Identifier
Mp00049:
Ordered trees
—to binary tree: left brother = left child⟶
Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1Cc0014;cc-rep-3
[[]]=>[.,.]=>[1]=>([],1)
[[],[]]=>[[.,.],.]=>[1,2]=>([(0,1)],2)
[[[]]]=>[.,[.,.]]=>[2,1]=>([],2)
[[],[],[]]=>[[[.,.],.],.]=>[1,2,3]=>([(0,2),(2,1)],3)
[[],[[]]]=>[[.,.],[.,.]]=>[1,3,2]=>([(0,1),(0,2)],3)
[[[]],[]]=>[[.,[.,.]],.]=>[2,1,3]=>([(0,2),(1,2)],3)
[[[],[]]]=>[.,[[.,.],.]]=>[2,3,1]=>([(1,2)],3)
[[[[]]]]=>[.,[.,[.,.]]]=>[3,2,1]=>([],3)
[[],[],[],[]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)
[[],[],[[]]]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>([(0,3),(3,1),(3,2)],4)
[[],[[]],[]]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[],[]]]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>([(0,2),(0,3),(3,1)],4)
[[],[[[]]]]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>([(0,1),(0,2),(0,3)],4)
[[[]],[],[]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4)
[[[]],[[]]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>([(0,2),(0,3),(1,2),(1,3)],4)
[[[],[]],[]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4)
[[[[]]],[]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>([(0,3),(1,3),(2,3)],4)
[[[],[],[]]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>([(1,2),(2,3)],4)
[[[],[[]]]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>([(1,2),(1,3)],4)
[[[[]],[]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>([(1,3),(2,3)],4)
[[[[],[]]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>([(2,3)],4)
[[[[[]]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>([],4)
[[],[],[],[],[]]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)
[[],[],[],[[]]]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>([(0,3),(3,4),(4,1),(4,2)],5)
[[],[],[[]],[]]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[],[],[[],[]]]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>([(0,4),(3,2),(4,1),(4,3)],5)
[[],[],[[[]]]]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>([(0,4),(4,1),(4,2),(4,3)],5)
[[],[[]],[],[]]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[[]]]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[],[[],[]],[]]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[],[[[]]],[]]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
[[],[[],[],[]]]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>([(0,2),(0,4),(3,1),(4,3)],5)
[[],[[],[[]]]]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>([(0,3),(0,4),(4,1),(4,2)],5)
[[],[[[]],[]]]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
[[],[[[],[]]]]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>([(0,2),(0,3),(0,4),(4,1)],5)
[[],[[[[]]]]]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4)],5)
[[[]],[],[],[]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5)
[[[]],[],[[]]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>([(0,4),(1,4),(4,2),(4,3)],5)
[[[]],[[]],[]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[[]],[[],[]]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[[]],[[[]]]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[[[],[]],[],[]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)
[[[[]]],[],[]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5)
[[[],[]],[[]]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[[[]]],[[]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[[],[],[]],[]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5)
[[[],[[]]],[]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[[[[]],[]],[]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>([(0,4),(1,3),(2,3),(3,4)],5)
[[[[],[]]],[]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[[[[]]]],[]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[[],[],[],[]]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5)
[[[],[],[[]]]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>([(1,4),(4,2),(4,3)],5)
[[[],[[]],[]]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>([(1,2),(1,3),(2,4),(3,4)],5)
[[[],[[],[]]]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>([(1,3),(1,4),(4,2)],5)
[[[],[[[]]]]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>([(1,2),(1,3),(1,4)],5)
[[[[]],[],[]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>([(1,4),(2,4),(4,3)],5)
[[[[]],[[]]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>([(1,3),(1,4),(2,3),(2,4)],5)
[[[[],[]],[]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>([(1,4),(2,3),(3,4)],5)
[[[[[]]],[]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>([(1,4),(2,4),(3,4)],5)
[[[[],[],[]]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>([(2,3),(3,4)],5)
[[[[],[[]]]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>([(2,3),(2,4)],5)
[[[[[]],[]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>([(2,4),(3,4)],5)
[[[[[],[]]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>([(3,4)],5)
[[[[[[]]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>([],5)
[[],[],[],[],[],[]]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[],[],[],[],[[]]]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
[[],[],[],[[]],[]]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[],[],[],[[],[]]]=>[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
[[],[],[],[[[]]]]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
[[],[],[[]],[],[]]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[],[],[[]],[[]]]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[],[],[[],[]],[]]=>[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[],[],[[[]]],[]]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[[],[],[[],[],[]]]=>[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
[[],[],[[],[[]]]]=>[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
[[],[],[[[]],[]]]=>[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[[],[],[[[],[]]]]=>[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
[[],[],[[[[]]]]]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
[[],[[]],[],[],[]]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[],[[]],[],[[]]]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
[[],[[]],[[]],[]]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[],[[]],[[],[]]]=>[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[],[[]],[[[]]]]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[],[[],[]],[],[]]=>[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[],[[[]]],[],[]]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
[[],[[],[]],[[]]]=>[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[],[[[]]],[[]]]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[],[[],[],[]],[]]=>[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
[[],[[],[[]]],[]]=>[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
[[],[[[]],[]],[]]=>[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
[[],[[[],[]]],[]]=>[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
[[],[[[[]]]],[]]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
[[],[[],[],[],[]]]=>[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[[],[[],[],[[]]]]=>[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
[[],[[],[[]],[]]]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
[[],[[],[[],[]]]]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
[[],[[],[[[]]]]]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
[[],[[[]],[],[]]]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
[[],[[[]],[[]]]]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
[[],[[[],[]],[]]]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)
[[],[[[[]]],[]]]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
[[],[[[],[],[]]]]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
[[],[[[],[[]]]]]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
[[],[[[[]],[]]]]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
[[],[[[[],[]]]]]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
[[],[[[[[]]]]]]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
[[[]],[],[],[],[]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[[]],[],[],[[]]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
[[[]],[],[[]],[]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[[]],[],[[],[]]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
[[[]],[],[[[]]]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
[[[]],[[]],[],[]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[[]],[[]],[[]]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
[[[]],[[],[]],[]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[[]],[[[]]],[]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[]],[[],[],[]]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
[[[]],[[],[[]]]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
[[[]],[[[]],[]]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
[[[]],[[[],[]]]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[[[]],[[[[]]]]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[[[],[]],[],[],[]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[[[]]],[],[],[]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[[],[]],[],[[]]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
[[[[]]],[],[[]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
[[[],[]],[[]],[]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[[[]]],[[]],[]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[[],[]],[[],[]]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
[[[],[]],[[[]]]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[[]]],[[],[]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[[[]]],[[[]]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[],[],[]],[],[]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[[],[[]]],[],[]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[[]],[]],[],[]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[[[],[]]],[],[]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[[[]]]],[],[]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[[[],[],[]],[[]]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
[[[],[[]]],[[]]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[[]],[]],[[]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[[],[]]],[[]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[[[]]]],[[]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[[],[],[],[]],[]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[[],[],[[]]],[]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[[],[[]],[]],[]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[],[[],[]]],[]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[[],[[[]]]],[]]=>[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[[]],[],[]],[]]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[[[]],[[]]],[]]=>[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[[],[]],[]],[]]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[[[[]]],[]],[]]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[[[],[],[]]],[]]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[[[],[[]]]],[]]=>[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[[[[]],[]]],[]]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[[[[],[]]]],[]]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[[[[[]]]]],[]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[[],[],[],[],[]]]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6)
[[[],[],[],[[]]]]=>[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>([(1,4),(4,5),(5,2),(5,3)],6)
[[[],[],[[]],[]]]=>[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[[],[],[[],[]]]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>([(1,5),(4,3),(5,2),(5,4)],6)
[[[],[],[[[]]]]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>([(1,5),(5,2),(5,3),(5,4)],6)
[[[],[[]],[],[]]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[],[[]],[[]]]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[],[[],[]],[]]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[[],[[[]]],[]]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[],[[],[],[]]]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>([(1,3),(1,5),(4,2),(5,4)],6)
[[[],[[],[[]]]]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>([(1,4),(1,5),(5,2),(5,3)],6)
[[[],[[[]],[]]]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[[[],[[[],[]]]]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>([(1,3),(1,4),(1,5),(5,2)],6)
[[[],[[[[]]]]]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5)],6)
[[[[]],[],[],[]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>([(1,5),(2,5),(3,4),(5,3)],6)
[[[[]],[],[[]]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>([(1,5),(2,5),(5,3),(5,4)],6)
[[[[]],[[]],[]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[[]],[[],[]]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[[[]],[[[]]]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[[],[]],[],[]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6)
[[[[[]]],[],[]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>([(1,5),(2,5),(3,5),(5,4)],6)
[[[[],[]],[[]]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>([(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[[[]]],[[]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[[[],[],[]],[]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6)
[[[[],[[]]],[]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[[[[]],[]],[]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6)
[[[[[],[]]],[]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[[[[[]]]],[]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[[[],[],[],[]]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>([(2,3),(3,5),(5,4)],6)
[[[[],[],[[]]]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>([(2,3),(3,4),(3,5)],6)
[[[[],[[]],[]]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>([(2,3),(2,4),(3,5),(4,5)],6)
[[[[],[[],[]]]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>([(2,3),(2,4),(4,5)],6)
[[[[],[[[]]]]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>([(2,3),(2,4),(2,5)],6)
[[[[[]],[],[]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>([(2,5),(3,5),(5,4)],6)
[[[[[]],[[]]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>([(2,4),(2,5),(3,4),(3,5)],6)
[[[[[],[]],[]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>([(2,5),(3,4),(4,5)],6)
[[[[[[]]],[]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>([(2,5),(3,5),(4,5)],6)
[[[[[],[],[]]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>([(3,4),(4,5)],6)
[[[[[],[[]]]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>([(3,4),(3,5)],6)
[[[[[[]],[]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>([(3,5),(4,5)],6)
[[[[[[],[]]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>([(4,5)],6)
[[[[[[[]]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>([],6)
[[],[],[],[],[],[],[]]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[],[],[],[],[],[[]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
