Identifier
Mp00014: Binary trees to 132-avoiding permutationPermutations
Mp00235: Permutations descent views to invisible inversion bottomsPermutations
Mp00108: Permutations cycle type Integer partitions
Images
=>
Cc0010;cc-rep-0Cc0002;cc-rep-3
[.,.]=>[1]=>[1]=>[1] [.,[.,.]]=>[2,1]=>[2,1]=>[2] [[.,.],.]=>[1,2]=>[1,2]=>[1,1] [.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>[3] [.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[2,1] [[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>[3] [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1] [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,1,1] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>[4] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>[3,1] [.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>[4] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[2,2] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[2,1,1] [[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>[4] [[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>[3,1] [[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>[4] [[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>[4] [[.,[.,[.,.]]],.]=>[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]=>[2,1,1] [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,1,1,1] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[5] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[4,1] [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[5] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[3,2] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[3,1,1] [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[5] [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[4,1] [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[5] [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[5] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[3,2] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[2,2,1] [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[3,2] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[2,2,1] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[2,1,1,1] [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[5] [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[4,1] [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[5] [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[3,2] [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[3,1,1] [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[5] [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[4,1] [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[5] [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[4,1] [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[5] [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[5] [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[5] [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[5] [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5] [[.,[.,[.,[.,.]]]],.]=>[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]=>[4,1] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[2,2,1] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[2,1,1,1] [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[4,1] [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[3,1,1] [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[4,1] [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[3,1,1] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,1,1,1] [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,1] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,1,1] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,1,1,1,1] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[5,1] [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[6] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[4,2] [.,[.,[.,[[[.,.],.],.]]]]=>[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]=>[6] [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[5,1] [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[6] [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[6] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[3,3] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[3,2,1] [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[3,3] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[3,2,1] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[3,1,1,1] [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[6] [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[5,1] [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[6] [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[4,2] [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[4,1,1] [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[6] [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[5,1] [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[6] [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[5,1] [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6] [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[6] [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[6] [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6] [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[4,2] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[3,2,1] [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[4,2] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[2,2,2] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[2,2,1,1] [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[4,2] [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[3,2,1] [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[4,2] [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[4,2] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[3,2,1] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[2,2,1,1] [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[3,2,1] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[2,2,1,1] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,1,1,1,1] [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[6] [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[5,1] [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[6] [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[4,2] [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[4,1,1] [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6] [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[5,1] [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[6] [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[6] [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[3,3] [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[3,2,1] [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[3,3] [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[3,2,1] [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[3,1,1,1] [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[6] [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[5,1] [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[6] [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[4,2] [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[4,1,1] [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6] [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[5,1] [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[6] [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[4,2] [[[.,.],.],[[[.,.],.],.]]=>[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]=>[6] [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[5,1] [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[6] [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[5,1] [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6] [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[5,1] [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[6] [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[5,1] [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6] [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,1] [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6] [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[6] [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[6] [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[6] [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6] [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6] [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[6] [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[6] [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6] [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6] [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6] [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6] [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6] [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6] [[.,[.,[.,[.,[.,.]]]]],.]=>[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]=>[5,1] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[3,2,1] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[3,1,1,1] [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[5,1] [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[4,1,1] [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,1] [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,1] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[3,2,1] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[2,2,1,1] [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[3,2,1] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[2,2,1,1] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,1,1,1,1] [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,1] [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[4,1,1] [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[5,1] [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[3,2,1] [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[3,1,1,1] [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[5,1] [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[4,1,1] [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,1] [[[[.,.],.],[[.,.],.]],.]=>[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]=>[5,1] [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,1] [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,1] [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,1] [[[[[.,.],.],.],[.,.]],.]=>[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]=>[4,1,1] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[3,1,1,1] [[[.,[[.,.],[.,.]]],.],.]=>[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]=>[2,2,1,1] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,1,1,1,1] [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,1,1] [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,1,1,1] [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,1,1] [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,1] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,1,1] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,1,1,1,1] [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,1,1] [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,1,1,1] [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[6,1] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[7] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[5,2] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[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]=>[7] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[6,1] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[7] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[7] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[4,3] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[4,2,1] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[4,3] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[4,2,1] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[4,1,1,1] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[7] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[6,1] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[7] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[5,2] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[5,1,1] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[6,1] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[6,1] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[7] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[7] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[7] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[7] [.