Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=> [.,[.,.]]=>[2,1]=>[2,1]=>0 [[.,.],.]=>[1,2]=>[1,2]=>1 [.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>00 [.,[[.,.],.]]=>[2,3,1]=>[2,3,1]=>00 [[.,.],[.,.]]=>[1,3,2]=>[3,1,2]=>00 [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>01 [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>11 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>000 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,4,2,1]=>000 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>000 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>000 [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>000 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[4,3,1,2]=>000 [[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1,4,2]=>000 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[4,2,1,3]=>000 [[[.,.],.],[.,.]]=>[1,2,4,3]=>[4,1,2,3]=>000 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>001 [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>001 [[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1,2,4]=>001 [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>011 [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>111 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,5,3,2,1]=>0000 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,3,4,2,1]=>0000 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1]=>0000 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1]=>0000 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,2,3,1]=>0000 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[4,2,5,3,1]=>0000 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>0000 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>0000 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1]=>0000 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>0000 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,2,3,5,1]=>0000 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1]=>0000 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1]=>0000 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[5,4,3,1,2]=>0000 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,5,1,3,2]=>0000 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[5,3,1,4,2]=>0000 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[4,3,1,5,2]=>0000 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[3,1,4,5,2]=>0000 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[5,4,2,1,3]=>0000 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[4,2,1,5,3]=>0000 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[5,4,1,2,3]=>0000 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1,2,5,3]=>0000 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[5,3,2,1,4]=>0000 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[5,2,3,1,4]=>0000 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[5,3,1,2,4]=>0000 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[5,2,1,3,4]=>0000 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[5,1,2,3,4]=>0000 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1,5]=>0001 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>0001 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5]=>0001 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5]=>0001 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[4,3,1,2,5]=>0001 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,1,4,2,5]=>0001 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[4,2,1,3,5]=>0001 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1,2,3,5]=>0001 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>0011 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4,5]=>0011 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[3,1,2,4,5]=>0011 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>0111 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>1111 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>00000 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>00000 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>00000 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>00000 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>00000 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>00000 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>00000 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>00000 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>00000 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>00000 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>00000 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>00000 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>00000 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>00000 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>00000 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>00000 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>00000 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>00000 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>00000 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>00000 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>00000 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>00000 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>00000 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>00000 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>00000 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>00000 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>00000 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>00000 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>00000 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>00000 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>00000 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>00000 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>00000 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>00000 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>00000 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>00000 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>00000 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>00000 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>00000 