[[],[],[],[],[[]],[]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
[[],[],[],[],[[],[]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
[[],[],[],[],[[[]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
[[],[],[],[[]],[],[]]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[],[],[],[[]],[[]]]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
[[],[],[],[[],[]],[]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
[[],[],[],[[[]]],[]]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[[],[],[],[[],[],[]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
[[],[],[],[[],[[]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)
[[],[],[],[[[]],[]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[[],[],[],[[[],[]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)
[[],[],[],[[[[]]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
[[],[],[[]],[],[],[]]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[],[],[[]],[],[[]]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
[[],[],[[]],[[]],[]]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
[[],[],[[]],[[],[]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
[[],[],[[]],[[[]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)
[[],[],[[],[]],[],[]]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[],[],[[[]]],[],[]]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[[],[],[[],[]],[[]]]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
[[],[],[[[]]],[[]]]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[[],[],[[],[],[]],[]]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
[[],[],[[],[[]]],[]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[[],[],[[[]],[]],[]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
[[],[],[[[],[]]],[]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[[],[],[[[[]]]],[]]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[[],[],[[],[],[],[]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
[[],[],[[],[],[[]]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
[[],[],[[],[[]],[]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[[],[],[[],[[],[]]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)
[[],[],[[],[[[]]]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
[[],[],[[[]],[],[]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[[],[],[[[]],[[]]]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[[],[],[[[],[]],[]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>([(0,5),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[[],[],[[[[]]],[]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[[],[],[[[],[],[]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
[[],[],[[[],[[]]]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)
[[],[],[[[[]],[]]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[[],[],[[[[],[]]]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)
[[],[],[[[[[]]]]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
[[],[[]],[],[],[],[]]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[[],[[]],[],[],[[]]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
[[],[[]],[],[[]],[]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[],[[]],[],[[],[]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
[[],[[]],[],[[[]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)
[[],[[]],[[]],[],[]]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
[[],[[]],[[]],[[]]]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[],[[]],[[],[]],[]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
[[],[[]],[[[]]],[]]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[],[[]],[[],[],[]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
[[],[[]],[[],[[]]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)
[[],[[]],[[[]],[]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[],[[]],[[[],[]]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)
[[],[[]],[[[[]]]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[],[[],[]],[],[],[]]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
[[],[[[]]],[],[],[]]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
[[],[[],[]],[],[[]]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
[[],[[[]]],[],[[]]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
[[],[[],[]],[[]],[]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
[[],[[[]]],[[]],[]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[],[[],[]],[[],[]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
[[],[[],[]],[[[]]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
[[],[[[]]],[[],[]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[[],[[[]]],[[[]]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[],[[],[],[]],[],[]]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
[[],[[],[[]]],[],[]]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
[[],[[[]],[]],[],[]]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
[[],[[[],[]]],[],[]]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
[[],[[[[]]]],[],[]]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
[[],[[],[],[]],[[]]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
[[],[[],[[]]],[[]]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
[[],[[[]],[]],[[]]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[[],[]]],[[]]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
[[],[[[[]]]],[[]]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[],[],[],[]],[]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
[[],[[],[],[[]]],[]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
[[],[[],[[]],[]],[]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
[[],[[],[[],[]]],[]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
[[],[[],[[[]]]],[]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
[[],[[[]],[],[]],[]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
[[],[[[]],[[]]],[]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[],[[[],[]],[]],[]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
[[],[[[[]]],[]],[]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[],[[[],[],[]]],[]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
[[],[[[],[[]]]],[]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
[[],[[[[]],[]]],[]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[],[[[[],[]]]],[]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
[[],[[[[[]]]]],[]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[],[[],[],[],[],[]]]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
[[],[[],[],[],[[]]]]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
[[],[[],[],[[]],[]]]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>([(0,3),(0,4),(1,6),(2,6),(4,5),(5,1),(5,2)],7)
[[],[[],[],[[],[]]]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
[[],[[],[],[[[]]]]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
[[],[[],[[]],[],[]]]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
[[],[[],[[]],[[]]]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7)
[[],[[],[[],[]],[]]]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>([(0,3),(0,5),(1,6),(2,6),(4,2),(5,1),(5,4)],7)
[[],[[],[[[]]],[]]]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[[],[[],[[],[],[]]]]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
[[],[[],[[],[[]]]]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
[[],[[],[[[]],[]]]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[[],[[],[[[],[]]]]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
[[],[[],[[[[]]]]]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
[[],[[[]],[],[],[]]]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
[[],[[[]],[],[[]]]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
[[],[[[]],[[]],[]]]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[],[[[]],[[],[]]]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[[],[[[]],[[[]]]]]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[],[[[],[]],[],[]]]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7)
[[],[[[[]]],[],[]]]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
[[],[[[],[]],[[]]]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(3,5),(3,6),(4,1)],7)
[[],[[[[]]],[[]]]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[[],[],[]],[]]]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>([(0,2),(0,3),(0,5),(1,6),(3,6),(4,1),(5,4)],7)
[[],[[[],[[]]],[]]]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)
[[],[[[[]],[]],[]]]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
[[],[[[[],[]]],[]]]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)
[[],[[[[[]]]],[]]]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
[[],[[[],[],[],[]]]]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
[[],[[[],[],[[]]]]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)
[[],[[[],[[]],[]]]]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7)
[[],[[[],[[],[]]]]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
[[],[[[],[[[]]]]]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
[[],[[[[]],[],[]]]]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
[[],[[[[]],[[]]]]]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[[[],[]],[]]]]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)
[[],[[[[[]]],[]]]]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
[[],[[[[],[],[]]]]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)
[[],[[[[],[[]]]]]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
[[],[[[[[]],[]]]]]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
[[],[[[[[],[]]]]]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
[[],[[[[[[]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
[[[]],[],[],[],[],[]]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[[]],[],[],[],[[]]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
[[[]],[],[],[[]],[]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
[[[]],[],[],[[],[]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
[[[]],[],[],[[[]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)
[[[]],[],[[]],[],[]]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
[[[]],[],[[]],[[]]]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
[[[]],[],[[],[]],[]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
[[[]],[],[[[]]],[]]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[]],[],[[],[],[]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
[[[]],[],[[],[[]]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)
[[[]],[],[[[]],[]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)
[[[]],[],[[[],[]]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)
[[[]],[],[[[[]]]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[[[]],[[]],[],[],[]]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
[[[]],[[]],[],[[]]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
[[[]],[[]],[[]],[]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[[[]],[[]],[[],[]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[[[]],[[]],[[[]]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)
[[[]],[[],[]],[],[]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
[[[]],[[[]]],[],[]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
[[[]],[[],[]],[[]]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)
[[[]],[[[]]],[[]]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[]],[[],[],[]],[]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
[[[]],[[],[[]]],[]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[[]],[[[]],[]],[]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)
[[[]],[[[],[]]],[]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[]],[[[[]]]],[]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[]],[[],[],[],[]]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
[[[]],[[],[],[[]]]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7)
[[[]],[[],[[]],[]]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7)
[[[]],[[],[[],[]]]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7)
[[[]],[[],[[[]]]]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[[[]],[[[]],[],[]]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(5,3),(6,3)],7)
[[[]],[[[]],[[]]]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)
[[[]],[[[],[]],[]]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(5,2),(6,3)],7)
[[[]],[[[[]]],[]]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[[[]],[[[],[],[]]]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(6,2)],7)
[[[]],[[[],[[]]]]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[[]],[[[[]],[]]]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7)
[[[]],[[[[],[]]]]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[[]],[[[[[]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[[],[]],[],[],[],[]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[[[]]],[],[],[],[]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[],[]],[],[],[[]]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
[[[[]]],[],[],[[]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[[[],[]],[],[[]],[]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[[[[]]],[],[[]],[]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[[[],[]],[],[[],[]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
[[[],[]],[],[[[]]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
[[[[]]],[],[[],[]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[[[[]]],[],[[[]]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[[[],[]],[[]],[],[]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
[[[[]]],[[]],[],[]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[[[],[]],[[]],[[]]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[[]]],[[]],[[]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[],[]],[[],[]],[]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
[[[],[]],[[[]]],[]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[]]],[[],[]],[]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
[[[[]]],[[[]]],[]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7)
[[[],[]],[[],[],[]]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)
[[[],[]],[[],[[]]]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)
[[[],[]],[[[]],[]]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[],[]],[[[],[]]]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)
[[[],[]],[[[[]]]]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[[]]],[[],[],[]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[[[[]]],[[],[[]]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[[[[]]],[[[]],[]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[[]]],[[[],[]]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[[[[]]],[[[[]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[],[],[]],[],[],[]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[[],[[]]],[],[],[]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[[[]],[]],[],[],[]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[[[[],[]]],[],[],[]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[]]]],[],[],[]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[],[],[]],[],[[]]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
