5,4,2]=>00111 [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,3,5,6,4,2]=>00101 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,4,3,6,5,2]=>00111 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,4,3,6,5,2]=>00111 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,3,4,6,5,2]=>00011 [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,3,4,6,5,2]=>00011 [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,5,4,3,6,2]=>00111 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,4,5,3,6,2]=>00011 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,3,5,4,6,2]=>00011 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,4,3,5,6,2]=>00101 [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,3,4,5,6,2]=>00001 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,6,5,4,3,2]=>01111 [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,5,6,4,3,2]=>01101 [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,4,6,5,3,2]=>01011 [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,5,4,6,3,2]=>01011 [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,4,5,6,3,2]=>01001 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,3,6,5,4,2]=>00111 [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,3,5,6,4,2]=>00101 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,4,3,6,5,2]=>00111 [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,3,4,6,5,2]=>00011 [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,5,4,3,6,2]=>00111 [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,4,5,3,6,2]=>00011 [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,3,5,4,6,2]=>00011 [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,4,3,5,6,2]=>00101 [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,3,4,5,6,2]=>00001 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,6,5,4,3]=>10111 [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,6,5,4,3]=>10111 [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,5,6,4,3]=>10101 [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,6,5,4,3]=>10111 [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,5,6,4,3]=>10101 [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,4,6,5,3]=>10011 [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,4,6,5,3]=>10011 [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,5,4,6,3]=>10011 [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,4,5,6,3]=>10001 [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,6,5,4,3]=>10111 [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,5,6,4,3]=>10101 [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,4,6,5,3]=>10011 [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,5,4,6,3]=>10011 [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,4,5,6,3]=>10001 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,6,5,4,3]=>00111 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,6,5,4,3]=>00111 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,5,6,4,3]=>00101 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,6,5,4,3]=>00111 [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,5,6,4,3]=>00101 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,4,6,5,3]=>00011 [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,4,6,5,3]=>00011 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,5,4,6,3]=>00011 [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,4,5,6,3]=>00001 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,6,5,4,3]=>00111 [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,5,6,4,3]=>00101 [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,4,6,5,3]=>00011 [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,5,4,6,3]=>00011 [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,4,5,6,3]=>00001 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[3,2,1,6,5,4]=>11011 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,2,1,6,5,4]=>11011 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,2,1,5,6,4]=>11001 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,2,1,6,5,4]=>11011 [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[3,2,1,5,6,4]=>11001 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[2,3,1,6,5,4]=>01011 [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[2,3,1,6,5,4]=>01011 [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[2,3,1,5,6,4]=>01001 [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[2,3,1,6,5,4]=>01011 [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[2,3,1,5,6,4]=>01001 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,6,5,4]=>01011 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,6,5,4]=>01011 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,5,6,4]=>01001 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,6,5,4]=>01011 [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,5,6,4]=>01001 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,6,5,4]=>10011 [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,6,5,4]=>10011 [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,5,6,4]=>10001 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[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6]=>10100 [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[2,4,3,1,5,6]=>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 [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6]=>01100 [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,3,4,2,5,6]=>00100 [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6]=>10100 [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6]=>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 [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6]=>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 [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[5,7,6,4,3,2,1]=>111011 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>111011 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[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 [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[4,7,6,5,3,2,1]=>110111 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[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 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[4,7,6,5,3,2,1]=>110111 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,3,2,1]=>110001 [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[3,7,6,5,4,2,1]=>101111 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[3,5,7,6,4,2,1]=>101011 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[3,5,6,7,4,2,1]=>101001 [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[3,4,7,6,5,2,1]=>100111 [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[3,4,5,7,6,2,1]=>100011 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[4,3,6,5,7,2,1]=>101011 [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[5,7,6,4,3,2,1]=>111011 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,2,1]=>110101 [.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[4,3,5,6,7,2,1]=>101001 [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[2,7,6,5,4,3,1]=>011111 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[2,6,7,5,4,3,1]=>011101 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[2,5,6,7,4,3,1]=>011001 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[2,4,7,6,5,3,1]=>010111 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[2,4,6,7,5,3,1]=>010101 [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[2,7,6,5,4,3,1]=>011111 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[2,3,5,6,7,4,1]=>001001 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[2,3,5,6,7,4,1]=>001001 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[4,3,2,7,6,5,1]=>011111 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[3,4,2,7,6,5,1]=>001111 [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[2,4,3,7,6,5,1]=>001111 [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[3,2,4,7,6,5,1]=>010111 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[2,3,4,7,6,5,1]=>000111 [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[5,4,3,2,7,6,1]=>011111 [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[5,4,3,2,7,6,1]=>011111 [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[2,5,4,3,7,6,1]=>001111 [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[2,5,4,3,7,6,1]=>001111 [.