Identifier
Mp00014: Binary trees to 132-avoiding permutationPermutations
Mp00071: Permutations descent compositionInteger compositions
Mp00231: Integer compositions bounce path Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-3
[.,.]=>[1]=>[1]=>[1,0] [.,[.,.]]=>[2,1]=>[1,1]=>[1,0,1,0] [[.,.],.]=>[1,2]=>[2]=>[1,1,0,0] [.,[.,[.,.]]]=>[3,2,1]=>[1,1,1]=>[1,0,1,0,1,0] [.,[[.,.],.]]=>[2,3,1]=>[2,1]=>[1,1,0,0,1,0] [[.,.],[.,.]]=>[3,1,2]=>[1,2]=>[1,0,1,1,0,0] [[.,[.,.]],.]=>[2,1,3]=>[1,2]=>[1,0,1,1,0,0] [[[.,.],.],.]=>[1,2,3]=>[3]=>[1,1,1,0,0,0] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,1,1,1]=>[1,0,1,0,1,0,1,0] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,1]=>[1,1,0,0,1,0,1,0] [.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,2,1]=>[1,0,1,1,0,0,1,0] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,2,1]=>[1,0,1,1,0,0,1,0] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,1]=>[1,1,1,0,0,0,1,0] [[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,1,2]=>[1,0,1,0,1,1,0,0] [[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,2]=>[1,1,0,0,1,1,0,0] [[.,[.,.]],[.,.]]=>[4,2,1,3]=>[1,1,2]=>[1,0,1,0,1,1,0,0] [[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,3]=>[1,0,1,1,1,0,0,0] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[1,1,2]=>[1,0,1,0,1,1,0,0] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,2]=>[1,1,0,0,1,1,0,0] [[[.,.],[.,.]],.]=>[3,1,2,4]=>[1,3]=>[1,0,1,1,1,0,0,0] [[[.,[.,.]],.],.]=>[2,1,3,4]=>[1,3]=>[1,0,1,1,1,0,0,0] [[[[.,.],.],.],.]=>[1,2,3,4]=>[4]=>[1,1,1,1,0,0,0,0] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0] [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,1,1]=>[1,1,1,0,0,0,1,0,1,0] [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0] [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,2,1]=>[1,1,0,0,1,1,0,0,1,0] [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0] [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[2,2,1]=>[1,1,0,0,1,1,0,0,1,0] [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,3,1]=>[1,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,1]=>[1,1,1,1,0,0,0,0,1,0] [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0] [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0] [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0] [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2]=>[1,1,1,0,0,0,1,1,0,0] [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0] [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0] [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0] [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0] [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0] [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0] [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,1,2]=>[1,1,0,0,1,0,1,1,0,0] [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[1,2,2]=>[1,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[3,2]=>[1,1,1,0,0,0,1,1,0,0] [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0] [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0] [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0] [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[1,1,3]=>[1,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3]=>[1,1,0,0,1,1,1,0,0,0] [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[1,4]=>[1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5]=>[1,1,1,1,1,0,0,0,0,0] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0] [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0] [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0] [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0] [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0] [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0] [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0] [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0] [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0] [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0] [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0] [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0] [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0] [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0] [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0] [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0] [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6]=>[1,1,1,1,1,1,0,0,0,0,0,0] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0] [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0] [.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0] [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0] [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0] [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0] [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0] [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0] [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0] [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0] [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0] [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0] [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0] [.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0] [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0] [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0] [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0] [.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0] [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0] [.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0] [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0] [.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0] [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0] [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0] [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0] [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0] [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0] [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] [.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] [[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] [[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] [[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] [[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] [[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
Map
bounce path
Description
The bounce path determined by an integer composition.