Identifier
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0010;cc-rep-0Cc0002;cc-rep-3
[.,.]=>[1]=>[1]=>[1] [.,[.,.]]=>[2,1]=>[2,1]=>[1,1] [[.,.],.]=>[1,2]=>[1,2]=>[2] [.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>[2,1] [.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[1,1,1] [[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>[2,1] [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1] [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[3] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>[3,1] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>[2,1,1] [.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>[2,1,1] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[1,1,1,1] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[2,1,1] [[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>[2,2] [[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>[2,1,1] [[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>[2,2] [[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>[3,1] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>[3,1] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[2,1,1] [[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2,4]=>[3,1] [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[3,1] [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[4] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[4,1] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[3,1,1] [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[3,1,1] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[2,1,1,1] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[3,1,1] [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[3,1,1] [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[2,2,1] [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[2,1,1,1] [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[2,2,1] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[2,1,1,1] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[1,1,1,1,1] [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[2,1,1,1] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[2,1,1,1] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[3,1,1] [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[3,2] [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[2,2,1] [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[2,2,1] [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[2,1,1,1] [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[3,1,1] [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[3,2] [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[2,2,1] [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[3,2] [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[3,1,1] [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[3,2] [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[2,2,1] [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[3,2] [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[3,2] [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[4,1] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[4,1] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[3,1,1] [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[3,1,1] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[2,1,1,1] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[3,1,1] [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[3,2] [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[3,1,1] [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[3,2] [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[4,1] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[3,1,1] [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[4,1] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[4,1] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[5,1] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[4,1,1] [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[4,1,1] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[3,1,1,1] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[4,1,1] [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[4,1,1] [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[3,2,1] [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[3,1,1,1] [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[3,2,1] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[3,1,1,1] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[2,1,1,1,1] [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[3,1,1,1] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[3,1,1,1] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[4,1,1] [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[4,1,1] [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[3,2,1] [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[3,2,1] [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[2,2,1,1] [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[3,2,1] [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[3,1,1,1] [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[2,2,1,1] [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[3,2,1] [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[3,2,1] [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[3,1,1,1] [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[2,1,1,1,1] [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[2,2,1,1] [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[2,2,1,1] [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[3,2,1] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[3,1,1,1] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[2,1,1,1,1] [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[2,1,1,1,1] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[2,1,1,1,1] [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[2,2,1,1] [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[2,1,1,1,1] [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[2,2,1,1] [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[3,1,1,1] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[3,1,1,1] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[2,1,1,1,1] [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[3,1,1,1] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[3,1,1,1] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[4,1,1] [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[4,2] [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[3,2,1] [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[3,2,1] [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[2,2,1,1] [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[3,2,1] [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[3,2,1] [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[3,2,1] [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[3,1,1,1] [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[3,2,1] [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[3,1,1,1] [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[2,1,1,1,1] [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[3,1,1,1] [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[3,1,1,1] [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[4,1,1] [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[4,2] [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[3,2,1] [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[3,2,1] [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[2,2,1,1] [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[3,2,1] [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[4,2] [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[3,2,1] [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[3,2,1] [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[3,1,1,1] [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,1,1] [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[4,2] [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[3,2,1] [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[3,2,1] [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[2,2,2] [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[3,3] [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[3,2,1] [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[3,3] [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[3,2,1] [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[4,2] [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[4,1,1] [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[4,2] [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[3,2,1] [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[3,2,1] [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[2,2,1,1] [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[3,2,1] [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[3,3] [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[3,2,1] [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[3,3] [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[4,2] [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[4,2] [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