Identifier
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00067: Permutations Foata bijectionPermutations
Mp00151: Permutations to cycle type 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]=>[3,2,1]=>{{1,3},{2}} [.,[[.,.],.]]=>[2,3,1]=>[2,3,1]=>{{1,2,3}} [[.,.],[.,.]]=>[1,3,2]=>[3,1,2]=>{{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]=>[4,3,2,1]=>{{1,4},{2,3}} [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,4,2,1]=>{{1,2,3,4}} [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>{{1,4},{2},{3}} [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>{{1,3,4},{2}} [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>{{1,2,3,4}} [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[4,3,1,2]=>{{1,2,3,4}} [[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1,4,2]=>{{1,2,3,4}} [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[4,2,1,3]=>{{1,3,4},{2}} [[[.,.],.],[.,.]]=>[1,2,4,3]=>[4,1,2,3]=>{{1,2,3,4}} [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}} [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>{{1,2,3},{4}} [[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1,2,4]=>{{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]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}} [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,5,3,2,1]=>{{1,2,4,5},{3}} [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,3,4,2,1]=>{{1,5},{2,3,4}} [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1]=>{{1,2,3,4,5}} [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1]=>{{1,3,5},{2,4}} [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,2,3,1]=>{{1,5},{2,3,4}} [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[4,2,5,3,1]=>{{1,3,4,5},{2}} [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}} [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}} [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1]=>{{1,4,5},{2,3}} [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>{{1,2,3,4,5}} [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}} [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}} [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}} [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[5,4,3,1,2]=>{{1,2,4,5},{3}} [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,5,1,3,2]=>{{1,3,4},{2,5}} [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[5,3,1,4,2]=>{{1,2,3,5},{4}} [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[4,3,1,5,2]=>{{1,2,3,4,5}} [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[3,1,4,5,2]=>{{1,2,3,4,5}} [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[5,4,2,1,3]=>{{1,2,3,4,5}} [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[4,2,1,5,3]=>{{1,3,4,5},{2}} [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[5,4,1,2,3]=>{{1,3,5},{2,4}} [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1,2,5,3]=>{{1,2,3,4,5}} [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[5,3,2,1,4]=>{{1,4,5},{2,3}} [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[5,2,3,1,4]=>{{1,4,5},{2},{3}} [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[5,3,1,2,4]=>{{1,2,3,4,5}} [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[5,2,1,3,4]=>{{1,3,4,5},{2}} [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[5,1,2,3,4]=>{{1,2,3,4,5}} [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}} [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1,5]=>{{1,2,3,4},{5}} [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}} [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}} [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}} [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[4,3,1,2,5]=>{{1,2,3,4},{5}} [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,1,4,2,5]=>{{1,2,3,4},{5}} [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[4,2,1,3,5]=>{{1,3,4},{2},{5}} [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1,2,3,5]=>{{1,2,3,4},{5}} [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}} [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}} [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[3,1,2,4,5]=>{{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]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}} [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}} [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}} [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}} [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}} [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}} [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>{{1,2,3,5,6},{4}} [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}} [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}} [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}} [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}} [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>{{1,2,3,4,5,6}} [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}} [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}} [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}} [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}} [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}} [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>{{1,2,3,4,5,6}} [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}} [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}} [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}} [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}} [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}} [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}} [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}} [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}} [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}} [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}} [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}} [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}} [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}} [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>{{1,2,3,4,5,6}} [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}} [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}} [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>{{1,3,4,5,6},{2}} [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}} [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}} [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}} [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>{{1,2,3,4,5,6}} [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}} [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}} [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}} [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}} [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}} [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}} [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>{{1,2,3,4,5,6}} [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>{{1,2,3,4,5,6}} [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>{{1,2,4,5,6},{3}} [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>{{1,2,3,4,5,6}} [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>{{1,2,4,6},{3},{5}} [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>{{1,2,3,6},{4},{5}} [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>{{1,2,4,5,6},{3}} [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>{{1,3,4},{2,5,6}} [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>{{1,2,3,5,6},{4}} [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>{{1,2,3,4,5,6}} [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}} [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