[[[],[[]]],[],[[]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[[[[]],[]],[],[[]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)
[[[[],[]]],[],[[]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[[[[[]]]],[],[[]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[[[],[],[]],[[]],[]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[],[[]]],[[]],[]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[[]],[]],[[]],[]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)
[[[[],[]]],[[]],[]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[[[]]]],[[]],[]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[],[],[]],[[],[]]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)
[[[],[],[]],[[[]]]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[],[[]]],[[],[]]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[[[],[[]]],[[[]]]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[[]],[]],[[],[]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)
[[[[]],[]],[[[]]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
[[[[],[]]],[[],[]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[[],[]]],[[[]]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[[[]]]],[[],[]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[[]]]],[[[]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[],[],[],[]],[],[]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[[],[],[[]]],[],[]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[[],[[]],[]],[],[]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)
[[[],[[],[]]],[],[]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[[],[[[]]]],[],[]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[[]],[],[]],[],[]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[[[[]],[[]]],[],[]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[[[],[]],[]],[],[]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[[[]]],[]],[],[]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[[[[],[],[]]],[],[]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[],[[]]]],[],[]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[[]],[]]],[],[]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[[],[]]]],[],[]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[[[]]]]],[],[]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[],[],[],[]],[[]]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)
[[[],[],[[]]],[[]]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[[[],[[]],[]],[[]]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>([(0,2),(0,3),(1,4),(1,5),(2,6),(3,6),(6,4),(6,5)],7)
[[[],[[],[]]],[[]]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[[[],[[[]]]],[[]]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[[]],[],[]],[[]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7)
[[[[]],[[]]],[[]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[],[]],[]],[[]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>([(0,6),(1,4),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[[[[[]]],[]],[[]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[[[[],[],[]]],[[]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[[],[[]]]],[[]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[]],[]]],[[]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[[[[[],[]]]],[[]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[[]]]]],[[]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[],[],[],[],[]],[]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[[],[],[],[[]]],[]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[[],[],[[]],[]],[]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)
[[[],[],[[],[]]],[]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[[],[],[[[]]]],[]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[],[[]],[],[]],[]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
[[[],[[]],[[]]],[]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[],[[],[]],[]],[]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)
[[[],[[[]]],[]],[]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[],[[],[],[]]],[]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[[],[[],[[]]]],[]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[[],[[[]],[]]],[]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[[],[[[],[]]]],[]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[],[[[[]]]]],[]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[[]],[],[],[]],[]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[[[[]],[],[[]]],[]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[[]],[[]],[]],[]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[[[[]],[[],[]]],[]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[[[[]],[[[]]]],[]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[],[]],[],[]],[]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[]]],[],[]],[]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[[[[],[]],[[]]],[]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[]]],[[]]],[]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[],[]],[]],[]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[[[],[[]]],[]],[]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[[]],[]],[]],[]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[[[[],[]]],[]],[]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[[[]]]],[]],[]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[[],[],[],[]]],[]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[[[],[],[[]]]],[]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[[]],[]]],[]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
[[[[],[[],[]]]],[]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[[],[[[]]]]],[]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[[]],[],[]]],[]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[[]],[[]]]],[]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[],[]],[]]],[]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[[[[[]]],[]]],[]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[[[[[],[],[]]]],[]]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[[],[[]]]]],[]]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[[]],[]]]],[]]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[[[[],[]]]]],[]]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[[]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[],[],[],[],[],[]]]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[[],[],[],[],[[]]]]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
[[[],[],[],[[]],[]]]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[[],[],[],[[],[]]]]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[[[],[],[],[[[]]]]]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
[[[],[],[[]],[],[]]]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[[],[],[[]],[[]]]]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[[[],[],[[],[]],[]]]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[[],[],[[[]]],[]]]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[],[],[[],[],[]]]]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[[[],[],[[],[[]]]]]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>([(1,6),(5,3),(5,4),(6,2),(6,5)],7)
[[[],[],[[[]],[]]]]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[],[],[[[],[]]]]]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[[[],[],[[[[]]]]]]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[[[],[[]],[],[],[]]]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[[],[[]],[],[[]]]]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[[[],[[]],[[]],[]]]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[],[[]],[[],[]]]]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[[[],[[]],[[[]]]]]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[],[[],[]],[],[]]]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[[],[[[]]],[],[]]]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[],[[],[]],[[]]]]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[[[],[[[]]],[[]]]]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[],[[],[],[]],[]]]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[[],[[],[[]]],[]]]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>([(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[[],[[[]],[]],[]]]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[[],[[[],[]]],[]]]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[],[[[[]]]],[]]]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[],[[],[],[],[]]]]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>([(1,3),(1,6),(4,5),(5,2),(6,4)],7)
[[[],[[],[],[[]]]]]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>([(1,4),(1,5),(5,6),(6,2),(6,3)],7)
[[[],[[],[[]],[]]]]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>([(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[],[[],[[],[]]]]]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>([(1,4),(1,6),(5,3),(6,2),(6,5)],7)
[[[],[[],[[[]]]]]]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[[[],[[[]],[],[]]]]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
[[[],[[[]],[[]]]]]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[],[[[],[]],[]]]]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[[[],[[[[]]],[]]]]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[[[],[[[],[],[]]]]]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[[[],[[[],[[]]]]]]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[[],[[[[]],[]]]]]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
[[[],[[[[],[]]]]]]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[[],[[[[[]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[[[]],[],[],[],[]]]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[[]],[],[],[[]]]]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>([(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[[[[]],[],[[]],[]]]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[[]],[],[[],[]]]]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>([(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[[[[]],[],[[[]]]]]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>([(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[[[[]],[[]],[],[]]]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[[[]],[[]],[[]]]]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[[]],[[],[]],[]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[[[[]],[[[]]],[]]]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[]],[[],[],[]]]]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[[[[]],[[],[[]]]]]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[[[[]],[[[]],[]]]]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[[]],[[[],[]]]]]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[[[[]],[[[[]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[[],[]],[],[],[]]]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[]]],[],[],[]]]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[[],[]],[],[[]]]]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>([(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[[[[[]]],[],[[]]]]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>([(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[[[[],[]],[[]],[]]]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>([(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[[[]]],[[]],[]]]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[[],[]],[[],[]]]]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[[],[]],[[[]]]]]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[[[]]],[[],[]]]]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[[]]],[[[]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[[],[],[]],[],[]]]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[],[[]]],[],[]]]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>([(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[[]],[]],[],[]]]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[[],[]]],[],[]]]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[[[]]]],[],[]]]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[[],[],[]],[[]]]]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>([(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[[],[[]]],[[]]]]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[]],[]],[[]]]]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[],[]]],[[]]]]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[[]]]],[[]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[[],[],[],[]],[]]]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[[[[],[],[[]]],[]]]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>([(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[[]],[]],[]]]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[],[[],[]]],[]]]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>([(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[[],[[[]]]],[]]]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[[]],[],[]],[]]]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[[]],[[]]],[]]]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[],[]],[]],[]]]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[[[]]],[]],[]]]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[[[],[],[]]],[]]]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[[],[[]]]],[]]]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[[]],[]]],[]]]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[[[[],[]]]],[]]]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[[]]]]],[]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[[],[],[],[],[]]]]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>([(2,6),(4,5),(5,3),(6,4)],7)
[[[[],[],[],[[]]]]]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>([(2,5),(5,6),(6,3),(6,4)],7)
[[[[],[],[[]],[]]]]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>([(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[],[[],[]]]]]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>([(2,6),(5,4),(6,3),(6,5)],7)
[[[[],[],[[[]]]]]]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>([(2,6),(6,3),(6,4),(6,5)],7)
[[[[],[[]],[],[]]]]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>([(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[],[[]],[[]]]]]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[],[[],[]],[]]]]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[[],[[[]]],[]]]]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[],[[],[],[]]]]]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>([(2,4),(2,6),(5,3),(6,5)],7)
[[[[],[[],[[]]]]]]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>([(2,5),(2,6),(6,3),(6,4)],7)