[3,2,1] [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[4,2] [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[4,2] [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[5,1] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,1] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[4,1,1] [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[4,1,1] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[3,1,1,1] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[4,1,1] [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[4,1,1] [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[3,2,1] [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[3,1,1,1] [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[3,2,1] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[3,1,1,1] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[2,1,1,1,1] [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[3,1,1,1] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[3,1,1,1] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[4,1,1] [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[4,2] [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[3,2,1] [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[3,2,1] [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[3,1,1,1] [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[4,1,1] [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[4,2] [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[3,2,1] [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[4,2] [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,1,1] [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[4,2] [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[3,2,1] [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[4,2] [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[4,2] [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1] [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[5,1] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[4,1,1] [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,1,1] [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[3,1,1,1] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[4,1,1] [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,2] [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[4,1,1] [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,2] [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[5,1] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[5,1] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[4,1,1] [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[5,1] [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[5,1] [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[6,1] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[5,1,1] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[5,1,1] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[4,1,1,1] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[5,1,1] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[5,1,1] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[4,2,1] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[4,1,1,1] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[4,2,1] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[4,1,1,1] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[4,1,1,1] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[4,1,1,1] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[5,1,1] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[5,1,1] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[4,2,1] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[4,2,1] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[3,2,1,1] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[4,2,1] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[4,1,1,1] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[3,2,1,1] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[4,2,1] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[4,2,1] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[4,1,1,1] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[3,1,1,1,1] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[3,2,1,1] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[3,2,1,1] [.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[4,2,1] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[4,1,1,1] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[3,1,1,1,1] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[3,1,1,1,1] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1] [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[3,1,1,1,1] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[3,2,1,1] [.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[3,1,1,1,1] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[3,2,1,1] [.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[4,1,1,1] [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[4,1,1,1] [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[3,1,1,1,1] [.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[4,1,1,1] [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[4,1,1,1] [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[5,1,1] [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[5,1,1] [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[4,2,1] [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[4,2,1] [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[3,2,1,1] [.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[4,2,1] [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[4,2,1] [.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[3,3,1] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[3,2,1,1] [.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[3,3,1] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[3,2,1,1] [.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[2,2,1,1,1] [.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[3,2,1,1] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[3,2,1,1] [.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[4,2,1] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[4,1,1,1] [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[3,2,1,1] [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[3,2,1,1] [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[2,2,2,1] [.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[3,2,1,1] [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[4,2,1] [.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[3,3,1] [.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[3,3,1] [.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[3,2,1,1] [.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[4,2,1] [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[4,1,1,1] [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[3,2,1,1] [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[3,1,1,1,1] [.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[2,2,1,1,1] [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[3,2,1,1] [.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[3,2,1,1] [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[3,2,1,1] [.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[3,2,1,1] [.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[4,2,1] [.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[4,2,1] [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[4,1,1,1] [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[3,1,1,1,1] [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[3,1,1,1,1] [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[2,1,1,1,1,1] [.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[2,2,1,1,1] [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[3,2,1,1] [.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[2,2,1,1,1] [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[3,2,1,1] [.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[3,2,1,1] [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[3,2,1,1] [.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[2,2,1,1,1] [.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[3,2,1,1] [.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[3,2,1,1] [.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[4,2,1] [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[4,1,1,1] [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[3,1,1,1,1] [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[3,1,1,1,1] [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[2,1,1,1,1,1] [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[3,1,1,1,1] [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[3,1,1,1,1] [.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[2,2,1,1,1] [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[2,1,1,1,1,1] [.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[2,2,1,1,1] [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[2,1,1,1,1,1] [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1] [.