Identifier
Mp00161:
Signed permutations
—reverse⟶
Signed permutations
Mp00245: Signed permutations —standardize⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00245: Signed permutations —standardize⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0010;cc-rep-3
[1]=>[1]=>[1]=>[.,.]
[-1]=>[-1]=>[1]=>[.,.]
[1,2]=>[2,1]=>[2,1]=>[[.,.],.]
[1,-2]=>[-2,1]=>[2,1]=>[[.,.],.]
[-1,2]=>[2,-1]=>[1,2]=>[.,[.,.]]
[-1,-2]=>[-2,-1]=>[1,2]=>[.,[.,.]]
[2,1]=>[1,2]=>[1,2]=>[.,[.,.]]
[2,-1]=>[-1,2]=>[2,1]=>[[.,.],.]
[-2,1]=>[1,-2]=>[1,2]=>[.,[.,.]]
[-2,-1]=>[-1,-2]=>[2,1]=>[[.,.],.]
[1,2,3]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[1,2,-3]=>[-3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[1,-2,3]=>[3,-2,1]=>[2,3,1]=>[[.,[.,.]],.]
[1,-2,-3]=>[-3,-2,1]=>[2,3,1]=>[[.,[.,.]],.]
[-1,2,3]=>[3,2,-1]=>[2,1,3]=>[[.,.],[.,.]]
[-1,2,-3]=>[-3,2,-1]=>[2,1,3]=>[[.,.],[.,.]]
[-1,-2,3]=>[3,-2,-1]=>[1,2,3]=>[.,[.,[.,.]]]
[-1,-2,-3]=>[-3,-2,-1]=>[1,2,3]=>[.,[.,[.,.]]]
[1,3,2]=>[2,3,1]=>[2,3,1]=>[[.,[.,.]],.]
[1,3,-2]=>[-2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,-3,2]=>[2,-3,1]=>[2,3,1]=>[[.,[.,.]],.]
[1,-3,-2]=>[-2,-3,1]=>[3,2,1]=>[[[.,.],.],.]
[-1,3,2]=>[2,3,-1]=>[1,2,3]=>[.,[.,[.,.]]]
[-1,3,-2]=>[-2,3,-1]=>[2,1,3]=>[[.,.],[.,.]]
[-1,-3,2]=>[2,-3,-1]=>[1,2,3]=>[.,[.,[.,.]]]
[-1,-3,-2]=>[-2,-3,-1]=>[2,1,3]=>[[.,.],[.,.]]
[2,1,3]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[2,1,-3]=>[-3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[2,-1,3]=>[3,-1,2]=>[2,3,1]=>[[.,[.,.]],.]
[2,-1,-3]=>[-3,-1,2]=>[2,3,1]=>[[.,[.,.]],.]
[-2,1,3]=>[3,1,-2]=>[2,1,3]=>[[.,.],[.,.]]
[-2,1,-3]=>[-3,1,-2]=>[2,1,3]=>[[.,.],[.,.]]
[-2,-1,3]=>[3,-1,-2]=>[1,3,2]=>[.,[[.,.],.]]
[-2,-1,-3]=>[-3,-1,-2]=>[1,3,2]=>[.,[[.,.],.]]
[2,3,1]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[2,3,-1]=>[-1,3,2]=>[3,2,1]=>[[[.,.],.],.]
[2,-3,1]=>[1,-3,2]=>[1,3,2]=>[.,[[.,.],.]]
[2,-3,-1]=>[-1,-3,2]=>[3,2,1]=>[[[.,.],.],.]
[-2,3,1]=>[1,3,-2]=>[1,2,3]=>[.,[.,[.,.]]]
[-2,3,-1]=>[-1,3,-2]=>[3,1,2]=>[[.,.],[.,.]]
[-2,-3,1]=>[1,-3,-2]=>[1,2,3]=>[.,[.,[.,.]]]
[-2,-3,-1]=>[-1,-3,-2]=>[3,1,2]=>[[.,.],[.,.]]
[3,1,2]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[3,1,-2]=>[-2,1,3]=>[3,1,2]=>[[.,.],[.,.]]
[3,-1,2]=>[2,-1,3]=>[1,3,2]=>[.,[[.,.],.]]
[3,-1,-2]=>[-2,-1,3]=>[2,3,1]=>[[.,[.,.]],.]
[-3,1,2]=>[2,1,-3]=>[2,1,3]=>[[.,.],[.,.]]
[-3,1,-2]=>[-2,1,-3]=>[3,1,2]=>[[.,.],[.,.]]
[-3,-1,2]=>[2,-1,-3]=>[1,3,2]=>[.,[[.,.],.]]