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[2,4,5,3,7,6,1]=>000111 [.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[3,4,2,5,7,6,1]=>001011 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[4,3,6,5,2,7,1]=>001111 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[3,2,6,5,4,7,1]=>010111 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[2,4,3,6,5,7,1]=>001011 [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[5,4,3,2,6,7,1]=>011101 [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[2,5,4,3,6,7,1]=>001101 [.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[2,4,3,5,6,7,1]=>001001 [.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[2,3,4,5,6,7,1]=>000001 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[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 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,1]=>101111 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,1]=>100111 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[4,3,6,5,7,2,1]=>101011 [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[2,5,4,7,6,3,1]=>010111 [.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[2,5,4,6,7,3,1]=>010101 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[3,2,6,5,7,4,1]=>011011 [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[4,3,2,7,6,5,1]=>011111 [.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[3,4,2,6,7,5,1]=>001101 [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[5,4,3,2,7,6,1]=>011111 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[4,3,5,2,7,6,1]=>001111 [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[2,5,4,3,7,6,1]=>001111 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[3,2,5,4,7,6,1]=>010111 [.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[2,3,5,4,7,6,1]=>000111 [.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[3,2,4,5,7,6,1]=>010011 [.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[2,4,3,6,5,7,1]=>001011 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[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 [.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[2,5,4,3,6,7,1]=>001101 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[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 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[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 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>011111 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>011111 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[1,6,7,5,4,3,2]=>011101 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[1,7,6,5,4,3,2]=>011111 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[1,6,7,5,4,3,2]=>011101 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[1,5,7,6,4,3,2]=>011011 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[1,7,6,5,4,3,2]=>011111 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[1,5,6,7,4,3,2]=>011001 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[1,4,7,6,5,3,2]=>010111 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[1,4,7,6,5,3,2]=>010111 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,3,5,7,6,4,2]=>001011 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[1,3,6,5,7,4,2]=>001011 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[1,3,5,6,7,4,2]=>001001 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,4,3,7,6,5,2]=>001111 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[1,4,3,7,6,5,2]=>001111 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[1,3,4,7,6,5,2]=>000111 [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>[1,3,4,5,7,6,2]=>000011 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[1,6,5,4,3,7,2]=>001111 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[1,5,6,4,3,7,2]=>001011 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[1,4,3,6,5,7,2]=>001011 [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[1,3,4,5,6,7,2]=>000001 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[1,5,4,3,6,7,2]=>001101 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[1,4,5,3,6,7,2]=>000101 [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[1,4,3,5,6,7,2]=>001001 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[1,3,4,5,6,7,2]=>000001 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>101111 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,6,7,5,4,3]=>101101 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[2,1,6,5,7,4,3]=>101011 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[2,1,7,6,5,4,3]=>101111 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,6,7,5,4,3]=>101101 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[2,1,6,5,7,4,3]=>101011 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[2,1,5,6,7,4,3]=>101001 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[2,1,4,7,6,5,3]=>100111 [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[2,1,4,5,7,6,3]=>100011 [[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[2,1,4,5,7,6,3]=>100011 [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[2,1,4,6,5,7,3]=>100011 [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,6,5,7,4,3]=>101011 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,5,4,7,6,3]=>100111 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[2,1,4,5,6,7,3]=>100001 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,6,7,5,4,3]=>001101 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,5,6,7,4,3]=>001001 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[1,2,4,7,6,5,3]=>000111 [[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[1,2,4,6,7,5,3]=>000101 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[1,2,6,5,4,7,3]=>000111 [[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[1,2,5,6,4,7,3]=>000011 [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[1,2,5,4,6,7,3]=>000101 [[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[1,2,4,5,6,7,3]=>000001 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[3,2,1,7,6,5,4]=>110111 [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[3,2,1,7,6,5,4]=>110111 [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[3,2,1,6,7,5,4]=>110101 [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[3,2,1,7,6,5,4]=>110111 [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[3,2,1,6,7,5,4]=>110101 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[3,2,1,5,7,6,4]=>110011 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[3,2,1,5,7,6,4]=>110011 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[3,2,1,6,5,7,4]=>110011 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[3,2,1,5,6,7,4]=>110001 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[3,2,1,7,6,5,4]=>110111 [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[3,2,1,6,7,5,4]=>110101 [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[3,2,1,5,7,6,4]=>110011 [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[3,2,1,6,5,7,4]=>110011 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[3,2,1,5,6,7,4]=>110001 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[2,3,1,7,6,5,4]=>010111 [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,7,6,5,4]=>010111 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,7,6,5,4]=>100111 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,7,6,5,4]=>000111 [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,7,6,5,4]=>000111 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,6,7,5,4]=>000101 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,7,6,5,4]=>000111 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,6,7,5,4]=>000101 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,5,7,6,4]=>000011 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,5,7,6,4]=>000011 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,6,5,7,4]=>000011 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,5,6,7,4]=>000001 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,7,6,5,4]=>000111 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,6,7,5,4]=>000101 