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[7] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[4,3] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[3,3,1] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[4,3] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[3,2,2] [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[3,2,1,1] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[4,3] [.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[3,3,1] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[4,3] [.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[4,3] [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[3,3,1] [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[3,2,1,1] [.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[3,3,1] [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[3,2,1,1] [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[3,1,1,1,1] [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[7] [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[6,1] [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[7] [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[5,2] [.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[5,1,1] [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[7] [.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[6,1] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[7] [.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[7] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[4,3] [.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[4,2,1] [.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[4,3] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[4,2,1] [.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[4,1,1,1] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[7] [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[6,1] [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[7] [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[5,2] [.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[5,1,1] [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[7] [.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[6,1] [.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[7] [.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[5,2] [.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[5,1,1] [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[7] [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[6,1] [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[7] [.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[6,1] [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[7] [.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[6,1] [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[7] [.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[6,1] [.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[7] [.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[6,1] [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7] [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[7] [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7] [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[7] [.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[7] [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[7] [.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[7] [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[7] [.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[7] [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7] [.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[7] [.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[7] [.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7] [.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7] [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[5,2] [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[4,2,1] [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[5,2] [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[3,2,2] [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[3,2,1,1] [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[5,2] [.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[4,2,1] [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[5,2] [.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[5,2] [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[3,2,2] [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[2,2,2,1] [.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[3,2,2] [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[2,2,2,1] [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[2,2,1,1,1] [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[5,2] [.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[4,2,1] [.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[5,2] [.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[3,2,2] [.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[3,2,1,1] [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[5,2] [.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[4,2,1] [.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[5,2] [.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[4,2,1] [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[5,2] [.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[5,2] [.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[5,2] [.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[5,2] [.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[5,2] [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[4,2,1] [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[3,2,1,1] [.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[4,2,1] [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[2,2,2,1] [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[2,2,1,1,1] [.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[4,2,1] [.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[3,2,1,1] [.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[4,2,1] [.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[4,2,1] [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[3,2,1,1] [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[2,2,1,1,1] [.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[3,2,1,1] [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[2,2,1,1,1] [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,1,1,1,1,1] [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[7] [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[6,1] [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[7] [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[5,2] [[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[5,1,1] [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[7] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[6,1] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[7] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[7] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[4,3] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[4,2,1] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[4,3] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[4,2,1] [[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[4,1,1,1] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[7] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[6,1] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[7] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[5,2] [[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[5,1,1] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[7] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[6,1] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[7] [[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[6,1] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[7] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[7] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[7] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[7] [[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[7] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[4,3] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[3,3,1] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[4,3] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[3,2,2] [[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[3,2,1,1] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[4,3] [[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[3,3,1] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[4,3] [[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[4,3] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[3,3,1] [[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[3,2,1,1] [[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[3,3,1] [[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[3,2,1,1] [[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[3,1,1,1,1] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[7] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[6,1] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[7] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[5,2] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[5,1,1] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[7] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[6,1] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[7] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[7] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[4,3] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[4,2,1] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[4,3] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[4,2,1] [[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[4,1,1,1] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[6,1] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[7] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[5,2] [[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[5,1,1] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[7] [[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[6,1] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[7] [[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[7] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[4,3] [[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[4,2,1] [[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[4,3] [[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[4,2,1] [[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[4,1,1,1] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[7] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[6,1] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[7] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[5,2] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[5,1,1] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[7] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[6,1] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[7] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[5,2] [[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[5,1,1] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[7] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[6,1] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[7] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[5,2] [[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[5,1,1] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[7] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[6,1] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[7] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[5,2] [[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[5,1,1] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7] [[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[6,1] [[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[7] [[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[5,2] [[[[.,.],.],.],[[[.,.],.],.]]