[-3,-1,-2]=>[-2,-1,-3]=>[2,3,1]=>[[.,[.,.]],.]
[3,2,1]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[3,2,-1]=>[-1,2,3]=>[3,1,2]=>[[.,.],[.,.]]
[3,-2,1]=>[1,-2,3]=>[1,3,2]=>[.,[[.,.],.]]
[3,-2,-1]=>[-1,-2,3]=>[3,2,1]=>[[[.,.],.],.]
[-3,2,1]=>[1,2,-3]=>[1,2,3]=>[.,[.,[.,.]]]
[-3,2,-1]=>[-1,2,-3]=>[3,1,2]=>[[.,.],[.,.]]
[-3,-2,1]=>[1,-2,-3]=>[1,3,2]=>[.,[[.,.],.]]
[-3,-2,-1]=>[-1,-2,-3]=>[3,2,1]=>[[[.,.],.],.]
[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,2,3,-4]=>[-4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,2,-3,4]=>[4,-3,2,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,2,-3,-4]=>[-4,-3,2,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,-2,3,4]=>[4,3,-2,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,-2,3,-4]=>[-4,3,-2,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,-2,-3,4]=>[4,-3,-2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,-2,-3,-4]=>[-4,-3,-2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[-1,2,3,4]=>[4,3,2,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-1,2,3,-4]=>[-4,3,2,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-1,2,-3,4]=>[4,-3,2,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-1,2,-3,-4]=>[-4,-3,2,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-1,-2,3,4]=>[4,3,-2,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-1,-2,3,-4]=>[-4,3,-2,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-1,-2,-3,4]=>[4,-3,-2,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[-1,-2,-3,-4]=>[-4,-3,-2,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,2,4,3]=>[3,4,2,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,2,4,-3]=>[-3,4,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,2,-4,3]=>[3,-4,2,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,2,-4,-3]=>[-3,-4,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,-2,4,3]=>[3,4,-2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,-2,4,-3]=>[-3,4,-2,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,-2,-4,3]=>[3,-4,-2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,-2,-4,-3]=>[-3,-4,-2,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[-1,2,4,3]=>[3,4,2,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-1,2,4,-3]=>[-3,4,2,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-1,2,-4,3]=>[3,-4,2,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-1,2,-4,-3]=>[-3,-4,2,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-1,-2,4,3]=>[3,4,-2,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[-1,-2,4,-3]=>[-3,4,-2,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-1,-2,-4,3]=>[3,-4,-2,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[-1,-2,-4,-3]=>[-3,-4,-2,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,3,2,4]=>[4,2,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,3,2,-4]=>[-4,2,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,3,-2,4]=>[4,-2,3,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,3,-2,-4]=>[-4,-2,3,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,-3,2,4]=>[4,2,-3,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,-3,2,-4]=>[-4,2,-3,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,-3,-2,4]=>[4,-2,-3,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,-3,-2,-4]=>[-4,-2,-3,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[-1,3,2,4]=>[4,2,3,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-1,3,2,-4]=>[-4,2,3,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-1,3,-2,4]=>[4,-2,3,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-1,3,-2,-4]=>[-4,-2,3,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-1,-3,2,4]=>[4,2,-3,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-1,-3,2,-4]=>[-4,2,-3,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-1,-3,-2,4]=>[4,-2,-3,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[-1,-3,-2,-4]=>[-4,-2,-3,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,3,4,2]=>[2,4,3,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,3,4,-2]=>[-2,4,3,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,3,-4,2]=>[2,-4,3,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,3,-4,-2]=>[-2,-4,3,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,-3,4,2]=>[2,4,-3,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,-3,4,-2]=>[-2,4,-3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,-3,-4,2]=>[2,-4,-3,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,-3,-4,-2]=>[-2,-4,-3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[-1,3,4,2]=>[2,4,3,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[-1,3,4,-2]=>[-2,4,3,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-1,3,-4,2]=>[2,-4,3,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[-1,3,-4,-2]=>[-2,-4,3,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-1,-3,4,2]=>[2,4,-3,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[-1,-3,4,-2]=>[-2,4,-3,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-1,-3,-4,2]=>[2,-4,-3,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[-1,-3,-4,-2]=>[-2,-4,-3,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,4,2,3]=>[3,2,4,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,4,2,-3]=>[-3,2,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,4,-2,3]=>[3,-2,4,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,4,-2,-3]=>[-3,-2,4,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,-4,2,3]=>[3,2,-4,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,-4,2,-3]=>[-3,2,-4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,-4,-2,3]=>[3,-2,-4,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,-4,-2,-3]=>[-3,-2,-4,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[-1,4,2,3]=>[