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,5,7,6,4]=>000011 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,6,5,7,4]=>000011 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,4]=>000001 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,7,6,5]=>111011 [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,7,6,5]=>111011 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,6,7,5]=>111001 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,7,6,5]=>111011 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,6,7,5]=>111001 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[3,4,2,1,7,6,5]=>101011 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[3,4,2,1,7,6,5]=>101011 [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[3,4,2,1,6,7,5]=>101001 [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[3,4,2,1,7,6,5]=>101011 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[3,4,2,1,6,7,5]=>101001 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[2,4,3,1,7,6,5]=>011011 [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[2,4,3,1,7,6,5]=>011011 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[2,4,3,1,6,7,5]=>011001 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[2,4,3,1,7,6,5]=>011011 [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[2,4,3,1,6,7,5]=>011001 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[3,2,4,1,7,6,5]=>011011 [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[3,2,4,1,7,6,5]=>011011 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[3,2,4,1,6,7,5]=>011001 [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[3,2,4,1,7,6,5]=>011011 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[3,2,4,1,6,7,5]=>011001 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[2,3,4,1,7,6,5]=>001011 [[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[2,3,4,1,7,6,5]=>001011 [[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[2,3,4,1,6,7,5]=>001001 [[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[2,3,4,1,7,6,5]=>001011 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[2,3,4,1,6,7,5]=>001001 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,7,6,5]=>011011 [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,4,3,2,7,6,5]=>011011 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[1,4,3,2,6,7,5]=>011001 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,3,4,2,7,6,5]=>001011 [[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,3,4,2,7,6,5]=>001011 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[1,3,4,2,6,7,5]=>001001 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,5]=>101011 [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,7,6,5]=>101011 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,6,7,5]=>101001 [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,7,6,5]=>101011 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,6,7,5]=>101001 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,7,6,5]=>001011 [[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,7,6,5]=>001011 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,6,7,5]=>001001 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,7,6,5]=>110011 [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[3,2,1,4,7,6,5]=>110011 [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[3,2,1,4,7,6,5]=>110011 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[3,2,1,4,6,7,5]=>110001 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[2,3,1,4,7,6,5]=>010011 [[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[2,3,1,4,7,6,5]=>010011 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[2,3,1,4,6,7,5]=>010001 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,7,6,5]=>010011 [[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,7,6,5]=>010011 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,6,7,5]=>010001 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,7,6,5]=>100011 [[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,7,6,5]=>100011 [[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,7,6,5]=>100011 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,6,7,5]=>100001 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,6,5]=>000011 [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,7,6,5]=>000011 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,7,6,5]=>000011 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,6,7,5]=>000001 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,7,6]=>111101 [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,7,6]=>111101 [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[4,5,3,2,1,7,6]=>110101 [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[3,5,4,2,1,7,6]=>101101 [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[4,3,5,2,1,7,6]=>101101 [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[3,4,5,2,1,7,6]=>100101 [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[2,5,4,3,1,7,6]=>011101 [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[2,4,5,3,1,7,6]=>010101 [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[3,2,5,4,1,7,6]=>011101 [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[2,3,5,4,1,7,6]=>001101 [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[4,3,2,5,1,7,6]=>011101 [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[3,4,2,5,1,7,6]=>001101 [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[2,4,3,5,1,7,6]=>001101 [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[3,2,4,5,1,7,6]=>010101 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[2,3,4,5,1,7,6]=>000101 [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,7,6]=>111001 [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,7,6]=>111001 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[3,2,4,1,5,7,6]=>011001 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[3,2,4,1,5,7,6]=>011001 [[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[2,3,4,1,5,7,6]=>001001 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[2,3,4,1,5,7,6]=>001001 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,7,6]=>110001 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[2,3,1,4,5,7,6]=>010001 [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,6]=>000001 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,7,6]=>000001 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,7]=>111110 [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[5,6,4,3,2,1,7]=>111010 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[4,5,6,3,2,1,7]=>110010 [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[3,6,5,4,2,1,7]=>101110 [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[4,3,6,5,2,1,7]=>101110 [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[5,4,3,6,2,1,7]=>101110 [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[4,5,3,6,2,1,7]=>100110 [[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[4,3,5,6,2,1,7]=>101010 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[2,3,6,5,4,1,7]=>001110 [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[2,4,3,6,5,1,7]=>001110 [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[5,4,3,2,6,1,7]=>011110 [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>[4,5,3,2,6,1,7]=>010110 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[4,3,5,2,6,1,7]=>001110 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[3,2,5,4,6,1,7]=>010110 [[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[4,3,2,5,6,1,7]=>011010 [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[2,3,4,5,6,1,7]=>000010 [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,5,6,4,3,2,8,7]=>[1,5,6,4,3,2,7]=>011010 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,7]=>101110 [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,5,6,4,3,7]=>101010 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,4,6,5,3,7]=>100110 [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,5,4,6,3,7]=>100110 [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,4,5,6,3,7]=>100010 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,7]=>111010 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[3,4,2,1,6,5,7]=>101010 