>{{1,2,3,4,5,6}} [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>{{1,4,5},{2,3,6}} [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>{{1,2,3,4,6},{5}} [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>{{1,2,3,4,5,6}} [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>{{1,3,4,5,6},{2}} [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}} [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>{{1,2,3,4,5,6}} [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>{{1,3,6},{2,4},{5}} [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}} [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}} [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}} [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>{{1,4,5,6},{2,3}} [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>{{1,2,3,4,5,6}} [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>{{1,4,5,6},{2},{3}} [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}} [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>{{1,2,3,4,5,6}} [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}} [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>{{1,3,4,5,6},{2}} [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>{{1,2,3,4,5,6}} [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}} [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}} [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}} [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}} [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}} [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}} [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}} [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>{{1,2,3,5,6},{4}} [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>{{1,2,3,4,5,6}} [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}} [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}} [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}} [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>{{1,2,3,4,5,6}} [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}} [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}} [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}} [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}} [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}} [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}} [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}} [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}} [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}} [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}} [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}} [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}} [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}} [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}} [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}} [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}} [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}} [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>{{1,3,4},{2,5},{6}} [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>{{1,2,3,5},{4},{6}} [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>{{1,2,3,4,5},{6}} [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}} [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}} [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>{{1,3,4,5},{2},{6}} [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}} [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}} [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}} [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}} [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}} [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}} [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}} [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}} [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}} [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}} [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}} [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}} [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}} [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}} [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}} [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}} [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}} [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}} [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>{{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]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}} [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}} [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}} [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>{{1,2,3,5,6,7},{4}} [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}} [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}} [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>{{1,2,3,4,5,6,7}} [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}} [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}} [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}} [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>{{1,3,4,5,7},{2,6}} [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>{{1,2,4,6,7},{3,5}} [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}} [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}} [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}} [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>{{1,2,6,7},{3},{4,5}} [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>{{1,7},{2,4,5,6},{3}} [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>{{1,2,4,5,6,7},{3}} [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>{{1,4,5,7},{2,3,6}} [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}} [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>{{1,2,4,6,7},{3},{5}} [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}} [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>{{1,2,3,4,6,7},{5}} [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}} [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}} [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}} [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}} [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}} [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>{{1,2,5,6,7},{3,4}} [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}} [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}} [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>{{1,5,7},{2,3,4,6}} [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}} [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>{{1,2,5,6,7},{3},{4}} [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>{{1,5,7},{2,3,6},{4}} [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>{{1,2,4,5,6,7},{3}} [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}} [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}} [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>{{1,2,4,5,6,7},{3}} [.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}} [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}} [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}} [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}} [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}} [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,5,6,2,4,3,1]=>{{1,7},{2,4,5},{3,6}} [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[6,5,7,2,4,3,1]=>{{1,3,6,7},{2,4,5}} [.