3,2,4,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-1,4,2,-3]=>[-3,2,4,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-1,4,-2,3]=>[3,-2,4,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[-1,4,-2,-3]=>[-3,-2,4,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-1,-4,2,3]=>[3,2,-4,-1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-1,-4,2,-3]=>[-3,2,-4,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-1,-4,-2,3]=>[3,-2,-4,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[-1,-4,-2,-3]=>[-3,-2,-4,-1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,4,3,2]=>[2,3,4,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,4,3,-2]=>[-2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,4,-3,2]=>[2,-3,4,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,4,-3,-2]=>[-2,-3,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,-4,3,2]=>[2,3,-4,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,-4,3,-2]=>[-2,3,-4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,-4,-3,2]=>[2,-3,-4,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,-4,-3,-2]=>[-2,-3,-4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[-1,4,3,2]=>[2,3,4,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[-1,4,3,-2]=>[-2,3,4,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-1,4,-3,2]=>[2,-3,4,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[-1,4,-3,-2]=>[-2,-3,4,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-1,-4,3,2]=>[2,3,-4,-1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[-1,-4,3,-2]=>[-2,3,-4,-1]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-1,-4,-3,2]=>[2,-3,-4,-1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[-1,-4,-3,-2]=>[-2,-3,-4,-1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[2,1,3,4]=>[4,3,1,2]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[2,1,3,-4]=>[-4,3,1,2]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[2,1,-3,4]=>[4,-3,1,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[2,1,-3,-4]=>[-4,-3,1,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[2,-1,3,4]=>[4,3,-1,2]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[2,-1,3,-4]=>[-4,3,-1,2]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[2,-1,-3,4]=>[4,-3,-1,2]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[2,-1,-3,-4]=>[-4,-3,-1,2]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[-2,1,3,4]=>[4,3,1,-2]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-2,1,3,-4]=>[-4,3,1,-2]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-2,1,-3,4]=>[4,-3,1,-2]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-2,1,-3,-4]=>[-4,-3,1,-2]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-2,-1,3,4]=>[4,3,-1,-2]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[-2,-1,3,-4]=>[-4,3,-1,-2]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[-2,-1,-3,4]=>[4,-3,-1,-2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[-2,-1,-3,-4]=>[-4,-3,-1,-2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[2,1,4,3]=>[3,4,1,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[2,1,4,-3]=>[-3,4,1,2]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[2,1,-4,3]=>[3,-4,1,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[2,1,-4,-3]=>[-3,-4,1,2]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[2,-1,4,3]=>[3,4,-1,2]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[2,-1,4,-3]=>[-3,4,-1,2]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[2,-1,-4,3]=>[3,-4,-1,2]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[2,-1,-4,-3]=>[-3,-4,-1,2]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[-2,1,4,3]=>[3,4,1,-2]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-2,1,4,-3]=>[-3,4,1,-2]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-2,1,-4,3]=>[3,-4,1,-2]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[-2,1,-4,-3]=>[-3,-4,1,-2]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[-2,-1,4,3]=>[3,4,-1,-2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[-2,-1,4,-3]=>[-3,4,-1,-2]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[-2,-1,-4,3]=>[3,-4,-1,-2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[-2,-1,-4,-3]=>[-3,-4,-1,-2]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[2,3,1,4]=>[4,1,3,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[2,3,1,-4]=>[-4,1,3,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[2,3,-1,4]=>[4,-1,3,2]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[2,3,-1,-4]=>[-4,-1,3,2]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[2,-3,1,4]=>[4,1,-3,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[2,-3,1,-4]=>[-4,1,-3,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[2,-3,-1,4]=>[4,-1,-3,2]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[2,-3,-1,-4]=>[-4,-1,-3,2]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[-2,3,1,4]=>[4,1,3,-2]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-2,3,1,-4]=>[-4,1,3,-2]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[-2,3,-1,4]=>[4,-1,3,-2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[-2,3,-1,-4]=>[-4,-1,3,-2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[-2,-3,1,4]=>[4,1,-3,-2]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-2,-3,1,-4]=>[-4,1,-3,-2]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[-2,-3,-1,4]=>[4,-1,-3,-2]=>[1,4,2,3]=>[.,[[.,.],[.,.]]]
[-2,-3,-1,-4]=>[-4,-1,-3,-2]=>[1,4,2,3]=>[.,[[.,.],[.,.]]]
[2,3,4,1]=>[1,4,3,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[2,3,4,-1]=>[-1,4,3,2]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[2,3,-4,1]=>[1,-4,3,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[2,3,-4,-1]=>[-1,-4,3,2]=>[4,3,2,1]=>[[[[.,.],.],.],.]
