Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Images
=>
Cc0010;cc-rep-0Cc0009;cc-rep-3
[.,.]=>[1]=>[1]=>{{1}} [.,[.,.]]=>[2,1]=>[2,1]=>{{1,2}} [[.,.],.]=>[1,2]=>[1,2]=>{{1},{2}} [.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>{{1,2,3}} [.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>{{1,3},{2}} [[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>{{1},{2,3}} [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}} [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}} [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>{{1,2,3,4}} [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>{{1,2,4},{3}} [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[3,2,4,1]=>{{1,3,4},{2}} [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>{{1,4},{2,3}} [.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>{{1,4},{2},{3}} [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,3,4,2]=>{{1},{2,3,4}} [[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}} [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>{{1,2},{3,4}} [[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}} [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>{{1,2,3},{4}} [[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}} [[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}} [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}} [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}} [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>{{1,2,3,5},{4}} [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,4,3,5,1]=>{{1,2,4,5},{3}} [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>{{1,2,5},{3,4}} [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}} [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}} [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}} [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[4,3,2,5,1]=>{{1,4,5},{2,3}} [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}} [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}} [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}} [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}} [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}} [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}} [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,3,4,5,2]=>{{1},{2,3,4,5}} [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}} [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}} [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}} [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}} [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,4,5,3]=>{{1,2},{3,4,5}} [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}} [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}} [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}} [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[2,3,1,5,4]=>{{1,2,3},{4,5}} [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}} [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}} [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}} [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}} [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}} [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}} [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}} [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}} [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}} [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}} [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}} [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}} [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}} [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}} [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}} [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}} [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}} [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}} [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}} [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}} [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}} [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}} [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}} [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}} [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}} [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}} [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}} [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}} [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}} [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}} [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}} [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}} [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}} [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}} [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}} [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}} [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}} [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}} [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}} [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}} [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}} [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}} [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}} [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}} [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}} [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}} [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}} [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}} [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}} [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}} [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}} [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}} [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}} [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}} [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}} [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}} [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}} [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}} [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}} [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}} [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}} [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}} [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}} [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}} [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}} [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}} [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}} [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}} [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}} [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}} [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}} [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}} [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}} [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}} [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}} [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}} [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}} [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}} [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}} [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}} [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}} [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}} [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}} [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}} [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}} [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}} [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}} [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}} [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}} [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}} [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}} [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}} [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}} [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}} [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}} [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}} [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}} [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}} [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}} [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}} [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}} [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}} [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}} [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}} [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}} [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}} [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}} [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}} [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}} [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}} [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}} [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}} [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}} [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}} [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}} [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}} [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}} [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}} [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}} [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}} [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}} [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}} [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}} [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}} [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}} [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}} [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}} [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}} [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}} [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}} [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}} [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}} [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}} [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}} [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}} [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}} [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}} [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}} [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}} [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}} [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}} [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}} [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}} [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}} [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}} [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}} [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}} [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}} [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}} [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}} [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}} [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}} [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}} [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}} [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}} [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}} [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}} [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}} [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}} [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}} [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}} [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}} [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}} [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}} [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}} [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}} [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}} [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}} [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}} [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}} [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}} [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}} [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}} [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}} [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}} [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}} [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}} [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}} [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}} [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}} [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}} [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}} [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}} [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}} [.