Identifier
Mp00020:
Binary trees
—to Tamari-corresponding Dyck path⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Images
=>
Cc0010;cc-rep-0Cc0005;cc-rep-1Cc0020;cc-rep-3
[.,.]=>[1,0]=>[1]=>([],1)
[.,[.,.]]=>[1,1,0,0]=>[2,1]=>([(0,1)],2)
[[.,.],.]=>[1,0,1,0]=>[1,2]=>([],2)
[.,[.,[.,.]]]=>[1,1,1,0,0,0]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)
[.,[[.,.],.]]=>[1,1,0,1,0,0]=>[2,3,1]=>([(0,2),(1,2)],3)
[[.,.],[.,.]]=>[1,0,1,1,0,0]=>[1,3,2]=>([(1,2)],3)
[[.,[.,.]],.]=>[1,1,0,0,1,0]=>[2,1,3]=>([(1,2)],3)
[[[.,.],.],.]=>[1,0,1,0,1,0]=>[1,2,3]=>([],3)
[.,[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[.,[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0]=>[4,2,3,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[.,[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>([(0,3),(1,2),(1,3),(2,3)],4)
[.,[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>([(0,3),(1,2),(1,3),(2,3)],4)
[.,[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)
[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>([(1,3),(2,3)],4)
[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>([(0,3),(1,2)],4)
[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>([(2,3)],4)
[[.,[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)
[[.,[[.,.],.]],.]=>[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>([(1,3),(2,3)],4)
[[[.,.],[.,.]],.]=>[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>([(2,3)],4)
[[[.,[.,.]],.],.]=>[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>([(2,3)],4)
[[[[.,.],.],.],.]=>[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>([],4)
[.,[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[.,[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>([(1,4),(2,4),(3,4)],5)
[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>([(0,1),(2,3),(2,4),(3,4)],5)
[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>([(0,1),(2,4),(3,4)],5)
[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)
[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>([(2,4),(3,4)],5)
[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>([(0,1),(2,3),(2,4),(3,4)],5)
[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>([(0,1),(2,4),(3,4)],5)
[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>([(1,4),(2,3)],5)
[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>([(1,4),(2,3)],5)
[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>([(3,4)],5)
[[.,[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[.,[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[.,[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[.,[[[.,.],.],.]],.]=>[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)
[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)
[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>([(2,4),(3,4)],5)
[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>([(1,4),(2,3)],5)
[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>([(3,4)],5)
[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)
[[[.,[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)
[[[[.,.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>([(3,4)],5)
[[[[.,[.,.]],.],.],.]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>([(3,4)],5)
[[[[[.,.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>([],5)
[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,3,4,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[6,4,3,5,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[.,[[[.,.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[6,4,3,2,5,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[[.,[.,.]],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[.,[[[[.,.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,.],[.,[.,[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,.],[.,[[.,.],.]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,.],[[.,.],[.,.]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,.],[[.,[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,.],[[[.,.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,.],.],[[.,.],.]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[.,[.,.]]],[.,.]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[[.,.],.]],[.,.]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,.],[.,.]],[.,.]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[.,[[[[.,.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[.,[.,[.,.]]]],.]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[.,[[.,.],.]]],.]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[[.,.],[.,.]]],.]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[[.,[.,.]],.]],.]]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[.,[[[.,.],.],.]],.]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,.],[.,[.,.]]],.]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,.],[[.,.],.]],.]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[.,[[[[.,.],.],[.,.]],.]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,[.,[.,.]]],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[.,[[.,.],.]],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[[.,.],[.,.]],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[[.,[.,.]],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[.,[[[[[.,.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[.,[.,[[.,.],.]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[.,[[.,.],[.,.]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[.,.],[.,[.,.]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[.,.],[[.,.],.]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[.,[.,.]],[.,.]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[.,.],[[[.,.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[.,[.,[.,.]]],.]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[.,[[.,.],.]],.]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[[.,.],[.,.]],.]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[[.,[.,.]],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[.,.],[[[[.,.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>([(0,1),(2,5),(3,5),(4,5)],6)
[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],.],[[[.,.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>([(2,5),(3,5),(4,5)],6)
[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>([(0,5),(1,5),(2,4),(3,4)],6)
[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[.,.],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>([(1,2),(3,5),(4,5)],6)
[[[.,[.,.]],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[.,[.,.]],.],[[.,.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>([(1,2),(3,5),(4,5)],6)
[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)
[[[[.,.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>([(3,5),(4,5)],6)
[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6)
[[[.,.],[.,[.,.]]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[.,.],[[.,.],.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>([(1,2),(3,5),(4,5)],6)
[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>([(0,5),(1,4),(2,3)],6)
[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>([(2,5),(3,4)],6)
[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>([(1,2),(3,5),(4,5)],6)
[[[[.,.],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>([(2,5),(3,4)],6)
[[[[.,[.,.]],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>([(2,5),(3,4)],6)