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[4,-2,3,-1]=>[-1,3,-2,4]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[4,-2,-3,1]=>[1,-3,-2,4]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
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[4,3,1,2]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
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[4,-3,1,2]=>[2,1,-3,4]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
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[1,-2,-3,-4,5]=>[5,-4,-3,-2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
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[-1,2,-3,-4,5]=>[5,-4,-3,2,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
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[-1,-2,3,-4,5]=>[5,-4,3,-2,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
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[-1,-2,-3,4,5]=>[5,4,-3,-2,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
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[-1,-2,-3,-4,5]=>[5,-4,-3,-2,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[1,2,3,-5,4]=>[4,-5,3,2,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
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[1,2,-3,5,4]=>[4,5,-3,2,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
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[1,2,-3,-5,4]=>[4,-5,-3,2,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,2,-3,-5,-4]=>[-4,-5,-3,2,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,-2,3,5,4]=>[4,5,3,-2,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
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[1,-2,3,-5,4]=>[4,-5,3,-2,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-2,3,-5,-4]=>[-4,-5,3,-2,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-2,-3,5,4]=>[4,5,-3,-2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
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[1,-2,-3,-5,4]=>[4,-5,-3,-2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
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[-1,-2,-3,5,4]=>[4,5,-3,-2,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[-1,-2,-3,-5,4]=>[4,-5,-3,-2,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[1,2,4,-3,5]=>[5,-3,4,2,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,2,4,-3,-5]=>[-5,-3,4,2,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,2,-4,3,5]=>[5,3,-4,2,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
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[1,-2,-4,-3,5]=>[5,-3,-4,-2,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
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[-1,-2,-4,5,3]=>[3,5,-4,-2,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-2,-4,5,-3]=>[-3,5,-4,-2,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-2,-4,-5,3]=>[3,-5,-4,-2,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-2,-4,-5,-3]=>[-3,-5,-4,-2,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,2,5,3,4]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,2,5,3,-4]=>[-4,3,5,2,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,2,5,-3,4]=>[4,-3,5,2,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,2,5,-3,-4]=>[-4,-3,5,2,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,2,-5,3,4]=>[4,3,-5,2,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,2,-5,3,-4]=>[-4,3,-5,2,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,2,-5,-3,4]=>[4,-3,-5,2,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,2,-5,-3,-4]=>[-4,-3,-5,2,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,-2,5,3,4]=>[4,3,5,-2,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-2,5,3,-4]=>[-4,3,5,-2,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-2,5,-3,4]=>[4,-3,5,-2,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-2,5,-3,-4]=>[-4,-3,5,-2,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-2,-5,3,4]=>[4,3,-5,-2,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-2,-5,3,-4]=>[-4,3,-5,-2,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-2,-5,-3,4]=>[4,-3,-5,-2,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-2,-5,-3,-4]=>[-4,-3,-5,-2,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[-1,2,5,3,4]=>[4,3,5,2,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,2,5,3,-4]=>[-4,3,5,2,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,2,5,-3,4]=>[4,-3,5,2,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,2,5,-3,-4]=>[-4,-3,5,2,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,2,-5,3,4]=>[4,3,-5,2,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,2,-5,3,-4]=>[-4,3,-5,2,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,2,-5,-3,4]=>[4,-3,-5,2,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,2,-5,-3,-4]=>[-4,-3,-5,2,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,-2,5,3,4]=>[4,3,5,-2,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-2,5,3,-4]=>[-4,3,5,-2,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-2,5,-3,4]=>[4,-3,5,-2,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-2,5,-3,-4]=>[-4,-3,5,-2,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-2,-5,3,4]=>[4,3,-5,-2,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-2,-5,3,-4]=>[-4,3,-5,-2,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-2,-5,-3,4]=>[4,-3,-5,-2,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-2,-5,-3,-4]=>[-4,-3,-5,-2,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,2,5,4,3]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,2,5,4,-3]=>[-3,4,5,2,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,2,5,-4,3]=>[3,-4,5,2,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,2,5,-4,-3]=>[-3,-4,5,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,2,-5,4,3]=>[3,4,-5,2,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,2,-5,4,-3]=>[-3,4,-5,2,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,2,-5,-4,3]=>