Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices
St001878: Lattices ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0014;cc-rep-2
Cc0029;cc-rep
[[[.,.],.],.]=>[1,2,3]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],.],.]]=>[2,3,4,1]=>([(1,2),(2,3)],4)=>([(0,2),(2,1)],3)=>1
[[.,.],[[.,.],.]]=>[3,4,1,2]=>([(0,3),(1,2)],4)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[[.,.],.],[.,.]]=>[4,1,2,3]=>([(1,2),(2,3)],4)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],.]],.]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,.]],.]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],.],.]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4)=>([(0,2),(2,1)],3)=>1
[[[[.,.],.],.],.]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>([(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>([(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>([(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>([(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>([(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>([(1,4),(2,4),(4,3)],5)=>([(0,2),(2,1)],3)=>1
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>([(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>([(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>([(0,4),(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>([(0,3),(1,4),(4,2)],5)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>([(0,4),(1,4),(2,3)],5)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>([(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>([(0,3),(1,4),(4,2)],5)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>([(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>([(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>([(1,4),(2,4),(4,3)],5)=>([(0,2),(2,1)],3)=>1
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>([(0,4),(1,3),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>([(0,3),(1,2),(2,4),(3,4)],5)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>([(0,4),(1,3),(2,3),(3,4)],5)=>([(0,2),(2,1)],3)=>1
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5)=>([(0,2),(2,1)],3)=>1
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>([(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>([(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>([(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>([(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>([(2,5),(3,5),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>([(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>([(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>([(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>([(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>([(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>([(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>([(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>([(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>([(2,5),(3,5),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>([(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>([(1,4),(2,3),(3,5),(4,5)],6)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>([(1,5),(2,5),(3,5),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>([(1,5),(2,5),(3,4),(5,3)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>([(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>([(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>([(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>([(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>([(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>([(0,5),(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>([(0,5),(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>([(0,5),(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>([(0,5),(1,5),(2,3),(5,4)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>([(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>([(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>([(0,5),(1,5),(2,3),(3,4)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>([(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>([(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>([(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>([(0,5),(1,5),(2,3),(3,4)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>([(0,5),(1,5),(2,5),(3,4)],6)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>([(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>([(0,5),(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>([(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>([(0,5),(1,3),(2,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>([(2,5),(3,5),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>([(0,5),(1,5),(2,3),(5,4)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>([(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>([(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>([(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>([(1,4),(2,3),(3,5),(4,5)],6)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>([(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>([(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>([(1,5),(2,5),(3,5),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>([(1,5),(2,5),(3,4),(5,3)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>([(0,2),(2,1)],3)=>1
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>([(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>([(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>([(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>([(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>([(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>([(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>([(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>([(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>([(2,6),(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>([(2,6),(3,6),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>([(2,6),(4,5),(5,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>([(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>([(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>([(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>([(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>([(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>([(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>([(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>([(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>([(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>([(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>([(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>([(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>([(2,6),(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>([(2,6),(3,6),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>([(2,6),(4,5),(5,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>([(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>([(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>([(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>([(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>([(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>([(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>([(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>([(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>([(0,6),(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>([(0,6),(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>([(0,6),(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>([(0,6),(1,5),(2,5),(3,4),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>([(0,6),(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>([(0,6),(1,5),(2,5),(3,4),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>([(0,6),(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>([(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>([(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>([(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>([(0,6),(1,5),(2,5),(3,4),(4,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>([(0,6),(1,5),(2,5),(3,4),(4,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>([(0,6),(1,6),(2,5),(3,5),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>([(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>([(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>([(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>([(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>([(0,6),(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>([(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>([(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>([(0,6),(1,6),(2,6),(3,4),(4,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>([(0,6),(1,5),(2,5),(3,4),(4,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>([(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>([(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>([(0,6),(1,5),(2,5),(3,4),(4,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>([(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>([(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>([(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>([(0,6),(1,6),(2,5),(3,5),(6,4)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>([(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5)],7)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>([(0,6),(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>([(0,6),(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>([(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>([(0,6),(1,5),(2,5),(3,4),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>([(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>([(0,6),(1,6),(2,4),(3,5),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>([(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>([(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>([(0,6),(1,5),(2,5),(3,4),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>([(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>([(2,6),(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>([(0,6),(1,6),(2,6),(3,4),(6,5)],7)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>([(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>([(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>([(2,6),(3,6),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>([(2,6),(4,5),(5,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>([(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>([(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>([(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3)=>1
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>2
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>([(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>([(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>([(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>([(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>([(3,4),(4,7),(6,5),(7,6)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>([(2,7),(3,7),(4,6),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>([(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>([(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>([(3,4),(4,7),(6,5),(7,6)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>([(2,7),(3,7),(4,6),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>([(2,7),(3,7),(4,6),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>([(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>([(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>([(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>([(3,4),(4,7),(6,5),(7,6)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)=>([(0,2),(2,1)],3)=>1
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)=>([(0,2),(2,1)],3)=>1
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>([(4,7),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>([(2,7),(3,7),(4,6),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)=>([(0,1),(0,2),(1,3),(2,3)],4)=>2
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>([(2,7),(3,7),(4,5),(7,6)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>([(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>([(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>([(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>([(3,4),(4,7),(6,5),(7,6)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7)],8)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)=>([(0,2),(2,1)],3)=>1
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[8,5,4,2,3,6,1,7]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>([(0,2),(2,1)],3)=>1
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>([(1,6),(2,4),(3,5),(4,7),(5,6),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)=>([(0,2),(2,1)],3)=>1
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>([(1,7),(2,7),(3,6),(4,5),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,3,1,2,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)=>([(0,3),(2,1),(3,2)],4)=>1
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
search for individual values
searching the database for the individual values of this statistic
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Map
maximal antichains
Description
The lattice of maximal antichains in a poset.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains can be ordered by setting $A \leq B \Leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow}B$, where $\mathop{\downarrow}A$ is the order ideal generated by $A$.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains can be ordered by setting $A \leq B \Leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow}B$, where $\mathop{\downarrow}A$ is the order ideal generated by $A$.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
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