[[[[],[[[]],[]]]]]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
[[[[],[[[],[]]]]]]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>([(2,4),(2,5),(2,6),(6,3)],7)
[[[[],[[[[]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>([(2,3),(2,4),(2,5),(2,6)],7)
[[[[[]],[],[],[]]]]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>([(2,6),(3,6),(4,5),(6,4)],7)
[[[[[]],[],[[]]]]]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>([(2,6),(3,6),(6,4),(6,5)],7)
[[[[[]],[[]],[]]]]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[]],[[],[]]]]]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>([(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[[]],[[[]]]]]]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[[[],[]],[],[]]]]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7)
[[[[[[]]],[],[]]]]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>([(2,6),(3,6),(4,6),(6,5)],7)
[[[[[],[]],[[]]]]]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>([(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[[]]],[[]]]]]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[],[],[]],[]]]]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7)
[[[[[],[[]]],[]]]]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[[]],[]],[]]]]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7)
[[[[[[],[]]],[]]]]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[[]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[[[[],[],[],[]]]]]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>([(3,4),(4,6),(6,5)],7)
[[[[[],[],[[]]]]]]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>([(3,4),(4,5),(4,6)],7)
[[[[[],[[]],[]]]]]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>([(3,4),(3,5),(4,6),(5,6)],7)
[[[[[],[[],[]]]]]]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>([(3,4),(3,5),(5,6)],7)
[[[[[],[[[]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>([(3,4),(3,5),(3,6)],7)
[[[[[[]],[],[]]]]]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>([(3,6),(4,6),(6,5)],7)
[[[[[[]],[[]]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>([(3,5),(3,6),(4,5),(4,6)],7)
[[[[[[],[]],[]]]]]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>([(3,6),(4,5),(5,6)],7)
[[[[[[[]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>([(3,6),(4,6),(5,6)],7)
[[[[[[],[],[]]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>([(4,5),(5,6)],7)
[[[[[[],[[]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>([(4,5),(4,6)],7)
[[[[[[[]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>([(4,6),(5,6)],7)
[[[[[[[],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>([(5,6)],7)
[[[[[[[[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>([],7)
[[],[],[],[],[],[],[],[]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[],[],[],[],[],[],[[]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>([(0,6),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],8)
[[],[],[],[],[],[[]],[]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
[[],[],[],[],[],[[],[]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8)
[[],[],[],[],[],[[[]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>([(0,6),(4,5),(5,7),(6,4),(7,1),(7,2),(7,3)],8)
[[],[],[],[],[[]],[],[]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
[[],[],[],[],[[]],[[]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,3),(5,1),(5,2)],8)
[[],[],[],[],[[],[]],[]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)
[[],[],[],[],[[[]]],[]]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[[],[],[],[],[[],[],[]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>([(0,6),(3,7),(4,5),(5,1),(6,3),(7,2),(7,4)],8)
[[],[],[],[],[[],[[]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>([(0,5),(4,7),(5,4),(6,2),(6,3),(7,1),(7,6)],8)
[[],[],[],[],[[[]],[]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>([(0,5),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[[],[],[],[],[[[],[]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>([(0,6),(4,7),(5,3),(6,4),(7,1),(7,2),(7,5)],8)
[[],[],[],[],[[[[]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>([(0,6),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],8)
[[],[],[],[[]],[],[],[]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[],[],[],[[]],[[]],[]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2),(5,7),(6,7)],8)
[[],[],[],[[]],[[],[]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3),(7,1)],8)
[[],[],[],[[]],[[[]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>([(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,1),(4,2)],8)
[[],[],[],[[],[]],[],[]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8)
[[],[],[],[[],[]],[[]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,2),(4,5),(5,1),(5,3)],8)
[[],[],[],[[[]]],[[]]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[[],[],[],[[],[],[]],[]]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8)
[[],[],[],[[],[[]]],[]]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[[],[],[],[[[]],[]],[]]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>([(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3),(6,7)],8)
[[],[],[],[[[],[]]],[]]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>([(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[[],[],[],[[[[]]]],[]]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[[],[],[],[[],[],[],[]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8)
[[],[],[],[[],[],[[]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>([(0,5),(4,7),(5,6),(6,3),(6,4),(7,1),(7,2)],8)
[[],[],[],[[],[[]],[]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>([(0,4),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[[],[],[],[[],[[],[]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>([(0,5),(4,3),(5,6),(6,2),(6,7),(7,1),(7,4)],8)
[[],[],[],[[],[[[]]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>([(0,5),(5,6),(6,4),(6,7),(7,1),(7,2),(7,3)],8)
[[],[],[],[[[]],[],[]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>([(0,5),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
[[],[],[],[[[]],[[]]]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[[],[],[],[[[],[]],[]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>([(0,5),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[[],[],[],[[[[]]],[]]]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>([(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[[],[],[],[[[],[],[]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>([(0,6),(4,5),(5,3),(6,7),(7,1),(7,2),(7,4)],8)
[[],[],[],[[[],[[]]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>([(0,5),(5,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[[],[],[],[[[[]],[]]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>([(0,5),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[[],[],[],[[[[],[]]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>([(0,6),(5,4),(6,7),(7,1),(7,2),(7,3),(7,5)],8)
[[],[],[],[[[[[]]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>([(0,6),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[[],[],[[]],[],[],[],[]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
[[],[],[[]],[],[],[[]]]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>([(0,6),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(7,5)],8)
[[],[],[[]],[],[[],[]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>([(0,6),(2,7),(3,7),(5,1),(6,2),(6,3),(7,4),(7,5)],8)
[[],[],[[]],[[]],[],[]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7),(7,1)],8)
[[],[],[[]],[[]],[[]]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>([(0,1),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[],[],[[]],[[],[]],[]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>([(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(4,3),(5,6),(7,1)],8)
[[],[],[[]],[[],[],[]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(5,3),(7,4)],8)
[[],[],[[]],[[],[[]]]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>([(0,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4),(7,1),(7,2)],8)
[[],[],[[]],[[[]],[]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>([(0,1),(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[],[[]],[[[],[]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>([(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3),(7,1)],8)
[[],[],[[]],[[[[]]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>([(0,1),(1,2),(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[],[[[]]],[],[[]]]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>([(0,6),(1,7),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4),(7,5)],8)
[[],[],[[],[]],[[[]]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,2),(4,1),(4,3)],8)
[[],[],[[[]]],[[],[]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[[],[],[[],[],[]],[],[]]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>([(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4),(7,3)],8)
[[],[],[[[[]]]],[],[]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[[],[],[[[]],[],[]],[]]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8)
[[],[],[[[],[]],[]],[]]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>([(0,5),(1,7),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4),(6,7)],8)
[[],[],[[[],[],[]]],[]]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>([(0,6),(1,7),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4)],8)
[[],[],[[[],[[]]]],[]]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>([(0,6),(1,7),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8)
[[],[],[[],[],[[],[]]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>([(0,7),(4,6),(5,3),(6,2),(6,5),(7,1),(7,4)],8)
[[],[],[[],[[]],[[]]]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(5,1),(5,4)],8)
[[],[],[[],[[[]]],[]]]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>([(0,5),(2,7),(3,7),(4,7),(5,1),(5,6),(6,2),(6,3),(6,4)],8)
[[],[],[[],[[],[],[]]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>([(0,7),(4,5),(5,3),(6,2),(6,4),(7,1),(7,6)],8)
[[],[],[[],[[],[[]]]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>([(0,7),(5,2),(5,6),(6,3),(6,4),(7,1),(7,5)],8)
[[],[],[[],[[[],[]]]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>([(0,6),(5,4),(6,3),(6,7),(7,1),(7,2),(7,5)],8)
[[],[],[[],[[[[]]]]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>([(0,6),(6,5),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[],[[[]],[],[[]]]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>([(0,6),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4),(7,5)],8)
[[],[],[[[]],[[],[]]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>([(0,5),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[[],[],[[[]],[[[]]]]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>([(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(4,2),(4,3)],8)
[[],[],[[[[]]],[[]]]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>([(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[[],[],[[[],[],[]],[]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>([(0,6),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4)],8)
[[],[],[[[],[[]]],[]]]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>([(0,6),(2,7),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8)
[[],[],[[[],[],[],[]]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>([(0,7),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],8)
[[],[],[[[],[[]],[]]]]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>([(0,6),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(6,5)],8)
[[],[],[[[[]],[],[]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>([(0,6),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[[],[],[[[[]],[[]]]]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>([(0,5),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[[],[],[[[[[]]],[]]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>([(0,6),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[[],[],[[[[],[],[]]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>([(0,7),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],8)
[[],[],[[[[[[]]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>([(0,7),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[],[[]],[],[],[],[],[]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[],[[]],[],[],[[]],[]]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
[[],[[]],[],[[]],[],[]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[],[[]],[],[[]],[[]]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(7,1),(7,2)],8)
[[],[[]],[],[[[]]],[]]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
[[],[[]],[],[[],[],[]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>([(0,3),(0,4),(3,7),(4,7),(5,1),(6,5),(7,2),(7,6)],8)
[[],[[]],[],[[],[[]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>([(0,4),(0,5),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],8)
[[],[[]],[],[[[]],[]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>([(0,4),(0,5),(2,6),(3,6),(4,7),(5,7),(7,1),(7,2),(7,3)],8)
[[],[[]],[],[[[[]]]]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>([(0,5),(0,6),(5,7),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[[]],[[]],[],[],[]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7),(7,4)],8)
[[],[[]],[[]],[[]],[]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[],[[]],[[]],[[],[]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>([(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(5,1),(6,4),(6,5),(7,4),(7,5)],8)
[[],[[]],[[]],[[[]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[[],[[]],[[[]],[]],[]]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[[],[[]],[[[]],[],[]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>([(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(6,4),(7,4)],8)
[[],[[]],[[[]],[[]]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[],[[]],[[[[]]],[]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[1,3,2,7,6,5,8,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[],[[]],[[[],[[]]]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>([(0,3),(0,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1),(7,2)],8)
[[],[[]],[[[[[]]]]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[],[[],[]],[],[],[],[]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8)
[[],[[[]]],[],[],[],[]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[[],[[[]]],[],[],[[]]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(6,2),(7,6)],8)
[[],[[[]]],[],[[]],[]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
[[],[[],[]],[],[[],[]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>([(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,3),(7,5)],8)
[[],[[[]]],[],[[[]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>([(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1),(7,2),(7,3)],8)