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>00000 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>00000 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>00000 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>00000 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>00000 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>00000 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>00000 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>00000 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>00000 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>00000 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>00000 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>00000 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>00000 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>00000 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>00000 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>00000 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>00000 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>00000 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>00000 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>00000 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>00000 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>00000 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>00000 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>00000 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>00000 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>00000 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>00000 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>00000 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>00000 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>00000 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>00000 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>00000 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>00000 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>00000 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>00000 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>00000 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>00000 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>00000 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>00000 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>00000 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>00000 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>00000 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>00000 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>00000 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>00000 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>00000 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>00000 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>00000 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>00000 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>00001 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>00001 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>00001 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>00001 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>00001 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>00001 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>00001 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>00001 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>00001 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>00001 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>00001 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>00001 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>00001 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>00001 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>00001 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>00001 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>00001 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>00001 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>00001 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>00001 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>00001 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>00001 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>00001 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>00001 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>00001 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>00001 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[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000 [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,5,6,4,3,2,1]=>0000000 [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[8,5,6,7,4,3,2,1]=>0000000 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,8,4,3,2,1]=>0000000 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[6,7,5,8,4,3,2,1]=>0000000 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>0000000 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[6,7,5,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[7,5,6,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,8,3,2,1]=>0000000 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[5,6,7,4,8,3,2,1]=>0000000 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[7,6,4,5,8,3,2,1]=>0000000 [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[6,4,7,5,8,3,2,1]=>0000000 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[7,5,4,6,8,3,2,1]=>0000000 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[7,4,5,6,8,3,2,1]=>0000000 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[6,5,4,7,8,3,2,1]=>0000000 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[5,6,4,7,8,3,2,1]=>0000000 [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[6,4,5,7,8,3,2,1]=>0000000 [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[5,4,6,7,8,3,2,1]=>0000000 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,8,3,2,1]=>0000000 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,5,3,6,4,2,1]=>0000000 [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[6,7,3,5,8,4,2,1]=>0000000 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[5,3,6,7,8,4,2,1]=>0000000 [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[6,4,3,7,8,5,2,1]=>0000000 [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,6,3,4,5,2,1]=>0000000 [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[5,4,3,8,7,6,2,1]=>[8,7,5,4,3,6,2,1]=>0000000 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,8,2,1]=>0000000 [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,5,6,7,3,8,2,1]=>0000000 [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[3,6,7,5,4,8,2,1]=>[6,7,3,5,4,8,2,1]=>0000000 [.