=>[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]=>[7] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[6,1] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[7] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[6,1] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[7] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[6,1] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[7] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[6,1] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[7] [[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[6,1] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[7] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[6,1] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7] [[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[6,1] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[7] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[6,1] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7] [[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[6,1] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[7] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[6,1] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[7] [[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[6,1] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7] [[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[6,1] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[7] [[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[6,1] [[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7] [[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,1] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[7] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[7] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[7] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[7] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[7] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[7] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[7] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[7] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[7] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[7] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[7] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[7] [[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[7] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[7] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[7] [[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[7] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[7] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[7] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7] [[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[7] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[7] [[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[7] [[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7] [[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[7] [[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7] [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7] [[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[7] [[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[7] [[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[7] [[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7] [[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7] [[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[7] [[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[7] [[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7] [[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7] [[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7] [[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7] [[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7] [[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7] [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[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]=>[6,1] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[4,2,1] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[4,1,1,1] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,1] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[5,1,1] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[6,1] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[6,1] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[3,3,1] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[3,2,1,1] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[3,3,1] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[3,2,1,1] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[3,1,1,1,1] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[6,1] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[5,1,1] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[6,1] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[4,2,1] [[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[4,1,1,1] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[6,1] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[5,1,1] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[6,1] [[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[5,1,1] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,1] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[6,1] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[6,1] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,1] [[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,1] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[4,2,1] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[3,2,1,1] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[4,2,1] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[2,2,2,1] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[2,2,1,1,1] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[4,2,1] [[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[3,2,1,1] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[4,2,1] [[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[4,2,1] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[3,2,1,1] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[2,2,1,1,1] [[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[3,2,1,1] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[2,2,1,1,1] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,1,1,1,1,1] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[6,1] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[5,1,1] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[6,1] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[4,2,1] [[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[4,1,1,1] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,1] [[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[5,1,1] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[6,1] [[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[6,1] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[3,3,1] [[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[3,2,1,1] [[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[3,3,1] [[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[3,2,1,1] [[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[3,1,1,1,1] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[6,1] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[5,1,1] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[6,1] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[4,2,1] [[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[4,1,1,1] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,1] [[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[5,1,1] [[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[6,1] [[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[4,2,1] [[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,1,1,1] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[6,1] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[5,1,1] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[6,1] [[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[5,1,1] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,1] [[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[5,1,1] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[6,1] [[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[5,1,1] [[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,1] [[[[[.,.],.],.],[[.,.],.]],.]=>[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]=>[6,1] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[6,1] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[6,1] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[6,1] [[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,1] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,1] [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[6,1] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[6,1] [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,1] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,1] [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,1] [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,1] [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,1] [[[[[[.,.],.],.],.],[.,.]],.]=>[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]=>[5,1,1] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[4,1,1,1] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[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]=>[3,2,1,1] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[3,1,1,1,1] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[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]=>[4,1,1,1] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,1,1] [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,1,1] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[3,2,1,1] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[2,2,1,1,1] [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[3,2,1,1] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[2,2,1,1,1] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,1,1,1,1,1] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,1,1] [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[4,1,1,1] [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[5,1,1] [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[3,2,1,1] [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[3,1,1,1,1] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,1,1] [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[4,1,1,1] [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,1,1] [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,1,1,1] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,1,1] [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,1,1] [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,1,1] [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,1,1] [[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,1,1] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,1,1] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[3,1,1,1,1] [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,1,1,1] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,2,1,1,1] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,1,1,1,1,1] [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,1,1,1] [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,1,1,1,1] [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,1,1,1] [[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,1,1] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,1,1,1] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,1,1,1,1,1] [[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,1,1,1] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,1,1,1,1] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
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
cycle type
Description
The cycle type of a permutation as a partition.