[[],[[],[]],[[],[]],[]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8)
[[],[[[]]],[[],[]],[]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,1)],8)
[[],[[[]]],[[[]]],[]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[[],[[],[]],[[],[],[]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(7,4)],8)
[[],[[],[]],[[],[[]]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>([(0,4),(0,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,1),(7,2)],8)
[[],[[],[]],[[[]],[]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>([(0,1),(0,3),(1,2),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[[],[]],[[[],[]]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>([(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(7,1)],8)
[[],[[],[]],[[[[]]]]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>([(0,1),(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[[[]]],[[],[],[]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>([(0,2),(0,3),(0,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(7,5)],8)
[[],[[[]]],[[[]],[]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[[[]]],[[[[]]]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[[],[[]]],[],[[]]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>([(0,5),(0,6),(1,7),(2,7),(5,7),(6,1),(6,2),(7,3),(7,4)],8)
[[],[[[]],[]],[[]],[]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>([(0,1),(0,2),(0,3),(1,7),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[[],[[],[[],[]]],[],[]]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>([(0,4),(0,6),(1,7),(2,7),(4,7),(5,2),(6,1),(6,5),(7,3)],8)
[[],[[[]],[[]]],[],[]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>([(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[[],[[[[]]],[]],[],[]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(7,6)],8)
[[],[[[],[],[]]],[],[]]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>([(0,3),(0,4),(0,6),(1,7),(3,7),(4,7),(5,1),(6,5),(7,2)],8)
[[],[[[],[[]]]],[],[]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,7),(6,1),(6,2),(7,3)],8)
[[],[[[[]],[]]],[],[]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,7),(7,1)],8)
[[],[[[[],[]]]],[],[]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>([(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1),(7,2)],8)
[[],[[],[[[]]]],[[]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3)],8)
[[],[[[[]],[]]],[[]]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[],[[],[],[],[],[]],[]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)
[[],[[],[[]],[[]]],[]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,1),(4,2),(5,7),(6,7)],8)
[[],[[],[[[]]],[]],[]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
[[],[[],[[],[],[]]],[]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>([(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,2),(6,1),(6,4)],8)
[[],[[],[[],[[]]]],[]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>([(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,2),(5,3),(6,1),(6,5)],8)
[[],[[[]],[],[[]]],[]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
[[],[[[]],[[]],[]],[]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>([(0,1),(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[],[[[[]]],[],[]],[]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[1,5,4,3,6,7,2,8]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,6),(7,1)],8)
[[],[[[[]],[]],[]],[]]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[],[[[],[[]],[]]],[]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
[[],[[[[],[],[]]]],[]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>([(0,2),(0,3),(0,4),(0,6),(1,7),(2,7),(3,7),(4,7),(5,1),(6,5)],8)
[[],[[],[],[],[[[]]]]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[1,3,4,5,8,7,6,2]=>([(0,4),(0,6),(5,7),(6,5),(7,1),(7,2),(7,3)],8)
[[],[[],[],[[[]]],[]]]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>([(0,4),(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3)],8)
[[],[[],[],[[],[],[]]]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>([(0,3),(0,6),(4,5),(5,2),(6,7),(7,1),(7,4)],8)
[[],[[],[],[[[]],[]]]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>([(0,4),(0,5),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3)],8)
[[],[[],[],[[[[]]]]]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>([(0,5),(0,6),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[[],[[]],[[]],[]]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2),(5,7),(6,7)],8)
[[],[[],[[[]]],[[]]]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,1),(5,2),(5,3)],8)
[[],[[],[[],[],[],[]]]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)
[[],[[],[[],[[],[]]]]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8)
[[],[[],[[],[[[]]]]]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>([(0,5),(0,6),(6,4),(6,7),(7,1),(7,2),(7,3)],8)
[[],[[],[[[]],[],[]]]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>([(0,5),(0,6),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4)],8)
[[],[[],[[[],[],[]]]]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>([(0,4),(0,7),(5,6),(6,3),(7,1),(7,2),(7,5)],8)
[[],[[],[[[],[[]]]]]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>([(0,5),(0,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[[],[[],[[[[[]]]]]]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>([(0,6),(0,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[[],[[[]],[],[[],[]]]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>([(0,3),(0,4),(0,5),(4,7),(5,7),(6,1),(7,2),(7,6)],8)
[[],[[[]],[],[[[]]]]]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>([(0,4),(0,5),(0,6),(5,7),(6,7),(7,1),(7,2),(7,3)],8)
[[],[[[]],[[]],[],[]]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[1,4,3,6,5,7,8,2]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[[],[[[]],[[]],[[]]]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>([(0,1),(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[],[[[]],[[],[[]]]]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>([(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1),(7,2)],8)
[[],[[[]],[[[]],[]]]]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>([(0,1),(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[[[]],[[[],[]]]]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1)],8)
[[],[[[]],[[[[]]]]]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[[[[]]],[],[],[]]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>([(0,2),(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
[[],[[[[]]],[],[[]]]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>([(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1),(7,2)],8)
[[],[[[[]]],[[[]]]]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[],[[[],[[]]],[[]]]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>([(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(4,6),(4,7),(5,1),(5,2)],8)
[[],[[[[],[]]],[[]]]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(3,6),(3,7),(4,6),(4,7),(5,1)],8)
[[],[[[[[]]]],[[]]]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[],[[[[[],[]]]],[]]]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1)],8)
[[],[[[],[[]],[[]]]]]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>([(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(5,1),(5,2)],8)
[[],[[[],[[[]]],[]]]]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(6,1),(6,2),(6,3)],8)
[[],[[[],[[],[],[]]]]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>([(0,3),(0,4),(0,7),(5,6),(6,2),(7,1),(7,5)],8)
[[],[[[],[[],[[]]]]]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>([(0,4),(0,5),(0,7),(6,2),(6,3),(7,1),(7,6)],8)
[[],[[[],[[[],[]]]]]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>([(0,4),(0,5),(0,7),(6,3),(7,1),(7,2),(7,6)],8)
[[],[[[],[[[[]]]]]]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>([(0,5),(0,6),(0,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[[[[]],[],[],[]]]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>([(0,2),(0,3),(0,4),(0,5),(4,7),(5,7),(6,1),(7,6)],8)
[[],[[[[[]]],[],[]]]]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1)],8)
[[],[[[[],[],[],[]]]]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)
[[],[[[[],[[]],[]]]]]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(6,1),(6,2)],8)
[[],[[[[[]],[],[]]]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(5,7),(6,7),(7,1)],8)
[[],[[[[[],[]],[]]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(5,7),(6,1)],8)
[[],[[[[[[]]],[]]]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7)],8)
[[],[[[[[],[],[]]]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
[[],[[[[[],[[]]]]]]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(7,1),(7,2)],8)
[[],[[[[[[]],[]]]]]]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(5,7),(6,7)],8)
[[],[[[[[[],[]]]]]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
[[],[[[[[[[]]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)],8)
[[[]],[],[],[],[],[],[]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[[[]],[],[],[],[],[[]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>([(0,7),(1,7),(4,6),(5,4),(6,2),(6,3),(7,5)],8)
[[[]],[],[],[[]],[],[]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>([(0,6),(1,6),(3,7),(4,7),(5,3),(5,4),(6,5),(7,2)],8)
[[[]],[],[],[[]],[[]]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(7,4)],8)
[[[]],[],[],[[],[],[]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>([(0,7),(1,7),(4,5),(5,3),(6,2),(6,4),(7,6)],8)
[[[]],[],[],[[[]],[]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>([(0,7),(1,7),(3,6),(4,6),(5,2),(5,3),(5,4),(7,5)],8)
[[[]],[],[],[[[[]]]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>([(0,7),(1,7),(6,2),(6,3),(6,4),(6,5),(7,6)],8)
[[[]],[],[[]],[],[[]]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>([(0,7),(1,7),(2,6),(3,6),(6,4),(6,5),(7,2),(7,3)],8)
[[[]],[],[[]],[[[]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(7,2),(7,3)],8)
[[[]],[],[[[]]],[[]]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[[]],[],[[[],[]]],[]]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>([(0,6),(1,6),(2,7),(3,7),(4,7),(5,2),(6,3),(6,4),(6,5)],8)
[[[]],[],[[[],[[]]]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>([(0,7),(1,7),(6,2),(6,3),(7,4),(7,5),(7,6)],8)
[[[]],[],[[[[],[]]]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>([(0,7),(1,7),(6,2),(7,3),(7,4),(7,5),(7,6)],8)
[[[]],[],[[[[[]]]]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>([(0,7),(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[[]],[[]],[],[],[],[]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,7),(6,7),(7,3)],8)
[[[]],[[]],[],[],[[]]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,4),(6,5),(7,5)],8)
[[[]],[[]],[[]],[],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>([(0,6),(0,7),(1,6),(1,7),(3,2),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[]],[[]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[],[]],[]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(3,2),(5,4),(6,3),(6,5),(7,3),(7,5)],8)
[[[]],[[]],[[],[],[]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[],[[]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[[]],[]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>([(0,6),(0,7),(1,6),(1,7),(4,3),(5,3),(6,2),(6,4),(6,5),(7,2),(7,4),(7,5)],8)
[[[]],[[]],[[[],[]]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[[[]],[[]],[[[[]]]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8)
[[[]],[[],[]],[],[[]]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>([(0,5),(0,6),(1,5),(1,6),(4,7),(5,7),(6,4),(7,2),(7,3)],8)
[[[]],[[[]]],[],[[]]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7),(7,2),(7,3)],8)
[[[]],[[],[[]]],[],[]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(6,3),(7,4)],8)
[[[]],[[[],[]]],[],[]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(4,7),(5,7),(6,2),(7,3)],8)
[[[]],[[],[],[]],[[]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,4),(3,5),(6,2),(7,4),(7,5)],8)
[[[]],[[],[[]]],[[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>([(0,4),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[[]],[[[]],[]],[[]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(4,6),(5,6),(6,2),(6,3),(7,2),(7,3)],8)
[[[]],[[[],[]]],[[]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[[[]],[[[[]]]],[[]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[]],[[[],[],[]]],[]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,7),(4,7),(5,7),(6,2)],8)
[[[]],[[],[],[],[],[]]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>([(0,6),(0,7),(1,6),(1,7),(3,5),(4,3),(5,2),(7,4)],8)
[[[]],[[],[],[],[[]]]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>([(0,6),(0,7),(1,6),(1,7),(4,5),(5,2),(5,3),(7,4)],8)
[[[]],[[],[],[[],[]]]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(5,4),(7,5)],8)
[[[]],[[],[],[[[]]]]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(5,4),(7,5)],8)
[[[]],[[],[[]],[[]]]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(7,2),(7,3)],8)
[[[]],[[],[[],[]],[]]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[2,1,4,6,7,5,8,3]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,5),(4,3),(7,2),(7,4)],8)
[[[]],[[],[[[]]],[]]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4)],8)
[[[]],[[],[[],[],[]]]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>([(0,6),(0,7),(1,6),(1,7),(4,5),(5,3),(7,2),(7,4)],8)
[[[]],[[],[[],[[]]]]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>([(0,6),(0,7),(1,6),(1,7),(5,3),(5,4),(7,2),(7,5)],8)
[[[]],[[],[[[],[]]]]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>([(0,6),(0,7),(1,6),(1,7),(5,4),(7,2),(7,3),(7,5)],8)
[[[]],[[],[[[[]]]]]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>([(0,6),(0,7),(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[[[]],[[[]],[[]],[]]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>([(0,3),(0,6),(0,7),(1,3),(1,6),(1,7),(4,2),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[[],[]],[],[]]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[2,1,5,6,4,7,8,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(6,3),(7,4)],8)
[[[]],[[[],[],[]],[]]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4),(6,2),(7,4)],8)
[[[]],[[[[]],[]],[]]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>([(0,3),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(4,2),(5,4),(6,4),(7,2)],8)
[[[]],[[[],[],[],[]]]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(7,3)],8)
[[[]],[[[],[[],[]]]]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,3),(7,2),(7,4)],8)
[[[]],[[[[]],[],[]]]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(3,2),(6,3),(7,3)],8)
[[[]],[[[[]],[[]]]]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8)
[[[]],[[[[],[]],[]]]]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(6,2),(7,3)],8)
[[[]],[[[[[]]],[]]]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7)],8)