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[5,6,2,7,4,3,1]=>{{1,4,5,7},{2,3,6}} [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>{{1,7},{2,3,4,6},{5}} [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>{{1,2,3,4,6,7},{5}} [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>{{1,7},{2,3,4,5,6}} [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}} [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>{{1,2,3,4,5,6,7}} [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>{{1,5,7},{2,3,6},{4}} [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}} [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>{{1,5,7},{2,3,4,6}} [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}} [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}} [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[6,7,3,2,5,4,1]=>{{1,2,4,6,7},{3},{5}} [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,5,3,2,6,4,1]=>{{1,7},{2,4,5,6},{3}} [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[6,5,3,2,7,4,1]=>{{1,2,4,5,6,7},{3}} [.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[5,3,2,6,7,4,1]=>{{1,5,7},{2,3},{4,6}} [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}} [.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[6,7,2,3,5,4,1]=>{{1,2,3,4,6,7},{5}} [.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}} [.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}} [.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[5,2,3,6,7,4,1]=>{{1,5,7},{2},{3},{4,6}} [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,6,4,3,2,5,1]=>{{1,7},{2,5,6},{3,4}} [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[6,4,3,2,7,5,1]=>{{1,5,6,7},{2,4},{3}} [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,6,3,4,2,5,1]=>{{1,7},{2,5,6},{3},{4}} [.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[6,3,4,2,7,5,1]=>{{1,5,6,7},{2,3,4}} [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}} [.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[6,4,2,3,7,5,1]=>{{1,5,6,7},{2,3,4}} [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,6,3,2,4,5,1]=>{{1,7},{2,4,5,6},{3}} [.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[6,3,2,4,7,5,1]=>{{1,5,6,7},{2,3},{4}} [.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}} [.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}} [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}} [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}} [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}} [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}} [.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}} [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}} [.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}} [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,5,3,2,4,6,1]=>{{1,7},{2,4,5},{3},{6}} [.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}} [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}} [.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}} [.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}} [.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}} [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}} [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>{{1,2,5,6,7},{3,4}} [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}} [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}} [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>{{1,3,4,6,7},{2,5}} [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}} [.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[5,3,6,4,2,7,1]=>{{1,2,3,5,6,7},{4}} [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}} [.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}} [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>{{1,2,4,5,6,7},{3}} [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}} [.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}} [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}} [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}} [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}} [.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[5,6,2,4,3,7,1]=>{{1,2,3,5,6,7},{4}} [.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[6,4,2,5,3,7,1]=>{{1,6,7},{2,3,4,5}} [.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}} [.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[4,2,5,6,3,7,1]=>{{1,4,6,7},{2},{3,5}} [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[6,5,3,2,4,7,1]=>{{1,6,7},{2,4,5},{3}} [.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[5,3,2,6,4,7,1]=>{{1,4,5,6,7},{2,3}} [.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}} [.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[5,2,3,6,4,7,1]=>{{1,4,5,6,7},{2},{3}} [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}} [.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}} [.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}} [.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}} [.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}} [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}} [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>{{1,2,4,5,6,7},{3}} [.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}} [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}} [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}} [.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}} [.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[4,2,5,3,6,7,1]=>{{1,3,4,5,6,7},{2}} [.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}} [.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}} [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}} [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}} [.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}} [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}} [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}} [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}} [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[6,7,5,4,1,3,2]=>{{1,3,5,6},{2,7},{4}} [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[7,5,6,4,1,3,2]=>{{1,2,5,7},{3,6},{4}} [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[6,5,7,4,1,3,2]=>{{1,2,3,5,6,7},{4}} [[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[5,6,7,1,4,3,2]=>{{1,4,5},{2,3,6,7}} [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}} [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>{{1,2,3,4,6,7},{5}} [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>{{1,2,5,7},{3,4,6}} [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>{{1,2,4,7},{3,5,6}} [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>{{1,2,3,4,5,6,7}} [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>{{1,2,3,4,5,6,7}} [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>{{1,2,3,4,5,6,7}} [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>{{1,2,4,5,7},{3,6}} [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>{{1,3,4,6},{2,5,7}} [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7}} [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>{{1,4,6},{2,7},{3},{5}} [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>{{1,2,4,5,6,7},{3}} [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>{{1,4,6},{2,5,7},{3}} [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>{{1,2,3,5,7},{4,6}} [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>{{1,2,5,6,7},{3,4}} [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>{{1,2,4,5,6,7},{3}} [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>{{1,2,4,5,6,7},{3}} [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>{{1,2,3,5,6,7},{4}} [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>{{1,2,5,7},{3,4},{6}} [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