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[2,1,1,1,1,1] [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[2,1,1,1,1,1] [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[3,1,1,1,1] [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[3,2,1,1] [.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[2,2,1,1,1] [.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[2,2,1,1,1] [.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[2,1,1,1,1,1] [.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[3,1,1,1,1] [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[3,2,1,1] [.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[2,2,1,1,1] [.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[3,2,1,1] [.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[3,1,1,1,1] [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[3,2,1,1] [.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[2,2,1,1,1] [.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[3,2,1,1] [.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[3,2,1,1] [.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[4,1,1,1] [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[4,1,1,1] [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[3,1,1,1,1] [.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[3,1,1,1,1] [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[2,1,1,1,1,1] [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[3,1,1,1,1] [.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[3,2,1,1] [.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[3,1,1,1,1] [.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[3,2,1,1] [.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[4,1,1,1] [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[4,1,1,1] [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[3,1,1,1,1] [.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[4,1,1,1] [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[4,1,1,1] [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[5,1,1] [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[5,2] [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[4,2,1] [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[4,2,1] [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[3,2,1,1] [[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[4,2,1] [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[4,2,1] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[3,3,1] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[3,2,1,1] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[3,3,1] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[3,2,1,1] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[2,2,1,1,1] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[3,2,1,1] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[3,2,1,1] [[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[4,2,1] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[4,2,1] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[3,3,1] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[3,3,1] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[3,2,1,1] [[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[4,2,1] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[4,1,1,1] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[3,2,1,1] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[4,2,1] [[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[4,2,1] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[4,1,1,1] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[3,1,1,1,1] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[3,2,1,1] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[3,2,1,1] [[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[4,2,1] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[4,1,1,1] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[3,1,1,1,1] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[3,1,1,1,1] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[2,1,1,1,1,1] [[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[3,1,1,1,1] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[3,2,1,1] [[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[3,1,1,1,1] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[3,2,1,1] [[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[4,1,1,1] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[4,1,1,1] [[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[3,1,1,1,1] [[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[4,1,1,1] [[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[4,1,1,1] [[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[5,1,1] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[5,2] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[4,2,1] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[4,2,1] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[3,2,1,1] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[4,2,1] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[4,2,1] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[3,3,1] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[3,2,1,1] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[3,3,1] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[3,2,1,1] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[2,2,1,1,1] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[3,2,1,1] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[3,2,1,1] [[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[4,2,1] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[5,2] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[4,2,1] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[4,2,1] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[3,2,1,1] [[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[4,2,1] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[4,2,1] [[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[4,2,1] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[4,1,1,1] [[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[4,2,1] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[4,1,1,1] [[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[3,1,1,1,1] [[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[4,1,1,1] [[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[4,1,1,1] [[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[5,1,1] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[5,2] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[4,2,1] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[4,2,1] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[3,2,1,1] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[4,2,1] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[4,2,1] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[3,2,2] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[3,2,2] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[2,2,2,1] [[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[3,2,2] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[4,3] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[3,3,1] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[3,3,1] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[3,2,1,1] [[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[4,2,1] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[4,3] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[3,3,1] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[3,3,1] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[3,2,1,1] [[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[4,2,1] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[5,2] [[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[4,2,1] [[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[4,2,1] [[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[4,1,1,1] [[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,1,1] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[5,2] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[4,2,1] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[4,2,1] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[3,2,2] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[4,2,1] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[3,2,2] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[3,2,1,1] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[2,2,2,1] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[3,3,1] [[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[3,2,2] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[4,3] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[3,3,1] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[3,3,1] [[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[3,2,2] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[4,3] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[3,3,1] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[4,3] [[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[4,2,1] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[4,3] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[4,2,1] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