[[[]],[[[[],[],[]]]]]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(7,2)],8)
[[[]],[[[[],[[]]]]]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8)
[[[]],[[[[[]],[]]]]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(6,2),(7,2)],8)
[[[]],[[[[[],[]]]]]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[[]],[[[[[[]]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[[],[]],[],[],[],[],[]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[[[]]],[],[],[],[],[]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[],[]],[],[],[[],[]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8)
[[[[]]],[],[],[[],[]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>([(0,7),(1,7),(2,7),(5,4),(6,3),(6,5),(7,6)],8)
[[[[]]],[],[],[[[]]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>([(0,7),(1,7),(2,7),(6,3),(6,4),(6,5),(7,6)],8)
[[[],[]],[],[[],[]],[]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>([(0,7),(1,2),(2,7),(3,6),(4,6),(5,4),(7,3),(7,5)],8)
[[[[]]],[],[[[]]],[]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>([(0,6),(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[],[]],[],[[],[],[]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>([(0,7),(1,3),(3,7),(5,2),(6,5),(7,4),(7,6)],8)
[[[],[]],[],[[[]],[]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>([(0,7),(1,3),(3,7),(4,6),(5,6),(7,2),(7,4),(7,5)],8)
[[[],[]],[],[[[],[]]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>([(0,7),(1,3),(3,7),(6,2),(7,4),(7,5),(7,6)],8)
[[[],[]],[],[[[[]]]]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>([(0,7),(1,2),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[[]]],[],[[],[],[]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>([(0,7),(1,7),(2,7),(5,3),(6,5),(7,4),(7,6)],8)
[[[[]]],[],[[],[[]]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>([(0,7),(1,7),(2,7),(6,3),(6,4),(7,5),(7,6)],8)
[[[[]]],[],[[[]],[]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>([(0,7),(1,7),(2,7),(4,6),(5,6),(7,3),(7,4),(7,5)],8)
[[[[]]],[],[[[],[]]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>([(0,7),(1,7),(2,7),(6,3),(7,4),(7,5),(7,6)],8)
[[[[]]],[],[[[[]]]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>([(0,7),(1,7),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[],[]],[[]],[[]],[]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>([(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[[]]],[[]],[[]],[]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(6,3),(6,4),(7,3),(7,4)],8)
[[[[]]],[[],[]],[],[]]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(6,5),(7,3)],8)
[[[],[]],[[[]]],[[]]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[]],[[],[],[]],[]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>([(0,6),(0,7),(1,3),(2,5),(3,6),(3,7),(4,2),(6,5),(7,4)],8)
[[[],[]],[[[]],[]],[]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>([(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[[[],[]],[[[],[]]],[]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>([(0,3),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,2)],8)
[[[[]]],[[],[[]]],[]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[]]],[[[]],[]],[]]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(5,4),(6,3),(7,3)],8)
[[[],[]],[[],[],[],[]]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(7,5)],8)
[[[],[]],[[[]],[[]]]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>([(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[[],[]],[[[],[],[]]]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>([(0,5),(0,6),(0,7),(1,3),(3,5),(3,6),(3,7),(4,2),(7,4)],8)
[[[],[]],[[[],[[]]]]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>([(0,5),(0,6),(0,7),(1,4),(4,5),(4,6),(4,7),(7,2),(7,3)],8)
[[[],[]],[[[[]],[]]]]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>([(0,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[[[],[]],[[[[[]]]]]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[[]]],[[],[],[],[]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[[[[]]],[[],[],[[]]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(7,3)],8)
[[[[]]],[[],[[]],[]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(7,3),(7,4)],8)
[[[[]]],[[],[[],[]]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(4,5),(7,3),(7,4)],8)
[[[[]]],[[],[[[]]]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[[[[]]],[[[]],[],[]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(6,4),(7,4)],8)
[[[[]]],[[[]],[[]]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[[[]]],[[[],[]],[]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(6,4),(7,3)],8)
[[[[]]],[[[[]]],[]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(5,3),(6,3),(7,3)],8)
[[[[]]],[[[],[],[]]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(7,3)],8)
[[[[]]],[[[],[[]]]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[[[[]]],[[[[]],[]]]]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[[[[]]],[[[[],[]]]]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[[[[]]],[[[[[]]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[],[],[]],[],[],[],[]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[[],[[]]],[],[],[],[]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[[[]],[]],[],[],[],[]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[[[[],[]]],[],[],[],[]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[]]]],[],[],[],[]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[],[],[]],[],[],[[]]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>([(0,7),(1,5),(4,7),(5,4),(6,2),(6,3),(7,6)],8)
[[[[]],[]],[],[],[[]]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>([(0,7),(1,6),(2,6),(3,4),(3,5),(6,7),(7,3)],8)
[[[[[]]]],[],[],[[]]]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[],[],[]],[],[[]],[]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(7,3),(7,4)],8)
[[[[]],[]],[],[[]],[]]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>([(0,6),(1,5),(2,5),(3,7),(4,7),(5,6),(6,3),(6,4)],8)
[[[[[]]]],[],[[]],[]]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[],[],[]],[],[[],[]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>([(0,7),(1,5),(3,7),(5,3),(6,2),(7,4),(7,6)],8)
[[[],[],[]],[],[[[]]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>([(0,7),(1,6),(2,7),(6,2),(7,3),(7,4),(7,5)],8)
[[[[]],[]],[],[[],[]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>([(0,7),(1,6),(2,6),(4,5),(6,7),(7,3),(7,4)],8)
[[[[]],[]],[],[[[]]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>([(0,7),(1,6),(2,6),(6,7),(7,3),(7,4),(7,5)],8)
[[[[[]]]],[],[[],[]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>([(0,7),(1,7),(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[[[[[]]]],[],[[[]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>([(0,7),(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[],[],[]],[[]],[],[]]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(5,7),(6,7),(7,2)],8)
[[[[]],[]],[[]],[],[]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>([(0,7),(1,7),(2,5),(2,6),(4,3),(5,4),(6,4),(7,5),(7,6)],8)
[[[[[]]]],[[]],[],[]]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[],[],[]],[[]],[[]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>([(0,2),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[],[[]]],[[]],[[]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[]],[]],[[]],[[]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>([(0,7),(1,7),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6)],8)
[[[[],[]]],[[]],[[]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[[]]]],[[]],[[]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[],[],[]],[[],[]],[]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>([(0,6),(0,7),(1,4),(2,6),(2,7),(3,5),(4,2),(6,5),(7,3)],8)
[[[],[],[]],[[[]]],[]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[]],[]],[[],[]],[]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>([(0,7),(1,7),(2,4),(2,6),(3,5),(4,3),(6,5),(7,4),(7,6)],8)
[[[[]],[]],[[[]]],[]]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[[]]]],[[],[]],[]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[[[[[]]]],[[[]]],[]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[[[],[],[]],[[],[],[]]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8)
[[[],[],[]],[[],[[]]]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>([(0,6),(0,7),(1,5),(4,6),(4,7),(5,4),(7,2),(7,3)],8)
[[[],[],[]],[[[]],[]]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>([(0,2),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[],[],[]],[[[],[]]]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>([(0,5),(0,6),(0,7),(1,4),(3,5),(3,6),(3,7),(4,3),(7,2)],8)
[[[],[],[]],[[[[]]]]]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>([(0,2),(1,4),(1,5),(1,6),(1,7),(2,3),(3,4),(3,5),(3,6),(3,7)],8)
[[[],[[]]],[[],[],[]]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>([(0,6),(0,7),(1,3),(1,4),(3,6),(3,7),(4,6),(4,7),(5,2),(7,5)],8)
[[[],[[]]],[[],[[]]]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>([(0,6),(0,7),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2),(7,3)],8)
[[[],[[]]],[[[]],[]]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[],[[]]],[[[[]]]]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[]],[]],[[],[],[]]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>([(0,6),(0,7),(1,5),(2,5),(3,4),(5,6),(5,7),(7,3)],8)
[[[[]],[]],[[],[[]]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[[[[]],[]],[[[]],[]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>([(0,7),(1,7),(2,4),(2,5),(2,6),(5,3),(6,3),(7,4),(7,5),(7,6)],8)
[[[[]],[]],[[[],[]]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>([(0,7),(1,7),(2,4),(2,5),(2,6),(6,3),(7,4),(7,5),(7,6)],8)
[[[[]],[]],[[[[]]]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(7,3),(7,4),(7,5),(7,6)],8)
[[[[],[]]],[[],[],[]]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[[[[],[]]],[[[]],[]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[[],[]]],[[[],[]]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[[[[],[]]],[[[[]]]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>([(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[[]]]],[[],[],[]]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[[]]]],[[],[[]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[[[]]]],[[[]],[]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[[[]]]],[[[],[]]]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[[[]]]],[[[[]]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[],[],[],[]],[],[],[]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[[],[],[[]]],[],[],[]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>([(0,7),(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[[],[[]],[]],[],[],[]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>([(0,7),(1,3),(1,4),(3,6),(4,6),(5,2),(6,7),(7,5)],8)
[[[],[[],[]]],[],[],[]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>([(0,7),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[[],[[[]]]],[],[],[]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[[[]],[],[]],[],[],[]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[[[[]],[[]]],[],[],[]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[[[[],[]],[]],[],[],[]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[[[]]],[]],[],[],[]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[[[[],[],[]]],[],[],[]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[],[[]]]],[],[],[]]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>([(0,7),(1,7),(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[[[[[]],[]]],[],[],[]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[[],[]]]],[],[],[]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[[]]]]],[],[],[]]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[],[[],[]]],[],[[]]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>([(0,7),(1,3),(1,6),(2,7),(3,7),(6,2),(7,4),(7,5)],8)
[[[],[[[]]]],[],[[]]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>([(0,7),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[]],[[]]],[],[[]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[[[[],[[]]]],[],[[]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>([(0,7),(1,7),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[],[]]]],[],[[]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>([(0,7),(1,7),(2,7),(3,4),(4,7),(7,5),(7,6)],8)
[[[[[[]]]]],[],[[]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[],[[]],[]],[[]],[]]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>([(0,2),(0,3),(1,5),(1,6),(2,7),(3,7),(5,4),(6,4),(7,5),(7,6)],8)
[[[],[[],[]]],[[]],[]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>([(0,6),(0,7),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(6,5),(7,5)],8)
[[[],[[[]]]],[[]],[]]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[]],[[]]],[[]],[]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[],[]],[]],[[]],[]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>([(0,3),(1,7),(2,5),(2,6),(3,7),(5,4),(6,4),(7,5),(7,6)],8)
[[[[],[[]]]],[[]],[]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[],[]]]],[[]],[]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[[]]]]],[[]],[]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[],[],[],[]],[[[]]]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,4),(2,5),(2,6),(2,7),(3,2),(4,3)],8)
[[[],[],[[]]],[[[]]]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3)],8)
[[[],[[]],[]],[[[]]]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[],[[],[]]],[[[]]]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[[[],[[[]]]],[[],[]]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[2,5,4,3,1,7,8,6]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[[[],[[[]]]],[[[]]]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[]],[],[]],[[[]]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(7,3)],8)
[[[[]],[[]]],[[],[]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[[[[]],[[]]],[[[]]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[],[]],[]],[[],[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>([(0,7),(1,5),(1,6),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[[[[],[]],[]],[[[]]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>([(0,3),(1,7),(2,4),(2,5),(2,6),(3,7),(7,4),(7,5),(7,6)],8)
[[[[[]]],[]],[[[]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5),(7,6)],8)
[[[[],[],[]]],[[[]]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4),(4,5),(4,6),(4,7)],8)
[[[[],[[]]]],[[],[]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[[[[],[[]]]],[[[]]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[[]],[]]],[[[]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,4),(4,5),(4,6),(4,7)],8)