>{{1,2,4,7},{3,5},{6}} [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>{{1,2,4,5,7},{3},{6}} [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>{{1,2,4,7},{3},{5},{6}} [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}} [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>{{1,2,5,6,7},{3,4}} [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>{{1,3,4,5},{2,6,7}} [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>{{1,2,4,6,7},{3,5}} [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>{{1,2,3,4,5,6,7}} [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>{{1,2,3,4,5,6,7}} [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>{{1,2,4,5,6,7},{3}} [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>{{1,2,3,4,5,6,7}} [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>{{1,2,4,6,7},{3},{5}} [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>{{1,2,3,6,7},{4},{5}} [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>{{1,2,4,5,6,7},{3}} [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>{{1,3,4},{2,5,6,7}} [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>{{1,2,3,5,6,7},{4}} [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}} [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>{{1,2,3,5,6,7},{4}} [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>{{1,2,4,5,6},{3,7}} [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>{{1,2,3,4,5,7},{6}} [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>{{1,2,3,4,7},{5},{6}} [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>{{1,4,5},{2,3,6,7}} [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>{{1,2,3,4,6,7},{5}} [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>{{1,2,3,4,5,6,7}} [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>{{1,3,4,5,6,7},{2}} [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}} [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>{{1,4,6},{2,3,5,7}} [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>{{1,3,4,6,7},{2,5}} [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>{{1,4,6},{2,5},{3,7}} [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>{{1,3,5,7},{2,4,6}} [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>{{1,3,4,7},{2,5,6}} [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>{{1,3,5,6,7},{2,4}} [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>{{1,3,4,7},{2,5},{6}} [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>{{1,3,7},{2,4},{5},{6}} [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>{{1,3,4,6,7},{2,5}} [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>{{1,2,3,4,5,6,7}} [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>{{1,3,6,7},{2,4},{5}} [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>{{1,3,5,6,7},{2,4}} [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}} [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}} [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>{{1,5,6},{2,4,7},{3}} [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>{{1,2,4,5,7},{3},{6}} [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>{{1,2,4,5,6,7},{3}} [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>{{1,4,5,6,7},{2,3}} [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>{{1,2,4,6,7},{3,5}} [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>{{1,5,6},{2,3,4,7}} [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>{{1,2,3,4,5,7},{6}} [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>{{1,2,3,4,5,6,7}} [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>{{1,4,5,6,7},{2},{3}} [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>{{1,3,4,5,7},{2,6}} [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>{{1,2,4,5,6,7},{3}} [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>{{1,4,7},{2,5},{3},{6}} [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>{{1,4,6,7},{2,5},{3}} [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}} [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}} [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7}} [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>{{1,4,7},{2,3,5},{6}} [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>{{1,4,6,7},{2,3,5}} [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>{{1,3,4,5,6,7},{2}} [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}} [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>{{1,3,5,6},{2,4,7}} [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>{{1,2,3,4,5,7},{6}} [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>{{1,2,3,4,5,6,7}} [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}} [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>{{1,2,5,6,7},{3,4}} [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>{{1,5,6,7},{2,4},{3}} [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>{{1,2,5,6,7},{3},{4}} [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>{{1,5,6,7},{2,3,4}} [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}} [[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>{{1,5,6,7},{2,3,4}} [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>{{1,2,4,5,6,7},{3}} [[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>{{1,5,6,7},{2,3},{4}} [[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}} [[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>{{1,5,6,7},{2},{3},{4}} [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>{{1,5,7},{2,6},{3,4}} [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>{{1,2,4,5,6,7},{3}} [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>{{1,4,5,7},{2,6},{3}} [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>{{1,2,3,5,6,7},{4}} [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>{{1,5,7},{2,3,4,6}} [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>{{1,2,3,4,5,6,7}} [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}} [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>{{1,3,5,6,7},{2,4}} [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>{{1,5,7},{2,4,6},{3}} [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>{{1,4,5,6,7},{2,3}} [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>{{1,5,7},{2,3,4,6}} [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>{{1,4,5,6,7},{2},{3}} [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>{{1,2,4,5,6,7},{3}} [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}} [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}} [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>{{1,3,4,5,6,7},{2}} [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}} [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}} [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>{{1,6,7},{2,5},{3,4}} [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>{{1,6,7},{2,3,4,5}} [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>{{1,6,7},{2,5},{3},{4}} [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>{{1,6,7},{2,4,5},{3}} [[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>{{1,6,7},{2,3,4,5}} [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>{{1,6,7},{2,3,4,5}} [[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>{{1,6,7},{2,3,4,5}} [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>{{1,6,7},{2,4,5},{3}} [[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>{{1,6,7},{2,3,4,5}} [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>{{1,6,7},{2,4},{3},{5}} [[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>{{1,6,7},{2,3,4},{5}} [[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>{{1,6,7},{2,3,4},{5}} [[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>{{1,6,7},{2,3},{4},{5}} [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