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[3,6,5,7,4,8,2,1]=>[6,5,3,7,4,8,2,1]=>0000000 [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>[7,6,3,4,5,8,2,1]=>0000000 [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[6,5,4,3,7,8,2,1]=>0000000 [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[2,6,7,8,5,4,3,1]=>[6,7,8,2,5,4,3,1]=>0000000 [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[2,7,6,5,8,4,3,1]=>[7,6,5,8,2,4,3,1]=>0000000 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[5,6,2,7,8,4,3,1]=>0000000 [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>[7,6,4,2,5,8,3,1]=>0000000 [.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>[6,5,4,2,7,8,3,1]=>0000000 [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[3,2,5,8,7,6,4,1]=>[8,7,5,3,2,6,4,1]=>0000000 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[8,7,6,5,2,3,4,1]=>0000000 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[5,2,3,6,7,8,4,1]=>0000000 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,6,4,2,3,7,5,1]=>0000000 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,7,6,2,3,4,5,1]=>0000000 [.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[2,3,4,5,7,8,6,1]=>[7,2,3,4,5,8,6,1]=>0000000 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,6,4,2,3,5,7,1]=>0000000 [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,5,6,7,3,2,8,1]=>0000000 [.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[5,3,6,7,4,2,8,1]=>0000000 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,8,1]=>0000000 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[6,4,5,3,7,2,8,1]=>0000000 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1]=>0000000 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[6,5,3,4,7,2,8,1]=>0000000 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[5,4,3,6,7,2,8,1]=>0000000 [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[7,5,4,2,6,3,8,1]=>0000000 [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[6,7,3,2,5,4,8,1]=>0000000 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>[7,6,5,2,3,4,8,1]=>0000000 [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[7,6,4,2,3,5,8,1]=>0000000 [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1]=>0000000 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[5,4,6,3,2,7,8,1]=>0000000 [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[5,4,3,6,2,7,8,1]=>0000000 [.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[5,4,2,6,3,7,8,1]=>0000000 [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>[6,5,2,3,4,7,8,1]=>0000000 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1]=>0000000 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1]=>0000000 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[6,7,8,5,1,4,3,2]=>0000000 [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[1,5,7,8,6,4,3,2]=>[7,5,8,6,1,4,3,2]=>0000000 [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[1,5,6,8,7,4,3,2]=>[8,5,6,7,1,4,3,2]=>0000000 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[7,6,5,8,4,1,3,2]=>0000000 [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[6,7,5,8,1,4,3,2]=>0000000 [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>[7,5,6,8,1,4,3,2]=>0000000 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>[6,5,7,8,1,4,3,2]=>0000000 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[5,6,7,1,8,4,3,2]=>0000000 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[1,4,5,6,7,8,3,2]=>[4,5,1,6,7,8,3,2]=>0000000 [[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>[6,7,3,1,8,5,4,2]=>0000000 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[8,7,5,3,1,6,4,2]=>0000000 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[7,5,3,1,8,6,4,2]=>0000000 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[6,7,3,1,5,8,4,2]=>0000000 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[5,3,1,6,7,8,4,2]=>0000000 [[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[1,4,3,6,7,8,5,2]=>[6,4,3,1,7,8,5,2]=>0000000 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[8,7,5,4,3,1,6,2]=>0000000 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[8,6,5,4,3,1,7,2]=>0000000 [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>[8,6,4,5,1,3,7,2]=>0000000 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[8,6,4,3,1,5,7,2]=>0000000 [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[8,3,1,4,5,6,7,2]=>0000000 [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[7,6,4,5,1,3,8,2]=>0000000 [[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[1,4,5,6,7,3,8,2]=>[4,5,1,6,7,3,8,2]=>0000000 [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[1,3,5,7,6,4,8,2]=>[7,5,3,1,6,4,8,2]=>0000000 [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>[6,4,3,1,5,7,8,2]=>0000000 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[5,4,3,1,6,7,8,2]=>0000000 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[4,5,1,3,6,7,8,2]=>0000000 [[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[1,3,5,4,6,7,8,2]=>[5,3,1,4,6,7,8,2]=>0000000 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,4,2,1,3]=>0000000 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[7,8,6,5,2,1,4,3]=>0000000 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[8,6,7,5,2,1,4,3]=>0000000 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[7,6,8,5,2,1,4,3]=>0000000 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[6,7,8,2,1,5,4,3]=>0000000 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[8,7,5,6,2,1,4,3]=>0000000 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[7,5,8,2,1,6,4,3]=>0000000 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[8,6,5,7,2,1,4,3]=>0000000 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[7,6,5,8,2,1,4,3]=>0000000 