[3,3,1] [[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[3,2,2] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[4,3] [[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[4,2,1] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[4,3] [[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[4,2,1] [[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[5,2] [[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[5,1,1] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[5,2] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[4,2,1] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[4,2,1] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[3,2,1,1] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[4,2,1] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[4,2,1] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[3,3,1] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[3,2,1,1] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[3,3,1] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[3,2,1,1] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[2,2,1,1,1] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[3,2,1,1] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[3,2,1,1] [[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[4,2,1] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[4,3] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[3,3,1] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[3,3,1] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[3,2,1,1] [[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[4,2,1] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[4,3] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[3,3,1] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[4,3] [[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[4,2,1] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[4,3] [[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[3,3,1] [[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[4,3] [[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[4,3] [[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[5,2] [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[5,2] [[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[4,2,1] [[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[4,2,1] [[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[3,2,1,1] [[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[4,2,1] [[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[4,3] [[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[4,2,1] [[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[4,3] [[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[5,2] [[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[5,2] [[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[4,2,1] [[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[5,2] [[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[5,2] [[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[6,1] [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,1] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[5,1,1] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[5,1,1] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[4,1,1,1] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[5,1,1] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[5,1,1] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[4,2,1] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[4,1,1,1] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[4,2,1] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[4,1,1,1] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[3,1,1,1,1] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[4,1,1,1] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[4,1,1,1] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[5,1,1] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[5,1,1] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[4,2,1] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[4,2,1] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[3,2,1,1] [[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[4,2,1] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[4,1,1,1] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[3,2,1,1] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[4,2,1] [[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[4,2,1] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[4,1,1,1] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[3,1,1,1,1] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[3,2,1,1] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[3,2,1,1] [[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[4,2,1] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[4,1,1,1] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[3,1,1,1,1] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[3,1,1,1,1] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[2,1,1,1,1,1] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[3,1,1,1,1] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[3,2,1,1] [[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[3,1,1,1,1] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[3,2,1,1] [[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[4,1,1,1] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[4,1,1,1] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[3,1,1,1,1] [[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[4,1,1,1] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[4,1,1,1] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[5,1,1] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[5,2] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[4,2,1] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[4,2,1] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[3,2,1,1] [[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[4,2,1] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[4,2,1] [[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[4,2,1] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[4,1,1,1] [[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[4,2,1] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[4,1,1,1] [[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[3,1,1,1,1] [[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[4,1,1,1] [[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[4,1,1,1] [[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[5,1,1] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[5,2] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[4,2,1] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[4,2,1] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[3,2,1,1] [[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[4,2,1] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[5,2] [[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[4,2,1] [[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[4,2,1] [[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[4,1,1,1] [[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[5,1,1] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[5,2] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[4,2,1] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[4,2,1] [[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[3,2,2] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[4,3] [[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[4,2,1] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[4,3] [[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[4,2,1] [[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[5,2] [[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,1,1] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[5,2] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[4,2,1] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[4,2,1] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[3,2,1,1] [[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[4,2,1] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[4,3] [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[4,2,1] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[4,3] [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[5,2] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[5,2] [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[4,2,1] [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[5,2] [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[5,2] [[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,1] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[6,1] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[5,1,1] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[5,1,1] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[4,1,1,1] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[5,1,1] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[5,1,1] [[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[4,2,1] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[4,1,1,1] [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[4,2,1] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[4,1,1,1] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[3,1,1,1,1] [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[4,1,1,1] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[4,1,1,1] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[5,1,1] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,2] [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[4,2,1] [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[4,2,1] [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[4,1,1,1] [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[5,1,1] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,2] [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[4,2,1] [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,2] [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[5,1,1] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,2] [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[4,2,1] [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,2] [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,2] [[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[6,1] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[6,1] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[5,1,1] [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[5,1,1] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,1,1,1] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[5,1,1] [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[5,2] [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[5,1,1] [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[5,2] [[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[6,1] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[6,1] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[5,1,1] [[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[6,1] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[6,1] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[7,1] [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[6,1,1] [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1] [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[6,1,1] [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>[5,2,1] [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[5,1,1,1] [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1] [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>[5,1,1,1] [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[5,1,1,1] [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[6,1,1] [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[6,1,1] [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>[5,2,1] [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,3,6,8,4,5,7,1]=>[5,2,1] [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[2,3,7,5,8,4,6,1]=>[4,2,1,1] [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[4,1,1,1,1] [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1] [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>[5,1,1,1] [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[6,1,1] [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]=>[6,1,1] [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[2,4,5,3,8,6,7,1]=>[5,2,1] [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>[4,3,1] [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>[3,2,1,1,1] [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[2,4,8,3,7,5,6,1]=>[4,2,1,1] [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[5,2,1] [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[3,2,2,1] [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>[4,2,1,1] [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[5,2,1] [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]=>[4,2,1,1] [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[4,2,1,1] [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[2,7,4,5,6,8,3,1]=>[5,1,1,1] [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>[3,1,1,1,1,1] [.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1] [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[3,1,1,1,1,1] [.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>[4,1,1,1,1] [.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>[5,1,1,1] [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]=>[6,1,1] [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>[4,2,1,1] [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>[3,2,1,1,1] [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[5,2,1] [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>[5,2,1] [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[4,3,1] [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[3,3,1,1] [.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[4,3,1] [.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>[4,3,1] [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[3,2,1,1,1] [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[3,2,1,1,1] [.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[2,2,1,1,1,1] [.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[3,8,2,5,4,6,7,1]=>[4,2,1,1] [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[5,1,1,1] [.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[4,2,1,1] [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>[3,2,2,1] [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[3,3,1,1] [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[2,2,2,1,1] [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>[3,2,2,1] [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[4,2,1,1] [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[5,2,1] [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[4,3,1] [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[4,3,1] [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[5,2,1] [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>[4,2,1,1] [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[3,2,1,1,1] [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[2,2,2,1,1] [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>[4,2,1,1] [.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>[4,2,1,1] [.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>[4,2,1,1] [.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>[5,2,1] [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>[4,2,1,1] [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[4,1,1,1,1] [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[3,2,1,1,1] [.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[6,5,2,3,8,4,7,1]=>[4,2,1,1] [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[3,2,1,1,1] [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>[3,1,1,1,1,1] [.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[2,1,1,1,1,1,1] [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[4,2,1,1] [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[3,2,1,1,1] [.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>[3,2,1,1,1] [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[3,3,1,1] [.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>[4,2,1,1] [.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[7,4,8,3,2,5,6,1]=>[3,2,1,1,1] [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[4,1,1,1,1] [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[3,2,1,1,1] [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>[2,2,1,1,1,1] [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>[3,1,1,1,1,1] [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>[2,1,1,1,1,1,1] [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[2,1,1,1,1,1,1] [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1] [.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[2,1,1,1,1,1,1] [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>[2,2,1,1,1,1] [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>[2,2,1,1,1,1] [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>[3,2,1,1,1] [.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[3,2,1,1,1] [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[8,6,2,5,7,4,3,1]=>[3,1,1,1,1,1] [.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>[3,2,1,1,1] [.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>[3,1,1,1,1,1] [.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>[4,1,1,1,1] [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>[4,2,1,1] [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]=>[3,2,1,1,1] [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>[3,3,1,1] [.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,5,7,3,4,2,6,1]=>[3,2,1,1,1] [.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]=>[4,2,1,1] [.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[8,5,6,3,4,2,7,1]=>[3,2,1,1,1] [.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,6,2,4,5,3,7,1]=>[4,1,1,1,1] [.