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>{{1,2,7},{3},{4,5},{6}} [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}} [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}} [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}} [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}} [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}} [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}} [.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}} [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}} [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}} [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}} [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}} [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}} [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}} [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}} [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}} [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}} [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}} [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}} [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}} [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}} [.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}} [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}} [.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}} [.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}} [.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}} [.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}} [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}} [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}} [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}} [.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}} [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}} [.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}} [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}} [.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}} [.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}} [.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}} [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}} [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}} [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}} [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}} [.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}} [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}} [.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}} [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}} [.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}} [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}} [.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}} [.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}} [.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}} [.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}} [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}} [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}} [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}} [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}} [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}} [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}} [.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}} [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}} [.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}} [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}} [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}} [.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}} [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}} [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}} [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}} [.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}} [.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}} [.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}} [.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}} [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}} [.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}} [.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}} [.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}} [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}} [.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}} [.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}} [.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}} [.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}} [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}} [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}} [.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}} [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}} [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}} [.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}} [.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}} [.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}} [.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}} [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}} [.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}} [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}} [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}} [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}} [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}} [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}} [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}} [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}} [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}} [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}} [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}} [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}} [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}} [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}} [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}} [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}} [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}} [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}} [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}} [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}} [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}} [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}} [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}} [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}} [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}} [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}} [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}} [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}} [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}} [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}} [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}} [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}} [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}} [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}} [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}} [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}} [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}} [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}} [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}} [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}} [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}} [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}} [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}} [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}} [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}} [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}} [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}} [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}} [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}} [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}} [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}} [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}} [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}} [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}} [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}} [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}} [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}} [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}} [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}} [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}} [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}} [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}} [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}} [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}} [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}} [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}} [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}} [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}} [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}} [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}} [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}} [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}} [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}} [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}} [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}} [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}} [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}} [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}} [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}} [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}} [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}} [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}} [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}} [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}} [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}} [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}} [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}} [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}} [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}} [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}} [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}} [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}} [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}} [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}} [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}} [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}} [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}} [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}} [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}} [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}} [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}} [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}} [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}} 