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[6,7,5,2,1,8,4,3]=>0000000 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[5,6,2,1,7,8,4,3]=>0000000 [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[7,8,4,2,1,6,5,3]=>0000000 [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[8,6,4,2,1,7,5,3]=>0000000 [[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>[8,4,2,1,5,6,7,3]=>0000000 [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>[7,6,4,2,1,5,8,3]=>0000000 [[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>[6,4,2,1,7,5,8,3]=>0000000 [[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>[5,6,2,1,4,7,8,3]=>0000000 [[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[5,4,2,1,6,7,8,3]=>0000000 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[6,7,8,1,2,5,4,3]=>0000000 [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[1,2,5,6,8,7,4,3]=>[8,5,6,1,2,7,4,3]=>0000000 [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[7,6,5,8,1,2,4,3]=>0000000 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[5,6,1,2,7,8,4,3]=>0000000 [[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[7,8,4,1,2,6,5,3]=>0000000 [[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[1,2,4,5,8,7,6,3]=>[8,7,4,1,2,5,6,3]=>0000000 [[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>[8,6,4,1,2,5,7,3]=>0000000 [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[7,6,4,1,2,5,8,3]=>0000000 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[6,4,1,2,7,5,8,3]=>0000000 [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[5,4,1,2,6,7,8,3]=>0000000 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[8,7,6,5,3,2,1,4]=>0000000 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[8,7,5,3,2,1,6,4]=>0000000 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[8,5,3,2,1,6,7,4]=>0000000 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[8,7,6,5,2,3,1,4]=>0000000 [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[8,6,7,2,3,1,5,4]=>0000000 [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[8,6,5,2,3,1,7,4]=>0000000 [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[6,7,2,3,1,5,8,4]=>0000000 [[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[6,5,2,3,1,7,8,4]=>0000000 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[5,2,3,1,6,7,8,4]=>0000000 [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[1,3,2,7,8,6,5,4]=>[7,8,6,3,1,2,5,4]=>0000000 [[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[6,5,3,1,2,7,8,4]=>0000000 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]=>0000000 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>[7,8,6,2,1,3,5,4]=>0000000 [[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[2,1,3,6,7,8,5,4]=>[6,7,2,1,3,8,5,4]=>0000000 [[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[2,1,3,5,6,7,8,4]=>[5,2,1,3,6,7,8,4]=>0000000 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[7,6,5,1,2,3,8,4]=>0000000 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[5,1,2,3,6,7,8,4]=>0000000 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[8,7,6,4,3,2,1,5]=>0000000 [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[7,8,4,3,2,1,6,5]=>0000000 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[8,6,4,3,2,1,7,5]=>0000000 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[7,6,4,3,2,1,8,5]=>0000000 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[6,4,3,2,1,7,8,5]=>0000000 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[8,7,6,3,4,2,1,5]=>0000000 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[7,8,3,4,2,1,6,5]=>0000000 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[8,7,6,4,2,3,1,5]=>0000000 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[8,6,4,2,3,1,7,5]=>0000000 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[8,7,6,3,2,4,1,5]=>0000000 [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[7,8,3,2,4,1,6,5]=>0000000 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[8,7,6,2,3,4,1,5]=>0000000 [[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[7,8,2,3,4,1,6,5]=>0000000 [[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[7,6,2,3,4,1,8,5]=>0000000 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]=>0000000 [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[7,6,4,3,1,2,8,5]=>0000000 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[6,4,3,1,2,7,8,5]=>0000000 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[8,7,6,3,1,4,2,5]=>0000000 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[7,8,3,1,4,2,6,5]=>0000000 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[6,3,1,4,2,7,8,5]=>0000000 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[8,7,6,4,2,1,3,5]=>0000000 [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[7,8,4,2,1,3,6,5]=>0000000 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[8,6,4,2,1,3,7,5]=>0000000 [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[7,6,4,2,1,3,8,5]=>0000000 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[6,4,2,1,3,7,8,5]=>0000000 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]=>0000000 [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[7,8,4,1,2,3,6,5]=>0000000 [[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[8,6,4,1,2,3,7,5]=>0000000 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]=>0000000 [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[7,8,3,2,1,4,6,5]=>0000000 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[6,3,2,1,4,7,8,5]=>0000000 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[8,7,6,2,3,1,4,5]=>0000000 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]=>0000000 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]=>0000000 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>0000000 [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[7,8,1,2,3,4,6,5]=>0000000 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[8,7,5,4,3,2,1,6]=>0000000 [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>[7,5,4,2,3,1,8,6]=>0000000 [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[8,7,4,2,5,3,1,6]=>0000000 [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>[7,5,3,2,4,1,8,6]=>0000000 [[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[7,2,3,4,5,1,8,6]=>0000000 [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>[8,7,4,1,2,5,3,6]=>0000000 [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>[8,7,5,2,1,3,4,6]=>0000000 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[8,7,5,1,2,3,4,6]=>0000000 [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[8,7,4,3,2,1,5,6]=>0000000 [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[7,4,3,2,1,5,8,6]=>0000000 [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[8,7,3,4,2,1,5,6]=>0000000 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[8,7,3,2,4,1,5,6]=>0000000 [[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[8,7,3,1,4,2,5,6]=>0000000 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[8,7,3,2,1,4,5,6]=>0000000 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[8,6,5,4,3,2,1,7]=>0000000 [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[8,5,6,4,3,2,1,7]=>0000000 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[8,4,5,6,3,2,1,7]=>0000000 [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[8,4,5,3,6,2,1,7]=>0000000 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[8,6,5,2,3,4,1,7]=>0000000 [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[8,6,4,2,3,5,1,7]=>0000000 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]=>0000000 [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[8,5,6,2,1,4,3,7]=>0000000 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[8,6,4,2,1,5,3,7]=>0000000 [[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[1,2,4,5,6,3,8,7]=>[8,4,1,2,5,6,3,7]=>0000000 [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[8,5,3,2,1,6,4,7]=>0000000 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[8,6,5,2,3,1,4,7]=>0000000 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[2,3,1,5,6,4,8,7]=>[8,5,2,3,1,6,4,7]=>0000000 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]=>0000000 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[8,6,4,3,2,1,5,7]=>0000000 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[8,6,3,4,2,1,5,7]=>0000000 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[8,6,4,2,3,1,5,7]=>0000000 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[8,6,3,2,4,1,5,7]=>0000000 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[8,6,4,2,1,3,5,7]=>0000000 [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]=>[8,6,3,2,1,4,5,7]=>0000000 [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[8,4,5,3,2,1,6,7]=>0000000 [[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[8,4,2,5,3,1,6,7]=>0000000 [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[8,5,4,2,1,3,6,7]=>0000000 [[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[8,4,2,1,5,3,6,7]=>0000000 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[8,4,3,2,1,5,6,7]=>0000000 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[8,2,3,4,1,5,6,7]=>0000000 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]=>[8,3,2,1,4,5,6,7]=>0000000 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[6,7,5,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,5,6,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1,8]=>0000001 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>0000001 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,4,5,3,2,1,8]=>0000001 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[6,5,4,7,3,2,1,8]=>0000001 [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[5,6,4,7,3,2,1,8]=>0000001 [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[4,5,6,7,3,2,1,8]=>0000001 [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[7,5,3,6,4,2,1,8]=>0000001 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>0000001 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[6,5,4,3,7,2,1,8]=>0000001 [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[5,4,6,3,7,2,1,8]=>0000001 [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[5,4,3,6,7,2,1,8]=>0000001 [[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[5,6,2,7,4,3,1,8]=>0000001 [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[2,4,7,6,5,3,1,8]=>[7,6,4,2,5,3,1,8]=>0000001 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[6,4,2,7,5,3,1,8]=>0000001 [[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[2,4,5,7,6,3,1,8]=>[7,4,2,5,6,3,1,8]=>0000001 [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[6,7,3,2,5,4,1,8]=>0000001 [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>[7,6,5,2,3,4,1,8]=>0000001 [[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[6,3,2,4,7,5,1,8]=>0000001 [[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,6,2,3,4,5,1,8]=>0000001 [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[7,4,5,3,2,6,1,8]=>0000001 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>0000001 [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[5,4,6,3,2,7,1,8]=>0000001 [[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[6,3,4,5,2,7,1,8]=>0000001 [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[5,4,3,6,2,7,1,8]=>0000001 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[4,5,3,6,2,7,1,8]=>0000001 [[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[3,4,5,6,2,7,1,8]=>0000001 [[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[5,4,2,6,3,7,1,8]=>0000001 [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1,8]=>0000001 [[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[1,4,5,6,7,3,2,8]=>[4,5,1,6,7,3,2,8]=>0000001 [[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>[7,4,3,1,5,6,2,8]=>0000001 [[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>[5,4,6,1,3,7,2,8]=>0000001 [[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>[6,5,3,1,4,7,2,8]=>0000001 [[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>[6,4,3,1,5,7,2,8]=>0000001 [[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>[5,4,3,1,6,7,2,8]=>0000001 [[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[2,1,4,7,6,5,3,8]=>[7,6,4,2,1,5,3,8]=>0000001 [[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[2,1,4,6,7,5,3,8]=>[6,4,2,1,7,5,3,8]=>0000001 [[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[2,1,5,4,6,7,3,8]=>[5,4,2,1,6,7,3,8]=>0000001 [[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,2,4,7,6,5,3,8]=>[7,6,4,1,2,5,3,8]=>0000001 [[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[1,2,4,5,7,6,3,8]=>[7,4,1,2,5,6,3,8]=>0000001 [[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>[5,4,1,2,6,7,3,8]=>0000001 [[[[.,.],.],[[[[.,.],.],.],.]],.]