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[2,4,3,1,6,5,7]=>011010 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[3,2,4,1,6,5,7]=>011010 [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[2,3,4,1,6,5,7]=>001010 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,7]=>101010 [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,7]=>111100 [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,7]=>101100 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,7]=>111000 [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[3,2,4,1,5,6,7]=>011000 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[2,3,4,1,5,6,7]=>001000 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,7]=>100000 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[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 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[5,7,6,4,3,2,1]=>111011 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[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 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[4,7,6,5,3,2,1]=>110111 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1]=>110111 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[3,4,7,6,5,2,1]=>100111 [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[3,2,7,6,5,4,1]=>011111 [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[3,2,6,7,5,4,1]=>011101 [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[5,4,3,2,7,6,1]=>011111 [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[4,5,3,2,7,6,1]=>010111 [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[3,5,4,2,7,6,1]=>001111 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[3,2,5,4,7,6,1]=>010111 [[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[2,3,4,5,7,6,1]=>000011 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[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 [[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[3,5,4,2,6,7,1]=>001101 [[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[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 [[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[1,3,4,6,7,5,2]=>000101 [[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[1,3,4,5,7,6,2]=>000011 [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[2,1,6,7,5,4,3,8]=>[2,1,6,7,5,4,3]=>101101 [[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[2,3,1,5,6,7,4]=>010001 [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5]=>111011 [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,6,7,5]=>111001 [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[3,2,4,1,7,6,5]=>011011 [[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[3,2,4,1,6,7,5]=>011001 [[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[2,3,4,1,7,6,5]=>001011 [[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[2,3,4,1,6,7,5]=>001001 [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5]=>011011 [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,3,4,2,6,7,5]=>001001 [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5]=>110011 [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6]=>111101 [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6]=>110101 [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[2,3,1,5,4,7,6]=>010101 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6]=>010101 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6]=>000101 [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6]=>111001 [[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[3,2,4,1,5,7,6]=>011001 [[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[2,3,4,1,5,7,6]=>001001 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6]=>010001 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6]=>000001 [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7]=>111110 [[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[2,3,4,6,5,1,7]=>000110 [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[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 [[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[2,3,4,5,6,1,7]=>000010 [[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[1,2,4,6,5,3,7]=>000110 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7]=>111010 [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[3,2,4,1,6,5,7]=>011010 [[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[2,3,4,1,6,5,7]=>001010 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7]=>001010 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7]=>111100 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[3,2,5,4,1,6,7]=>011100 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7]=>000100 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7]=>010100 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7]=>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 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7]=>110000 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7]=>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 [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[1,3,4,5,6,7,8,2]=>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 [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[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 [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,9]=>10101010 [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,8]=>0000000 [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,9]=>00000000 [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,1]=>0100001 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000 [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[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 [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,8,7]=>0000001 [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,7,8,6]=>0000001 [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,6,7,8,5]=>0000001 [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,5,6,7,8,4]=>0000001 [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,3]=>0000001 [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,7]=>0000001 [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,9,8]=>00000001 [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,8,7,6]=>0000011 [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,8,9,7]=>00000001 [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,7,6,8,5]=>0000011 [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,7,8,9,6]=>00000001 [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,3,6,5,7,8,9,4]=>[1,2,3,6,5,7,8,4]=>0000101 [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,6,7,8,9,5]=>00000001 [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[1,2,5,4,6,7,8,9,3]=>[1,2,5,4,6,7,8,3]=>0001001 [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,5,6,7,8,9,4]=>00000001 [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[1,4,3,5,6,7,8,9,2]=>[1,4,3,5,6,7,8,2]=>0010001 [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,4,5,6,7,8,9,3]=>00000001 [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[1,3,4,5,6,7,8,9,2]=>00000001 [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>0111111 [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[7,8,6,5,4,3,2,1]=>1111101 [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>0111111 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>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 [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>0111111 [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>01111111 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111 [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>10111111 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>11101111 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>11111011 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,9]=>11111110 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[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
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.
Map
restriction
Description
The permutation obtained by removing the largest letter.
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.