[3,-4,-5,2,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,2,-5,-4,-3]=>[-3,-4,-5,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,-2,5,4,3]=>[3,4,5,-2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-2,5,4,-3]=>[-3,4,5,-2,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-2,5,-4,3]=>[3,-4,5,-2,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-2,5,-4,-3]=>[-3,-4,5,-2,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-2,-5,4,3]=>[3,4,-5,-2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-2,-5,4,-3]=>[-3,4,-5,-2,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-2,-5,-4,3]=>[3,-4,-5,-2,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-2,-5,-4,-3]=>[-3,-4,-5,-2,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[-1,2,5,4,3]=>[3,4,5,2,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,2,5,4,-3]=>[-3,4,5,2,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,2,5,-4,3]=>[3,-4,5,2,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,2,5,-4,-3]=>[-3,-4,5,2,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,2,-5,4,3]=>[3,4,-5,2,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,2,-5,4,-3]=>[-3,4,-5,2,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,2,-5,-4,3]=>[3,-4,-5,2,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,2,-5,-4,-3]=>[-3,-4,-5,2,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,-2,5,4,3]=>[3,4,5,-2,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-2,5,4,-3]=>[-3,4,5,-2,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-2,5,-4,3]=>[3,-4,5,-2,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-2,5,-4,-3]=>[-3,-4,5,-2,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-2,-5,4,3]=>[3,4,-5,-2,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-2,-5,4,-3]=>[-3,4,-5,-2,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-2,-5,-4,3]=>[3,-4,-5,-2,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-2,-5,-4,-3]=>[-3,-4,-5,-2,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,3,2,4,5]=>[5,4,2,3,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,3,2,4,-5]=>[-5,4,2,3,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,3,2,-4,5]=>[5,-4,2,3,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,3,2,-4,-5]=>[-5,-4,2,3,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,3,-2,4,5]=>[5,4,-2,3,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,3,-2,4,-5]=>[-5,4,-2,3,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,3,-2,-4,5]=>[5,-4,-2,3,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,3,-2,-4,-5]=>[-5,-4,-2,3,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,-3,2,4,5]=>[5,4,2,-3,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-3,2,4,-5]=>[-5,4,2,-3,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-3,2,-4,5]=>[5,-4,2,-3,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-3,2,-4,-5]=>[-5,-4,2,-3,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-3,-2,4,5]=>[5,4,-2,-3,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-3,-2,4,-5]=>[-5,4,-2,-3,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-3,-2,-4,5]=>[5,-4,-2,-3,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-3,-2,-4,-5]=>[-5,-4,-2,-3,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[-1,3,2,4,5]=>[5,4,2,3,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,3,2,4,-5]=>[-5,4,2,3,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,3,2,-4,5]=>[5,-4,2,3,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,3,2,-4,-5]=>[-5,-4,2,3,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,3,-2,4,5]=>[5,4,-2,3,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,3,-2,4,-5]=>[-5,4,-2,3,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,3,-2,-4,5]=>[5,-4,-2,3,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,3,-2,-4,-5]=>[-5,-4,-2,3,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,-3,2,4,5]=>[5,4,2,-3,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-3,2,4,-5]=>[-5,4,2,-3,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-3,2,-4,5]=>[5,-4,2,-3,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-3,2,-4,-5]=>[-5,-4,2,-3,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-3,-2,4,5]=>[5,4,-2,-3,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-3,-2,4,-5]=>[-5,4,-2,-3,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-3,-2,-4,5]=>[5,-4,-2,-3,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-3,-2,-4,-5]=>[-5,-4,-2,-3,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,3,2,5,4]=>[4,5,2,3,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,3,2,5,-4]=>[-4,5,2,3,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,3,2,-5,4]=>[4,-5,2,3,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,3,2,-5,-4]=>[-4,-5,2,3,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,3,-2,5,4]=>[4,5,-2,3,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,3,-2,5,-4]=>[-4,5,-2,3,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,3,-2,-5,4]=>[4,-5,-2,3,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,3,-2,-5,-4]=>[-4,-5,-2,3,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,-3,2,5,4]=>[4,5,2,-3,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-3,2,5,-4]=>[-4,5,2,-3,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-3,2,-5,4]=>[4,-5,2,-3,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-3,2,-5,-4]=>[-4,-5,2,-3,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-3,-2,5,4]=>[4,5,-2,-3,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-3,-2,5,-4]=>[-4,5,-2,-3,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-3,-2,-5,4]=>[4,-5,-2,-3,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-3,-2,-5,-4]=>[-4,-5,-2,-3,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[-1,3,2,5,4]=>[4,5,2,3,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,3,2,5,-4]=>[-4,5,2,3,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,3,2,-5,4]=>[4,-5,2,3,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