=>[1,2,4,5,6,7,3,8]=>[4,1,2,5,6,7,3,8]=>0000001 [[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[6,7,2,3,1,5,4,8]=>0000001 [[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>[6,5,3,1,2,7,4,8]=>0000001 [[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>0000001 [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[7,6,4,3,2,1,5,8]=>0000001 [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[6,4,3,2,1,7,5,8]=>0000001 [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[7,6,3,2,4,1,5,8]=>0000001 [[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[7,6,2,3,4,1,5,8]=>0000001 [[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>[6,4,3,1,2,7,5,8]=>0000001 [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[6,3,1,4,2,7,5,8]=>0000001 [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[7,6,3,2,1,4,5,8]=>0000001 [[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[3,2,1,4,6,7,5,8]=>[6,3,2,1,4,7,5,8]=>0000001 [[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[2,3,5,4,1,7,6,8]=>[7,5,2,3,4,1,6,8]=>0000001 [[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[7,2,3,4,5,1,6,8]=>0000001 [[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[7,3,1,4,5,2,6,8]=>0000001 [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[7,5,3,2,1,4,6,8]=>0000001 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[7,5,3,1,2,4,6,8]=>0000001 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[7,5,1,2,3,4,6,8]=>0000001 [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[7,4,3,2,1,5,6,8]=>0000001 [[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>[7,4,3,1,2,5,6,8]=>0000001 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[7,3,1,2,4,5,6,8]=>0000001 [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[7,1,2,3,4,5,6,8]=>0000001 [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[5,4,6,3,2,1,7,8]=>0000011 [[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[4,5,6,3,2,1,7,8]=>0000011 [[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[3,5,6,4,2,1,7,8]=>[5,3,6,4,2,1,7,8]=>0000011 [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[5,4,3,6,2,1,7,8]=>0000011 [[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>[6,4,2,5,3,1,7,8]=>0000011 [[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[2,5,4,6,3,1,7,8]=>[5,4,2,6,3,1,7,8]=>0000011 [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>0000011 [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7,8]=>0000011 [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[4,5,3,2,6,1,7,8]=>0000011 [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[5,4,6,1,3,2,7,8]=>0000011 [[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[1,3,6,5,4,2,7,8]=>[6,5,3,1,4,2,7,8]=>0000011 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[5,3,1,6,4,2,7,8]=>0000011 [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[6,4,3,1,5,2,7,8]=>0000011 [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[5,4,3,1,6,2,7,8]=>0000011 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[5,6,2,1,4,3,7,8]=>0000011 [[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>[6,4,2,1,5,3,7,8]=>0000011 [[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[6,4,1,2,5,3,7,8]=>0000011 [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[4,1,2,5,6,3,7,8]=>0000011 [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>[5,3,2,1,6,4,7,8]=>0000011 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[6,4,3,2,1,5,7,8]=>0000011 [[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]=>[6,4,3,1,2,5,7,8]=>0000011 [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[6,4,2,1,3,5,7,8]=>0000011 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111 [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[4,5,3,2,1,6,7,8]=>0000111 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>0000111 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>0000111 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>0000111 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>0000111 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[4,2,5,3,1,6,7,8]=>0000111 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>0000111 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>0000111 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>0000111 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>0000111 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>0000111 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>0000111 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0000111 [[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>0000111 [[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[5,3,1,4,2,6,7,8]=>0000111 [[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]=>[5,4,2,1,3,6,7,8]=>0000111 [[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>0000111 [[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[2,3,1,5,4,6,7,8]=>[5,2,3,1,4,6,7,8]=>0000111 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>0000111 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>0000111 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>0001111 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>0001111 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>0001111 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>0001111 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0001111 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>0001111 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>0001111 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>0001111 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>0001111 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>0011111 [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0011111 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>0011111 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>0111111 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>1111111
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
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.