[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>([(4,5)],6)
[[.,[.,[.,[.,[.,.]]]]],.]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,[.,[[.,.],.]]]],.]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,[[.,.],[.,.]]]],.]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,[[.,[.,.]],.]]],.]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[.,[[[.,.],.],.]]],.]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[.,.],[.,[.,.]]]],.]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[.,.],[[.,.],.]]],.]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[.,[.,.]],[.,.]]],.]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
[[.,[[[.,.],.],[.,.]]],.]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[.,[.,[.,.]]],.]],.]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[.,[[.,.],.]],.]],.]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[[.,.],[.,.]],.]],.]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[[.,[.,.]],.],.]],.]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[.,[[[[.,.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[[.,.],[.,[.,[.,.]]]],.]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],[.,[[.,.],.]]],.]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],[[.,.],[.,.]]],.]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],[[.,[.,.]],.]],.]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[.,.],[[[.,.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>([(2,5),(3,5),(4,5)],6)
[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>([(1,2),(3,5),(4,5)],6)
[[[[.,.],.],[.,[.,.]]],.]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)
[[[[.,.],.],[[.,.],.]],.]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>([(3,5),(4,5)],6)
[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>([(1,2),(3,4),(3,5),(4,5)],6)
[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>([(1,2),(3,5),(4,5)],6)
[[[[.,.],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>([(2,5),(3,4)],6)
[[[[.,[.,.]],.],[.,.]],.]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>([(2,5),(3,4)],6)
[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>([(4,5)],6)
[[[.,[.,[.,[.,.]]]],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[.,[.,[[.,.],.]]],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[[.,[[.,.],[.,.]]],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[.,[[.,[.,.]],.]],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[[.,[[[.,.],.],.]],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)
[[[[.,.],[.,[.,.]]],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)
[[[[.,.],[[.,.],.]],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>([(3,5),(4,5)],6)
[[[[.,[.,.]],[.,.]],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>([(2,5),(3,4)],6)
[[[[[.,.],.],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>([(4,5)],6)
[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)
[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)
[[[[[.,.],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>([(4,5)],6)
[[[[[.,[.,.]],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>([(4,5)],6)
[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>([],6)
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7,3,4,6,5,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7,4,3,5,6,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,3,4,5,6,2,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7,2,4,6,5,3,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7,2,5,4,6,3,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,2,4,5,6,3,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7,3,2,6,5,4,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7,2,3,6,5,4,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7,4,3,2,6,5,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,4,2,6,5,1]=>([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7,3,5,4,2,6,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7,4,3,5,2,6,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,3,4,5,2,6,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7,2,5,4,3,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,2,4,5,3,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7,4,3,2,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7,3,4,2,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[.,[[[[[.,.],.],.],.],.]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,6,4,5,3,1]=>([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,7,4,6,5,3,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,5,4,6,3,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,7,4,5,6,3,1]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,7,3,6,5,4,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,7,5,4,3,6,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,7,4,5,3,6,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,.],[[[[.,.],.],.],.]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],.],[[[.,.],.],.]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],.],.],[[.,.],.]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,3,4,2,7,6,1]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[[[[.,.],.],.],.],[.,.]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,5,4,3,7,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,2,4,5,3,7,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[.,[[[[.,.],.],.],.]],.]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,4,5,3,7,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,.],[[[.,.],.],.]],.]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],.],[[.,.],.]],.]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[[[[.,.],.],.],[.,.]],.]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,3,4,2,6,7,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[.,[[[.,.],.],.]],.],.]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,.],[[.,.],.]],.],.]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[.,[[[[[.,.],.],[.,.]],.],.]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[.,[[.,.],.]],.],.],.]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[[.,.],[.,.]],.],.],.]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[[.,[.,.]],.],.],.],.]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[.,[[[[[[.,.],.],.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,.]],[[[[.,.],.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],.],[[[.,.],.],.]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>([(3,6),(4,6),(5,6)],7)
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,2,3,1,7,6,5]=>([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[.,[[[.,.],.],.]],[[.,.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>([(0,3),(1,2),(4,6),(5,6)],7)
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>([(2,3),(4,6),(5,6)],7)
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[.,[[.,.],.]],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>([(2,3),(4,6),(5,6)],7)
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,[.,.]],.],.],[[.,.],.]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>([(2,3),(4,6),(5,6)],7)
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>([(4,5),(4,6),(5,6)],7)
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>([(4,6),(5,6)],7)
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[[.,.],.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>([(2,3),(4,6),(5,6)],7)