[[[[[],[]]]],[[[]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[[[[]]]]],[[],[]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[[]]]]],[[[]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[],[[],[],[]]],[],[]]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>([(0,7),(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[[[],[[],[[]]]],[],[]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>([(0,7),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(7,5)],8)
[[[[[]]],[[]]],[],[]]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[[],[[]]],[]],[],[]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>([(0,7),(1,6),(2,3),(2,4),(3,7),(4,7),(6,5),(7,6)],8)
[[[[[],[]]],[]],[],[]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>([(0,7),(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[[[[[[]]]],[]],[],[]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[[],[],[],[]]],[],[]]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[],[[[]]]]],[],[]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[3,6,5,4,2,1,7,8]=>([(0,7),(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[]],[[]]]],[],[]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[[[[]]],[]]],[],[]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[[[[[],[],[]]]],[],[]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[[[[]],[]]]],[],[]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[[[[[[],[]]]]],[],[]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[],[],[],[],[]],[[]]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>([(0,6),(0,7),(1,5),(2,6),(2,7),(3,4),(4,2),(5,3)],8)
[[[],[],[[],[]]],[[]]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[2,3,5,6,4,1,8,7]=>([(0,6),(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4)],8)
[[[],[],[[[]]]],[[]]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>([(0,6),(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[[],[[],[]],[]],[[]]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[2,4,5,3,6,1,8,7]=>([(0,6),(0,7),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6),(5,7)],8)
[[[],[[[]]],[]],[[]]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[2,5,4,3,6,1,8,7]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[],[[],[[]]]],[[]]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>([(0,6),(0,7),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[[],[[[],[]]]],[[]]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[[[],[[[[]]]]],[[]]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[]],[[]],[]],[[]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[[[[],[]],[],[]],[[]]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[3,4,2,5,6,1,8,7]=>([(0,7),(1,5),(1,6),(2,3),(3,7),(4,5),(4,6),(7,4)],8)
[[[[],[],[]],[]],[[]]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>([(0,5),(1,6),(1,7),(2,3),(3,4),(4,5),(5,6),(5,7)],8)
[[[[],[[]]],[]],[[]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>([(0,7),(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[]],[]],[]],[[]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>([(0,4),(1,4),(2,7),(3,5),(3,6),(4,7),(7,5),(7,6)],8)
[[[[[],[]]],[]],[[]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>([(0,7),(1,7),(2,5),(2,6),(3,4),(4,7),(7,5),(7,6)],8)
[[[[[[]]]],[]],[[]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[[[[],[],[],[]]],[[]]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[[[[],[[],[]]]],[[]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[[[]]]]],[[]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[]],[[]]]],[[]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[],[]],[]]],[[]]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[[]]],[]]],[[]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>([(0,5),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[],[],[]]]],[[]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[],[[]]]]],[[]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[]],[]]]],[[]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[[[[[],[]]]]],[[]]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[[[[[]]]]]],[[]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[],[],[[[]]]],[]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>([(0,7),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[],[],[[],[],[]]],[]]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>([(0,7),(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[[[],[],[[],[[]]]],[]]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,3),(5,4),(6,2),(6,5)],8)
[[[],[],[[[]],[]]],[]]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[[],[],[[[],[]]]],[]]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[[],[],[[[[]]]]],[]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>([(0,7),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[],[[]],[[]],[]],[]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>([(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[],[[[]]],[],[]],[]]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>([(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[],[[[]],[]],[]],[]]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>([(0,7),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6),(6,7)],8)
[[[],[[],[[],[]]]],[]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>([(0,7),(1,4),(1,6),(2,7),(3,7),(4,7),(5,3),(6,2),(6,5)],8)
[[[],[[[],[],[]]]],[]]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[[[[]],[],[[],[]]],[]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>([(0,7),(1,6),(2,6),(3,5),(4,7),(5,7),(6,3),(6,4)],8)
[[[[]],[[]],[[]]],[]]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,3),(5,4),(6,3),(6,4)],8)
[[[[]],[[[]]],[]],[]]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[[[[]],[[],[[]]]],[]]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[]],[[[],[]]]],[]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[]],[[[[]]]]],[]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>([(0,7),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[[[]]],[],[[]]],[]]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[4,3,2,5,7,6,1,8]=>([(0,7),(1,6),(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[[],[]],[[]],[]],[]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>([(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[],[[]]],[],[]],[]]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>([(0,7),(1,6),(2,3),(2,4),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[[]]]],[],[]],[]]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[[[],[[]]],[[]]],[]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>([(0,5),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[],[]]],[[]]],[]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[[]]]],[[]]],[]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[[[[],[],[],[]],[]],[]]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[[[[],[],[[]]],[]],[]]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>([(0,3),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[],[[]],[]],[]],[]]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>([(0,6),(1,5),(2,3),(2,4),(3,7),(4,7),(5,6),(7,5)],8)
[[[[],[[[]]]],[]],[]]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>([(0,7),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[],[]],[]],[]],[]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[[]]],[]],[]],[]]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>([(0,6),(1,7),(2,7),(3,7),(4,5),(5,6),(7,5)],8)
[[[[[[]],[]]],[]],[]]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>([(0,7),(1,7),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[[[[],[],[[[]]]]],[]]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>([(0,7),(1,7),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[],[[]],[[]]]],[]]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>([(0,7),(1,7),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[],[[],[],[]]]],[]]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>([(0,7),(1,7),(2,4),(2,6),(3,7),(4,7),(5,3),(6,5)],8)
[[[[],[[],[[]]]]],[]]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>([(0,7),(1,7),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[[]],[],[[]]]],[]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[[[[]]],[],[]]],[]]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>([(0,7),(1,7),(2,6),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[],[]],[[]]]],[]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>([(0,7),(1,7),(2,5),(2,6),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[]],[]],[]]],[]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[[[[[[[]]]],[]]],[]]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[[[[[],[],[],[]]]],[]]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[],[],[[]]]]],[]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>([(0,4),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[]],[]]]],[]]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[[],[[],[]]]]],[]]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[[]]]]]],[]]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[[],[]],[]]]],[]]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[[[[[[]]],[]]]],[]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[[[[[],[],[]]]]],[]]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[[[[[],[[]]]]]],[]]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[]],[]]]]],[]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[[],[]]]]]],[]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[[[[[[]]]]]]],[]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[],[],[],[],[],[],[]]]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[[],[],[],[],[],[[]]]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>([(1,6),(4,5),(5,7),(6,4),(7,2),(7,3)],8)
[[[],[],[],[],[[]],[]]]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[2,3,4,5,7,6,8,1]=>([(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[[[],[],[],[],[[[]]]]]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[2,3,4,5,8,7,6,1]=>([(1,6),(5,7),(6,5),(7,2),(7,3),(7,4)],8)
[[[],[],[],[[]],[],[]]]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>([(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[[],[],[],[[]],[[]]]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>([(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3)],8)
[[[],[],[],[[[]]],[]]]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>([(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[],[],[],[[],[],[]]]]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[2,3,4,6,7,8,5,1]=>([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[[[],[],[],[[[[]]]]]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>([(1,6),(6,7),(7,2),(7,3),(7,4),(7,5)],8)
[[[],[],[[]],[],[],[]]]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[2,3,5,4,6,7,8,1]=>([(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[[],[],[[]],[[]],[]]]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7)],8)
[[[],[],[[]],[[[]]]]]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>([(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3)],8)
[[[],[],[[],[]],[],[]]]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[2,3,5,6,4,7,8,1]=>([(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[[[],[],[[[]]],[],[]]]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>([(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[[[],[],[[[[]]]],[]]]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>([(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[],[],[[],[],[],[]]]]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>([(1,7),(4,6),(5,4),(6,2),(7,3),(7,5)],8)
[[[],[],[[],[[],[]]]]]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[2,3,5,7,8,6,4,1]=>([(1,7),(5,4),(6,3),(6,5),(7,2),(7,6)],8)
[[[],[],[[],[[[]]]]]]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>([(1,6),(6,5),(6,7),(7,2),(7,3),(7,4)],8)
[[[],[],[[[[]]],[]]]]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[2,3,7,6,5,8,4,1]=>([(1,6),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[],[],[[[[[]]]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>([(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[[],[[]],[],[],[],[]]]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>([(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[[],[[]],[],[],[[]]]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>([(1,4),(1,5),(4,7),(5,7),(6,2),(6,3),(7,6)],8)
[[[],[[]],[],[[]],[]]]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>([(1,2),(1,3),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[],[[]],[[]],[],[]]]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[[[],[[]],[[]],[[]]]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>([(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[],[[]],[[[]]],[]]]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[],[[]],[[[[]]]]]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>([(1,2),(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[],[[],[]],[],[],[]]]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>([(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[[],[[[]]],[],[],[]]]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>([(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[[],[[[]]],[],[[]]]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>([(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[],[[[]]],[[]],[]]]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>([(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[],[[],[]],[[[]]]]]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>([(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[[[],[[[]]],[[],[]]]]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>([(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[[[],[[[]]],[[[]]]]]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[],[[[[]]]],[],[]]]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[],[[],[[]]],[[]]]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>([(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[[],[[],[],[],[]],[]]]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[2,4,5,6,7,3,8,1]=>([(1,3),(1,6),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[[],[[],[[]],[]],[]]]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>([(1,2),(1,5),(2,7),(3,6),(4,6),(5,3),(5,4),(6,7)],8)
[[[],[[[]],[[]]],[]]]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>([(1,2),(1,3),(1,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[],[[],[[[]]],[]]]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>([(1,2),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[],[[],[[],[[]]]]]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>([(1,5),(1,7),(6,3),(6,4),(7,2),(7,6)],8)
[[[],[[],[[[[]]]]]]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>([(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[[[],[[[]],[[[]]]]]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>([(1,2),(1,3),(1,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[],[[[[]]],[],[]]]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>([(1,2),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[],[[[],[]],[[]]]]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>([(1,2),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3)],8)