,3,2,-5,-4]=>[-4,-5,2,3,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,3,-2,5,4]=>[4,5,-2,3,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,3,-2,5,-4]=>[-4,5,-2,3,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,3,-2,-5,4]=>[4,-5,-2,3,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,3,-2,-5,-4]=>[-4,-5,-2,3,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,-3,2,5,4]=>[4,5,2,-3,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-3,2,5,-4]=>[-4,5,2,-3,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-3,2,-5,4]=>[4,-5,2,-3,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-3,2,-5,-4]=>[-4,-5,2,-3,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-3,-2,5,4]=>[4,5,-2,-3,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-3,-2,5,-4]=>[-4,5,-2,-3,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-3,-2,-5,4]=>[4,-5,-2,-3,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-3,-2,-5,-4]=>[-4,-5,-2,-3,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,3,4,2,5]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,4,2,-5]=>[-5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,4,-2,5]=>[5,-2,4,3,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,3,4,-2,-5]=>[-5,-2,4,3,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,3,-4,2,5]=>[5,2,-4,3,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,-4,2,-5]=>[-5,2,-4,3,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,-4,-2,5]=>[5,-2,-4,3,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,3,-4,-2,-5]=>[-5,-2,-4,3,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,-3,4,2,5]=>[5,2,4,-3,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,4,2,-5]=>[-5,2,4,-3,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,4,-2,5]=>[5,-2,4,-3,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-3,4,-2,-5]=>[-5,-2,4,-3,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-3,-4,2,5]=>[5,2,-4,-3,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,-4,2,-5]=>[-5,2,-4,-3,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,-4,-2,5]=>[5,-2,-4,-3,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-3,-4,-2,-5]=>[-5,-2,-4,-3,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[-1,3,4,2,5]=>[5,2,4,3,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,4,2,-5]=>[-5,2,4,3,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,4,-2,5]=>[5,-2,4,3,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,3,4,-2,-5]=>[-5,-2,4,3,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,3,-4,2,5]=>[5,2,-4,3,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,-4,2,-5]=>[-5,2,-4,3,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,-4,-2,5]=>[5,-2,-4,3,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,3,-4,-2,-5]=>[-5,-2,-4,3,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,-3,4,2,5]=>[5,2,4,-3,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,4,2,-5]=>[-5,2,4,-3,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,4,-2,5]=>[5,-2,4,-3,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-3,4,-2,-5]=>[-5,-2,4,-3,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-3,-4,2,5]=>[5,2,-4,-3,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,-4,2,-5]=>[-5,2,-4,-3,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,-4,-2,5]=>[5,-2,-4,-3,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-3,-4,-2,-5]=>[-5,-2,-4,-3,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[1,3,4,5,2]=>[2,5,4,3,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,3,4,5,-2]=>[-2,5,4,3,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,3,4,-5,2]=>[2,-5,4,3,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,3,4,-5,-2]=>[-2,-5,4,3,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,3,-4,5,2]=>[2,5,-4,3,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,3,-4,5,-2]=>[-2,5,-4,3,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,3,-4,-5,2]=>[2,-5,-4,3,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,3,-4,-5,-2]=>[-2,-5,-4,3,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,-3,4,5,2]=>[2,5,4,-3,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-3,4,5,-2]=>[-2,5,4,-3,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-3,4,-5,2]=>[2,-5,4,-3,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-3,4,-5,-2]=>[-2,-5,4,-3,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-3,-4,5,2]=>[2,5,-4,-3,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-3,-4,5,-2]=>[-2,5,-4,-3,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,-4,-5,2]=>[2,-5,-4,-3,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-3,-4,-5,-2]=>[-2,-5,-4,-3,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[-1,3,4,5,2]=>[2,5,4,3,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,3,4,5,-2]=>[-2,5,4,3,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,3,4,-5,2]=>[2,-5,4,3,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,3,4,-5,-2]=>[-2,-5,4,3,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,3,-4,5,2]=>[2,5,-4,3,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,3,-4,5,-2]=>[-2,5,-4,3,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,3,-4,-5,2]=>[2,-5,-4,3,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,3,-4,-5,-2]=>[-2,-5,-4,3,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,-3,4,5,2]=>[2,5,4,-3,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-3,4,5,-2]=>[-2,5,4,-3,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-3,4,-5,2]=>[2,-5,4,-3,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-3,4,-5,-2]=>[-2,-5,4,-3,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-3,-4,5,2]=>[2,5,-4,-3,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-3,-4,5,-2]=>[-2,5,-4,-3,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,-4,-5,2]=>[2,-5,-4,-3,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-3,-4,-5,-2]=>[-2,-5,-4,-3,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,3,5,2,4]=>[4,2,5,3,