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[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}} [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}} [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]=>{{1},{2,3,4,8},{5,7},{6}} [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,7,6,5,4,8,3,2]=>[1,3,8,5,6,7,4,2]=>{{1},{2,3,8},{4,5,6,7}} [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}} [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[1,3,6,7,5,8,4,2]=>[1,4,3,8,7,6,5,2]=>{{1},{2,4,8},{3},{5,7},{6}} [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>{{1},{2,5,6,7,8},{3,4}} [[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[1,4,5,3,6,8,7,2]=>[1,7,5,4,3,6,8,2]=>{{1},{2,7,8},{3,5},{4},{6}} [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>{{1},{2,8},{3,5},{4},{6},{7}} [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>{{1,2},{3,4,5,8},{6,7}} [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}} [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>{{1,2},{3,4,6,8},{5},{7}} [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]=>{{1,2},{3,4,8},{5,7},{6}} [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}} [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}} [[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[1,2,6,7,5,8,4,3]=>[1,2,4,8,7,6,5,3]=>{{1},{2},{3,4,8},{5,7},{6}} [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>{{1},{2},{3,8},{4,5},{6},{7}} [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>{{1,2,3},{4,8},{5,6,7}} [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>{{1,2,3},{4,8},{5,7},{6}} [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]=>{{1,3},{2},{4,5,6,7,8}} [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[3,2,1,5,6,8,7,4]=>{{1,3},{2},{4,5,6,8},{7}} [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]=>{{1,3},{2},{4,5,7,8},{6}} [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>{{1,3},{2},{4,5,8},{6,7}} [[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]=>{{1,3},{2},{4,5,8},{6},{7}} [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[2,3,1,5,8,7,6,4]=>[3,2,1,6,5,7,8,4]=>{{1,3},{2},{4,6,7,8},{5}} [[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[2,3,1,5,7,8,6,4]=>[3,2,1,6,5,8,7,4]=>{{1,3},{2},{4,6,8},{5},{7}} [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>[3,2,1,7,6,5,8,4]=>{{1,3},{2},{4,7,8},{5,6}} [[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[3,2,1,7,5,6,8,4]=>{{1,3},{2},{4,7,8},{5},{6}} [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,7,5,4]=>{{1,3},{2},{4,8},{5,6,7}} [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>{{1,3},{2},{4,8},{5,7},{6}} [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>{{1,3},{2},{4,8},{5},{6,7}} [[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[2,3,1,6,5,7,8,4]=>[3,2,1,8,6,5,7,4]=>{{1,3},{2},{4,8},{5,6},{7}} [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>{{1,3},{2},{4,8},{5},{6},{7}} [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>{{1},{2,3},{4,8},{5,7},{6}} [[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>{{1,2},{3},{4,8},{5,7},{6}} [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}} [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}} [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}} [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]=>{{1},{2},{3},{4,5,8},{6,7}} [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}} [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}} [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}} [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>{{1},{2},{3},{4,7,8},{5,6}} [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}} [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>{{1},{2},{3},{4,8},{5,6,7}} [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>{{1},{2},{3},{4,8},{5,7},{6}} [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>{{1},{2},{3},{4,8},{5},{6,7}} [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>{{1},{2},{3},{4,8},{5,6},{7}} 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[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}} [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}} [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}} [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>{{1,3,4},{2},{5,8},{6},{7}} [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}} [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>{{1,4},{2,3},{5,6,8},{7}} [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}} [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}} [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>{{1,4},{2,3},{5,8},{6},{7}} [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}} [[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}} [[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}} [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}} [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}} [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}} [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}} [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}} [[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,7,6,8,5]=>{{1},{2,4},{3},{5,7,8},{6}} [[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}} [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}} 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[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>{{1,3},{2},{4},{5,6,7,8}} [[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[2,3,1,4,6,8,7,5]=>[3,2,1,4,7,6,8,5]=>{{1,3},{2},{4},{5,7,8},{6}} [[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}} [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}} [[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]=>{{1},{2,3},{4},{5,7,8},{6}} [[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>{{1},{2,3},{4},{5,8},{6,7}} [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]=>{{1,2},{3},{4},{5,6,7,8}} [[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>{{1,2},{3},{4},{5,8},{6,7}} [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}} 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[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[2,3,5,4,1,7,8,6]=>[4,2,3,5,1,8,7,6]=>{{1,4,5},{2},{3},{6,8},{7}} [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>{{1,5},{2,3,4},{6,7,8}} [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[4,3,2,5,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>{{1,5},{2,3,4},{6,8},{7}} [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>{{1,5},{2,4},{3},{6,7,8}} [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>{{1,5},{2,4},{3},{6,8},{7}} [[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>{{1,5},{2},{3,4},{6,8},{7}} [[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[3,2,4,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>{{1,5},{2,3},{4},{6,8},{7}} [[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>{{1,5},{2},{3},{4},{6,8},{7}} [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}} [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}} [[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>{{1,3,4},{2},{5},{6,8},{7}} [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>{{1,4},{2,3},{5},{6,7,8}} [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>{{1,4},{2,3},{5},{6,8},{7}} [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>{{1,2,3,6},{4,5},{7,8}} [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}} [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>{{1,2,4,6},{3},{5},{7,8}} [[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[3,4,2,6,5,1,8,7]=>[5,4,3,2,6,1,8,7]=>{{1,5,6},{2,4},{3},{7,8}} [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}} [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}} [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>{{1,2},{3,4,6},{5},{7,8}} [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}} [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>{{1,2},{3,6},{4},{5},{7,8}} [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}} [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}} [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}} [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}} [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}} [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}} [[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>{{1,5},{2,4},{3},{6},{7,8}} [[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>{{1,2},{3,5},{4},{6},{7,8}} [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>{{1,2,3,4},{5},{6},{7,8}} [[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[2,4,3,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>{{1,3,4},{2},{5},{6},{7,8}} [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>{{1,4},{2,3},{5},{6},{7,8}} [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}} [[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]=>{{1,5,6,7},{2,4},{3},{8}} [[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[3,4,2,6,7,5,1,8]=>[5,4,3,2,7,6,1,8]=>{{1,5,7},{2,4},{3},{6},{8}} [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>{{1,7},{2,3,6},{4,5},{8}} [[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>{{1,7},{2},{3},{4,6},{5},{8}} [[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>{{1,3},{2},{4,7},{5},{6},{8}} [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}} [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>{{1,2,3,4},{5,7},{6},{8}} [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>{{1,4},{2,3},{5,6,7},{8}} [[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>{{1,4},{2,3},{5,7},{6},{8}} [[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>{{1,3},{2},{4},{5,7},{6},{8}} [[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>{{1,5},{2,4},{3},{6,7},{8}} [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>{{1,3},{2},{4,5},{6,7},{8}} [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}} [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}} [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{8}} [[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>{{1,4},{2,3},{5},{6,7},{8}} [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}} [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}} [[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[5,4,3,2,6,1,7,8]=>{{1,5,6},{2,4},{3},{7},{8}} [[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>{{1,6},{2},{3},{4,5},{7},{8}} [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}} [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>{{1,4},{2,3},{5,6},{7},{8}} [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>{{1,5},{2,4},{3},{6},{7},{8}} [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}} [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}} [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}} [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}} [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}} [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}} [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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 maxima 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 weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.