[[[],[[[[[]]]],[]]]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[],[[[],[],[],[]]]]]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[[[],[[[[[]],[]]]]]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(5,7),(6,7)],8)
[[[],[[[[[[]]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[[[]],[],[],[],[],[]]]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>([(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[[]],[],[],[[]],[]]]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>([(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(6,3)],8)
[[[[]],[],[[[]]],[]]]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>([(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[]],[],[[[[]]]]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>([(1,7),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[[]],[[]],[],[],[]]]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[3,2,5,4,6,7,8,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[[[[]],[[]],[[]],[]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>([(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[[]],[[[]],[]],[]]]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[[[[]],[[[],[]]],[]]]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[]],[[],[],[],[]]]]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>([(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[[[[]],[[[],[[]]]]]]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[[[[]],[[[[[]]]]]]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[[],[]],[],[],[],[]]]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[]]],[],[],[],[]]]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>([(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[],[]],[],[],[[]]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>([(1,7),(2,5),(5,7),(6,3),(6,4),(7,6)],8)
[[[[[]]],[],[],[[]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>([(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[[[]]],[],[[]],[]]]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[4,3,2,5,7,6,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[[[]]],[],[[[]]]]]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>([(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[[],[]],[[]],[],[]]]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[3,4,2,6,5,7,8,1]=>([(1,6),(1,7),(2,4),(4,6),(4,7),(5,3),(6,5),(7,5)],8)
[[[[[]]],[[]],[],[]]]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[],[]],[[]],[[]]]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>([(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[[]]],[[]],[[]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[],[]],[[[]]],[]]]=>[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[]]],[[],[]],[]]]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[4,3,2,6,7,5,8,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[[[[[]]],[[[]]],[]]]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[],[]],[[[],[]]]]]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>([(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[[[[],[]],[[[[]]]]]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>([(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[[]]],[[],[[]]]]]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[[[]]],[[[],[]]]]]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[[[]]],[[[[]]]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[],[[]]],[],[],[]]]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>([(1,7),(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[[[[[]],[]],[],[],[]]]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[[[]]]],[],[],[]]]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[[]]]],[],[[]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>([(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[]],[]],[[]],[]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[]]]],[[]],[]]]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[]],[]],[[[]]]]]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>([(1,4),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[[],[]]],[[[]]]]]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[[[[]]]],[[],[]]]]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[[]]]],[[[]]]]]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[],[],[],[]],[],[]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>([(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[],[[[]]]],[],[]]]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>([(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[[]]],[]],[],[]]]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>([(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[[[[]],[]]],[],[]]]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>([(1,7),(2,7),(3,6),(4,6),(6,7),(7,5)],8)
[[[[[[[]]]]],[],[]]]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[[],[[],[]]],[[]]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>([(1,6),(1,7),(2,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[[[]]]],[[]]]]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[]],[[]]],[[]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>([(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[]]],[]],[[]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>([(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[[[[[],[],[]]],[[]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[],[[]]]],[[]]]]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[]],[]]],[[]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[[[[[[]]]]],[[]]]]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[],[[[]]]],[]]]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>([(1,7),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[],[[]],[],[]],[]]]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[3,5,4,6,7,2,8,1]=>([(1,6),(2,3),(2,4),(3,7),(4,7),(5,6),(7,5)],8)
[[[[],[[],[]],[]],[]]]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>([(1,6),(2,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[[[[],[[[]]],[]],[]]]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>([(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[],[[],[],[]]],[]]]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>([(1,7),(2,4),(2,6),(3,7),(4,7),(5,3),(6,5)],8)
[[[[],[[],[[]]]],[]]]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>([(1,7),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[[]],[[]],[]],[]]]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[]],[[],[]]],[]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>([(1,7),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[[[[]],[[[]]]],[]]]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>([(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[[]]],[],[]],[]]]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>([(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[[[[[]]],[[]]],[]]]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>([(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[],[],[]],[]],[]]]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>([(1,7),(2,6),(3,4),(4,5),(5,6),(6,7)],8)
[[[[[],[[]]],[]],[]]]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>([(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[[]],[]],[]],[]]]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[[[[[[]]]],[]],[]]]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[[[],[],[],[]]],[]]]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[],[[]],[]]],[]]]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>([(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[[],[[[]]]]],[]]]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>([(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[],[],[[]],[],[]]]]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>([(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[[[[],[],[[[]]],[]]]]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>([(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[],[],[[[[]]]]]]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>([(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[[],[[],[],[],[]]]]]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>([(2,4),(2,7),(5,6),(6,3),(7,5)],8)
[[[[],[[],[[],[]]]]]]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>([(2,5),(2,7),(6,4),(7,3),(7,6)],8)
[[[[],[[],[[[]]]]]]]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>([(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[[[[],[[[[]]],[]]]]]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>([(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[[[],[[[[[]]]]]]]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>([(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[[[]],[],[],[[]]]]]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>([(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[[[]],[],[[]],[]]]]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>([(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[[[]],[],[[],[]]]]]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>([(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[[[[[]],[[]],[[]]]]]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[]],[[],[],[]]]]]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>([(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[[],[]],[],[[]]]]]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>([(2,7),(3,4),(4,7),(7,5),(7,6)],8)
[[[[[[]]],[],[[]]]]]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>([(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[],[]],[[]],[]]]]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>([(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[],[]],[[],[]]]]]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>([(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[[[[[[]]],[[],[]]]]]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[[[]]]],[],[]]]]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>([(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[],[],[]],[[]]]]]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>([(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[],[],[],[]],[]]]]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[],[[[]]]],[]]]]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[4,7,6,5,3,8,2,1]=>([(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[[]],[],[]],[]]]]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>([(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[[],[[]]]],[]]]]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[[]]]]],[]]]]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[[[],[],[],[],[]]]]]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>([(3,4),(4,7),(6,5),(7,6)],8)
[[[[[],[],[],[[]]]]]]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>([(3,4),(4,7),(7,5),(7,6)],8)
[[[[[],[],[[]],[]]]]]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>([(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[],[],[[],[]]]]]]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>([(3,4),(4,6),(4,7),(7,5)],8)
[[[[[],[],[[[]]]]]]]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>([(3,4),(4,5),(4,6),(4,7)],8)
[[[[[],[[]],[],[]]]]]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>([(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[],[[]],[[]]]]]]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>([(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[],[[],[]],[]]]]]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>([(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[[]]],[]]]]]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>([(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[],[[],[],[]]]]]]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>([(3,4),(3,5),(5,6),(6,7)],8)
[[[[[],[[],[[]]]]]]]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>([(3,4),(3,5),(5,6),(5,7)],8)
[[[[[],[[[]],[]]]]]]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>([(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[[[[[],[[[],[]]]]]]]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>([(3,4),(3,5),(3,6),(6,7)],8)
[[[[[],[[[[]]]]]]]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>([(3,4),(3,5),(3,6),(3,7)],8)
[[[[[[]],[],[],[]]]]]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>([(3,7),(4,7),(5,6),(7,5)],8)
[[[[[[]],[[]],[]]]]]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>([(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[],[]],[],[]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>([(3,7),(4,5),(5,7),(7,6)],8)
[[[[[[[]]],[],[]]]]]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>([(3,7),(4,7),(5,7),(7,6)],8)
[[[[[[],[],[]],[]]]]]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>([(3,7),(4,5),(5,6),(6,7)],8)
[[[[[[],[[]]],[]]]]]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>([(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[]],[]],[]]]]]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>([(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[[],[]]],[]]]]]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>([(3,7),(4,7),(5,6),(6,7)],8)
[[[[[[[[]]]],[]]]]]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>([(3,7),(4,7),(5,7),(6,7)],8)
[[[[[[],[],[],[]]]]]]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>([(4,5),(5,7),(7,6)],8)
[[[[[[],[],[[]]]]]]]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>([(4,5),(5,6),(5,7)],8)
[[[[[[],[[]],[]]]]]]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>([(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[],[[],[]]]]]]]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>([(4,5),(4,6),(6,7)],8)
[[[[[[],[[[]]]]]]]]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>([(4,5),(4,6),(4,7)],8)
[[[[[[[]],[],[]]]]]]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>([(4,7),(5,7),(7,6)],8)
[[[[[[[]],[[]]]]]]]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>([(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[[],[]],[]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>([(4,7),(5,6),(6,7)],8)
[[[[[[[[]]],[]]]]]]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>([(4,7),(5,7),(6,7)],8)
[[[[[[[],[],[]]]]]]]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>([(5,6),(6,7)],8)
[[[[[[[],[[]]]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>([(5,6),(5,7)],8)
[[[[[[[[]],[]]]]]]]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>([(5,7),(6,7)],8)
[[[[[[[[],[]]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>([(6,7)],8)
[[[[[[[[[]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>([],8)
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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