}} [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>{{1,2,5,6,7},{3,4}} [[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>{{1,2,4,6,7},{3,5}} [[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>{{1,2,4,5,6,7},{3}} [[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>{{1,2,4,6,7},{3},{5}} [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>{{1,2,3,6,7},{4},{5}} [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}} [[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>{{1,2,3,4,6,7},{5}} [[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}} [[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>{{1,3,6,7},{2,4},{5}} [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>{{1,2,4,5,6,7},{3}} [[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}} [[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>{{1,4,6,7},{2,5},{3}} [[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>{{1,4,6,7},{2,3,5}} [[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}} [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>{{1,5,6,7},{2,4},{3}} [[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>{{1,5,6,7},{2,3,4}} [[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>{{1,5,6,7},{2,3,4}} [[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>{{1,5,6,7},{2,3},{4}} [[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}} [[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>{{1,2,4,5,6,7},{3}} [[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>{{1,2,3,5,6,7},{4}} [[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}} [[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}} [[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>{{1,4,5,6,7},{2,3}} 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[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}} [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}} [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>{{1,2,5,6},{3,4},{7}} [[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>{{1,3,4,5},{2,6},{7}} [[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>{{1,2,4,6},{3,5},{7}} [[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>{{1,2,3,4,5,6},{7}} [[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>{{1,2,3,4,5,6},{7}} [[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>{{1,2,4,5,6},{3},{7}} [[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>{{1,2,3,4,5,6},{7}} [[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>{{1,2,4,6},{3},{5},{7}} [[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}} [[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>{{1,2,4,5,6},{3},{7}} [[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>{{1,3,4},{2,5,6},{7}} [[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>{{1,2,3,5,6},{4},{7}} [[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>{{1,2,3,4,5,6},{7}} [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}} [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}} [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>{{1,4,5},{2,3,6},{7}} [[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>{{1,2,3,4,6},{5},{7}} [[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>{{1,2,3,4,5,6},{7}} [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>{{1,3,4,5,6},{2},{7}} [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>{{1,3,4,6},{2,5},{7}} [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>{{1,2,3,4,5,6},{7}} [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>{{1,3,6},{2,4},{5},{7}} [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>{{1,3,5,6},{2,4},{7}} [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}} [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}} [[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>{{1,4,5,6},{2,3},{7}} [[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}} [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>{{1,4,5,6},{2},{3},{7}} [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>{{1,4,6},{2,5},{3},{7}} [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>{{1,2,3,4,5,6},{7}} [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>{{1,4,6},{2,3,5},{7}} [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>{{1,3,4,5,6},{2},{7}} [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}} [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}} [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>{{1,5,6},{2,4},{3},{7}} [[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>{{1,5,6},{2,3,4},{7}} [[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>{{1,5,6},{2,3,4},{7}} [[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>{{1,5,6},{2,3},{4},{7}} [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>{{1,5,6},{2},{3},{4},{7}} [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}} [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>{{1,2,3,5,6},{4},{7}} [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}} [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>{{1,3,5,6},{2,4},{7}} [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>{{1,4,5,6},{2,3},{7}} [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>{{1,4,5,6},{2},{3},{7}} [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}} [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}} [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}} [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}} [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>{{1,2,4,5},{3},{6},{7}} [[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}} [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}} [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}} [[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}} [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}} [[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}} [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}} [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}} [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}} [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}} [[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>{{1,2,4,5},{3},{6},{7}} [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>{{1,3,4},{2,5},{6},{7}} [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}} [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>{{1,2,3,4,5},{6},{7}} [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}} [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}} [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>{{1,3,4,5},{2},{6},{7}} [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}} [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}} [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>{{1,4,5},{2,3},{6},{7}} [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>{{1,4,5},{2},{3},{6},{7}} [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}} [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}} [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}} [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}} [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}} [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}} [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}} [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}} [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}} [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}} [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}} [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}} [[[[[[[[.,.],.],.],.],.],.],.],.]=>[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
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].