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,5,2,-4]=>[-4,2,5,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,5,-2,4]=>[4,-2,5,3,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,3,5,-2,-4]=>[-4,-2,5,3,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,3,-5,2,4]=>[4,2,-5,3,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,-5,2,-4]=>[-4,2,-5,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,3,-5,-2,4]=>[4,-2,-5,3,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,3,-5,-2,-4]=>[-4,-2,-5,3,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,-3,5,2,4]=>[4,2,5,-3,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,5,2,-4]=>[-4,2,5,-3,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,5,-2,4]=>[4,-2,5,-3,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-3,5,-2,-4]=>[-4,-2,5,-3,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-3,-5,2,4]=>[4,2,-5,-3,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,-5,2,-4]=>[-4,2,-5,-3,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,-5,-2,4]=>[4,-2,-5,-3,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-3,-5,-2,-4]=>[-4,-2,-5,-3,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[-1,3,5,2,4]=>[4,2,5,3,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,5,2,-4]=>[-4,2,5,3,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,5,-2,4]=>[4,-2,5,3,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,3,5,-2,-4]=>[-4,-2,5,3,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,3,-5,2,4]=>[4,2,-5,3,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,-5,2,-4]=>[-4,2,-5,3,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,3,-5,-2,4]=>[4,-2,-5,3,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,3,-5,-2,-4]=>[-4,-2,-5,3,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,-3,5,2,4]=>[4,2,5,-3,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,5,2,-4]=>[-4,2,5,-3,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,5,-2,4]=>[4,-2,5,-3,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-3,5,-2,-4]=>[-4,-2,5,-3,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-3,-5,2,4]=>[4,2,-5,-3,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,-5,2,-4]=>[-4,2,-5,-3,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,-5,-2,4]=>[4,-2,-5,-3,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-3,-5,-2,-4]=>[-4,-2,-5,-3,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[1,3,5,4,2]=>[2,4,5,3,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,3,5,4,-2]=>[-2,4,5,3,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,3,5,-4,2]=>[2,-4,5,3,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,3,5,-4,-2]=>[-2,-4,5,3,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,3,-5,4,2]=>[2,4,-5,3,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,3,-5,4,-2]=>[-2,4,-5,3,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,3,-5,-4,2]=>[2,-4,-5,3,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,3,-5,-4,-2]=>[-2,-4,-5,3,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,-3,5,4,2]=>[2,4,5,-3,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-3,5,4,-2]=>[-2,4,5,-3,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,5,-4,2]=>[2,-4,5,-3,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-3,5,-4,-2]=>[-2,-4,5,-3,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-3,-5,4,2]=>[2,4,-5,-3,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-3,-5,4,-2]=>[-2,4,-5,-3,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-3,-5,-4,2]=>[2,-4,-5,-3,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-3,-5,-4,-2]=>[-2,-4,-5,-3,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[-1,3,5,4,2]=>[2,4,5,3,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,3,5,4,-2]=>[-2,4,5,3,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,3,5,-4,2]=>[2,-4,5,3,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,3,5,-4,-2]=>[-2,-4,5,3,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,3,-5,4,2]=>[2,4,-5,3,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,3,-5,4,-2]=>[-2,4,-5,3,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,3,-5,-4,2]=>[2,-4,-5,3,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,3,-5,-4,-2]=>[-2,-4,-5,3,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,-3,5,4,2]=>[2,4,5,-3,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-3,5,4,-2]=>[-2,4,5,-3,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,5,-4,2]=>[2,-4,5,-3,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-3,5,-4,-2]=>[-2,-4,5,-3,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-3,-5,4,2]=>[2,4,-5,-3,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-3,-5,4,-2]=>[-2,4,-5,-3,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-3,-5,-4,2]=>[2,-4,-5,-3,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-3,-5,-4,-2]=>[-2,-4,-5,-3,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[1,4,2,3,5]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,4,2,3,-5]=>[-5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,4,2,-3,5]=>[5,-3,2,4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,4,2,-3,-5]=>[-5,-3,2,4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,4,-2,3,5]=>[5,3,-2,4,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,-2,3,-5]=>[-5,3,-2,4,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,-2,-3,5]=>[5,-3,-2,4,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,4,-2,-3,-5]=>[-5,-3,-2,4,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,-4,2,3,5]=>[5,3,2,-4,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-4,2,3,-5]=>[-5,3,2,-4,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-4,2,-3,5]=>[5,-3,2,-4,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-4,2,-3,-5]=>[-5,-3,2,-4,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-4,-2,3,5]=>[5,3,-2,-4,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-4,-2,3,-5]=>[-5,3,-2,-4,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