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>([(1,6),(2,5),(3,4)],7)
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>([(1,6),(2,5),(3,4)],7)
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>([(3,6),(4,5)],7)
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[[.,.],.],.]],.],[.,.]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>([(2,3),(4,6),(5,6)],7)
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>([(1,6),(2,5),(3,4)],7)
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>([(3,6),(4,5)],7)
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,[[.,.],.]],.],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>([(2,3),(4,6),(5,6)],7)
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>([(3,6),(4,5)],7)
[[[[[.,[.,.]],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>([(3,6),(4,5)],7)
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>([(5,6)],7)
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,4,3,5,2,1,7]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,3,4,5,2,1,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,4,2,5,1,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[.,[[[[.,.],.],.],.]]],.]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,.],[[[.,.],.],.]]],.]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,.],.],[[.,.],.]]],.]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,[[[[.,.],.],.],[.,.]]],.]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,3,4,2,6,1,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[.,[[[.,.],.],.]],.]],.]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,.],[[.,.],.]],.]],.]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[.,[[[[.,.],.],[.,.]],.]],.]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[.,[[.,.],.]],.],.]],.]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[[.,.],[.,.]],.],.]],.]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[[.,[.,.]],.],.],.]],.]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[.,[[[[[.,.],.],.],.],.]],.]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,.]],[[[.,.],.],.]],.]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>([(3,6),(4,6),(5,6)],7)
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
[[[.,[[.,.],.]],[[.,.],.]],.]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>([(1,6),(2,6),(3,5),(4,5)],7)
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>([(2,3),(4,6),(5,6)],7)
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,[.,.]],.],[[.,.],.]],.]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>([(2,3),(4,6),(5,6)],7)
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>([(4,5),(4,6),(5,6)],7)
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>([(4,6),(5,6)],7)
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[[.,.],.],.]],[.,.]],.]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7)
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>([(2,3),(4,6),(5,6)],7)
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>([(1,6),(2,5),(3,4)],7)
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>([(3,6),(4,5)],7)
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,[[.,.],.]],.],[.,.]],.]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>([(2,3),(4,6),(5,6)],7)
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>([(3,6),(4,5)],7)
[[[[[.,[.,.]],.],.],[.,.]],.]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>([(3,6),(4,5)],7)
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>([(5,6)],7)
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,2,4,3,1,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[.,[[[.,.],.],.]]],.],.]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,.],[[.,.],.]]],.],.]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[[.,[[[.,.],.],[.,.]]],.],.]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[.,[[.,.],.]],.]],.],.]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,2,3,5,1,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[[.,.],[.,.]],.]],.],.]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[[.,[.,.]],.],.]],.],.]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[[.,[[[[.,.],.],.],.]],.],.]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>([(3,6),(4,6),(5,6)],7)
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,[.,.]],[[.,.],.]],.],.]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>([(2,3),(4,6),(5,6)],7)
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>([(4,5),(4,6),(5,6)],7)
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>([(4,6),(5,6)],7)
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7)
[[[[.,[[.,.],.]],[.,.]],.],.]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>([(2,3),(4,6),(5,6)],7)
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>([(3,6),(4,5)],7)
[[[[[.,[.,.]],.],[.,.]],.],.]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>([(3,6),(4,5)],7)
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>([(5,6)],7)
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,[.,[[.,.],.]]],.],.],.]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,2,3,1,5,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,[[.,.],[.,.]]],.],.],.]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,[[.,[.,.]],.]],.],.],.]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[[[.,[[[.,.],.],.]],.],.],.]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>([(3,6),(4,6),(5,6)],7)
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>([(4,5),(4,6),(5,6)],7)
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>([(4,6),(5,6)],7)
[[[[[.,[.,.]],[.,.]],.],.],.]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>([(3,6),(4,5)],7)
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>([(5,6)],7)
[[[[[.,[.,[.,.]]],.],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>([(4,5),(4,6),(5,6)],7)
[[[[[.,[[.,.],.]],.],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>([(4,6),(5,6)],7)
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>([(5,6)],7)
[[[[[[.,[.,.]],.],.],.],.],.]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>([(5,6)],7)
[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>([],7)
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8,7,4,3,6,5,2,1]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8,3,2,7,6,5,4,1]=>([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8,5,4,3,2,7,6,1]=>([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8,3,2,5,4,7,6,1]=>([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,8,5,4,7,6,3]=>([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,2,3,1,8,6,7,5]=>([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>([(2,7),(3,7),(4,6),(5,6)],8)
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,3,2,5,4,1,8,7]=>([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>([(0,7),(1,6),(2,5),(3,4)],8)
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>([(4,7),(5,6)],8)
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>([(2,7),(3,7),(4,6),(5,6)],8)
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>([(4,7),(5,6)],8)
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>([(4,7),(5,6)],8)
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>([],8)
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
searching the database
Sorry, this map was not found in the database.