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[4,1,1,1,1] [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[4,1,1,1,1] [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>[6,2] [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>[5,2,1] [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>[3,2,1,1,1] [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>[4,2,1,1] [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[5,2,1] [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]=>[4,3,1] [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]=>[4,2,1,1] [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>[4,3,1] [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[3,1,7,6,4,8,5,2]=>[3,3,1,1] [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[3,1,8,6,7,5,4,2]=>[3,2,1,1,1] [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]=>[2,2,1,1,1,1] [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]=>[3,3,1,1] [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[3,1,8,5,7,4,6,2]=>[3,3,1,1] [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>[5,2,1] [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>[5,2,1] [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[4,1,5,3,8,7,6,2]=>[3,3,1,1] [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[4,3,1] [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[4,3,1] [[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]=>[4,3,1] [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[4,2,1,1] [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[5,2,1] [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[5,1,4,8,3,7,6,2]=>[3,2,2,1] [[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[5,1,7,3,4,8,6,2]=>[4,3,1] [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>[4,2,1,1] [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>[5,2,1] [[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]=>[4,2,1,1] [[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]=>[4,2,1,1] [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>[5,2,1] [[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[8,1,6,7,4,5,3,2]=>[3,2,1,1,1] [[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>[3,1,1,1,1,1] [[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]=>[2,1,1,1,1,1,1] [[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[8,1,7,6,4,5,3,2]=>[3,1,1,1,1,1] [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]=>[3,2,1,1,1] [[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[8,1,4,7,3,6,5,2]=>[3,2,1,1,1] [[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>[4,2,1,1] [[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>[5,1,1,1] [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>[4,1,1,1,1] [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>[4,2,1,1] [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>[5,1,1,1] [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>[4,1,1,1,1] [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[6,2] [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[4,3,1] [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>[3,2,1,1,1] [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[5,2,1] [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>[4,2,1,1] [[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>[4,3,1] [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>[2,2,1,1,1,1] [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[6,2] [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>[5,2,1] [[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[4,3,1] [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[4,3,1] [[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[3,2,1,1,1] [[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[4,2,1,1] [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[5,2,1] [[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>[4,3,1] [[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>[4,2,1,1] [[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[5,2,1] [[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[5,2,1] [[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[4,1,1,1,1] [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[5,1,1,1] [[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[4,1,1,1,1] [[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[3,1,1,1,1,1] [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[4,1,1,1,1] [[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[5,1,1,1] [[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[5,1,1,1] [[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[6,1,1] [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>[6,2] [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>[5,2,1] [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[4,3,1] [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>[4,2,1,1] [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[5,2,1] [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[5,2,1] [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[4,2,2] [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[2,2,2,1,1] [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[4,2,2] [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[5,3] [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[4,3,1] [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[4,3,1] [[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>[4,3,1] [[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[4,2,1,1] [[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[4,2,1,1] [[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[5,2,1] [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>[5,3] [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>[4,3,1] [[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[4,3,1] [[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>[4,3,1] [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>[4,2,1,1] [[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[5,2,1] [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[6,2] [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[5,2,1] [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[5,2,1] [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[4,2,1,1] [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[5,2,1] [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[5,2,1] [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[5,2,1] [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[5,1,1,1] [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[5,2,1] [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[5,1,1,1] [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[4,1,1,1,1] [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[5,1,1,1] [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[5,1,1,1] [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[6,1,1] [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[5,2,1] [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[4,2,1,1] [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[5,2,1] [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[3,2,2,1] [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>[4,3,1] [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[4,3,1] [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[5,3] [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>[4,3,1] [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[5,3] [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[4,3,1] [[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[4,3,1] [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[4,3,1] [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[4,3,1] [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>[4,3,1] [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[3,3,2] [[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[4,3,1] [[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>[4,3,1] [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[6,2] [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[5,2,1] [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[5,2,1] [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[5,1,1,1] [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,1,1] [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[5,2,1] [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[5,2,1] [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>[3,2,2,1] [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>[4,3,1] [[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[3,3,2] [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>[2,2,2,1,1] [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[4,3,1] [[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[3,3,2] [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>[5,3] [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[5,3] [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[4,3,1] [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[4,4] [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[4,3,1] [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[4,4] [[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>[4,3,1] [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[5,3] [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[5,2,1] [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[5,3] [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[5,2,1] [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[3,2,2,1] [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[4,2,2] [[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[5,3] [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>[5,3] [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>[5,2,1] [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>[4,2,2] [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]=>[5,2,1] [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>[4,3,1] [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>[4,3,1] [[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[3,6,2,8,4,5,1,7]=>[4,3,1] [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[3,3,1,1] [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>[4,2,1,1] [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[6,3,5,8,4,2,1,7]=>[3,2,1,1,1] [[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[6,5,8,3,4,2,1,7]=>[3,2,1,1,1] [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[5,3] [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>[4,3,1] [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]=>[4,3,1] [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>[3,3,2] [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>[4,4] [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[5,3] [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>[5,2,1] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[5,3] [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[4,3,1] [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>[3,3,1,1] [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[4,4] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[4,4] [[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[5,3] [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[6,2] [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>[4,2,1,1] [[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>[5,2,1] [[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[4,3,1] [[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>[4,2,1,1] [[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[5,3] [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[6,2] [[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>[5,2,1] [[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>[5,2,1] [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>[4,2,1,1] [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>[5,2,1] [[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[5,3] [[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[5,2,1] [[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[5,3] [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[6,2] [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[6,2] [[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>[5,2,1] [[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[6,2] [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[7,1] [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[5,1,1,1] [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[6,1,1] [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>[5,1,1,1] [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[4,1,1,1,1] [[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>[5,1,1,1] [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]=>[5,2,1] [[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[2,4,7,3,5,6,1,8]=>[5,2,1] [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>[5,1,1,1] [[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]=>[5,2,1] [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[4,3,1] [[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]=>[4,2,1,1] [[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]=>[4,2,1,1] [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>[5,2,1] [[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[4,3,1] [[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]=>[4,3,1] [[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[4,2,1,1] [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]=>[5,2,1] [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[3,1,1,1,1,1] [[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[7,3,4,5,2,6,1,8]=>[6,5,7,3,4,2,1,8]=>[3,2,1,1,1] [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>[4,2,1,1] [[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>[4,2,1,1] [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>[3,1,1,1,1,1] [[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>[3,2,1,1,1] [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>[3,1,1,1,1,1] [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1] [[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[4,2,1,1] [[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[7,4,5,3,2,6,1,8]=>[4,1,1,1,1] [[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>[5,1,1,1] [[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[3,1,4,7,5,6,2,8]=>[5,2,1] [[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[7,1,4,6,5,3,2,8]=>[4,1,1,1,1] [[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[7,1,5,3,6,4,2,8]=>[4,2,1,1] [[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[2,4,1,7,5,6,3,8]=>[5,2,1] [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]=>[6,2] [[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[4,1,2,5,7,6,3,8]=>[5,2,1] [[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]=>[5,2,1] [[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>[4,1,1,1,1] [[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>[5,1,1,1] [[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>[5,1,1,1] [[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[2,3,7,1,5,6,4,8]=>[5,2,1] [[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]=>[5,2,1] [[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]=>[5,2,1] [[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[6,2] [[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>[5,2,1] [[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[5,2,1] [[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[5,1,1,1] [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[6,1,1] [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>[5,2,1] [[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[4,1,6,3,2,7,5,8]=>[4,3,1] [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[5,3] [[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[5,3] [[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>[5,2,1] [[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[5,3] [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[3,5,2,1,7,4,6,8]=>[4,3,1] [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[5,3] [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[6,2] [[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>[5,2,1] [[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>[4,2,1,1] [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,1] [[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[4,2,1,1] [[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[5,3,6,2,4,1,7,8]=>[4,2,1,1] [[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[5,1,1,1] [[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]=>[5,2,1] [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>[4,2,1,1] [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[5,2,1] [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>[5,1,1,1] [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]=>[5,2,1] [[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]=>[5,2,1] [[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>[4,2,1,1] [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>[5,2,1] [[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[3,5,2,1,6,4,7,8]=>[5,2,1] [[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>[4,2,2] [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[7,1] [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[6,1,1] [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>[6,1,1] [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[5,1,1,1] [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>[6,1,1] [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[6,1,1] [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>[5,2,1] [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,1,1,1] [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,2,1] [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[5,1,1,1] [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[4,1,1,1,1] [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[5,1,1,1] [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,1,1,1] [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[6,1,1] [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[7,1] [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[7,1] [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[5,1,1,1] [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[7,1] [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[7,1] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8]
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 views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.