-4,-2,-3,5]=>[5,-3,-2,-4,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,-4,-2,-3,-5]=>[-5,-3,-2,-4,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[-1,4,2,3,5]=>[5,3,2,4,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,4,2,3,-5]=>[-5,3,2,4,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,4,2,-3,5]=>[5,-3,2,4,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,4,2,-3,-5]=>[-5,-3,2,4,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,4,-2,3,5]=>[5,3,-2,4,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,-2,3,-5]=>[-5,3,-2,4,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,-2,-3,5]=>[5,-3,-2,4,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,4,-2,-3,-5]=>[-5,-3,-2,4,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,-4,2,3,5]=>[5,3,2,-4,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-4,2,3,-5]=>[-5,3,2,-4,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-4,2,-3,5]=>[5,-3,2,-4,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-4,2,-3,-5]=>[-5,-3,2,-4,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-4,-2,3,5]=>[5,3,-2,-4,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-4,-2,3,-5]=>[-5,3,-2,-4,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-4,-2,-3,5]=>[5,-3,-2,-4,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,-4,-2,-3,-5]=>[-5,-3,-2,-4,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[1,4,2,5,3]=>[3,5,2,4,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,4,2,5,-3]=>[-3,5,2,4,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,4,2,-5,3]=>[3,-5,2,4,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,4,2,-5,-3]=>[-3,-5,2,4,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,4,-2,5,3]=>[3,5,-2,4,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,4,-2,5,-3]=>[-3,5,-2,4,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,4,-2,-5,3]=>[3,-5,-2,4,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,4,-2,-5,-3]=>[-3,-5,-2,4,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,-4,2,5,3]=>[3,5,2,-4,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-4,2,5,-3]=>[-3,5,2,-4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-4,2,-5,3]=>[3,-5,2,-4,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-4,2,-5,-3]=>[-3,-5,2,-4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-4,-2,5,3]=>[3,5,-2,-4,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-4,-2,5,-3]=>[-3,5,-2,-4,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-4,-2,-5,3]=>[3,-5,-2,-4,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-4,-2,-5,-3]=>[-3,-5,-2,-4,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[-1,4,2,5,3]=>[3,5,2,4,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,4,2,5,-3]=>[-3,5,2,4,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,4,2,-5,3]=>[3,-5,2,4,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,4,2,-5,-3]=>[-3,-5,2,4,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,4,-2,5,3]=>[3,5,-2,4,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,4,-2,5,-3]=>[-3,5,-2,4,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,4,-2,-5,3]=>[3,-5,-2,4,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,4,-2,-5,-3]=>[-3,-5,-2,4,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,-4,2,5,3]=>[3,5,2,-4,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-4,2,5,-3]=>[-3,5,2,-4,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-4,2,-5,3]=>[3,-5,2,-4,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-4,2,-5,-3]=>[-3,-5,2,-4,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-4,-2,5,3]=>[3,5,-2,-4,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-4,-2,5,-3]=>[-3,5,-2,-4,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-4,-2,-5,3]=>[3,-5,-2,-4,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-4,-2,-5,-3]=>[-3,-5,-2,-4,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,4,3,2,5]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,4,3,2,-5]=>[-5,2,3,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,4,3,-2,5]=>[5,-2,3,4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,4,3,-2,-5]=>[-5,-2,3,4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,4,-3,2,5]=>[5,2,-3,4,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,-3,2,-5]=>[-5,2,-3,4,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,-3,-2,5]=>[5,-2,-3,4,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,4,-3,-2,-5]=>[-5,-2,-3,4,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,-4,3,2,5]=>[5,2,3,-4,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,3,2,-5]=>[-5,2,3,-4,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,3,-2,5]=>[5,-2,3,-4,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-4,3,-2,-5]=>[-5,-2,3,-4,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-4,-3,2,5]=>[5,2,-3,-4,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-4,-3,2,-5]=>[-5,2,-3,-4,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-4,-3,-2,5]=>[5,-2,-3,-4,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,-4,-3,-2,-5]=>[-5,-2,-3,-4,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[-1,4,3,2,5]=>[5,2,3,4,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,4,3,2,-5]=>[-5,2,3,4,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,4,3,-2,5]=>[5,-2,3,4,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,4,3,-2,-5]=>[-5,-2,3,4,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,4,-3,2,5]=>[5,2,-3,4,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,-3,2,-5]=>[-5,2,-3,4,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,-3,-2,5]=>[5,-2,-3,4,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,4,-3,-2,-5]=>[-5,-2,-3,4,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,-4,3,2,5]=>[5,2,3,-4,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,3,2,-5]=>[-5,2,3,-4,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,3,-2,5]=>[5,-2,3,-4,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-4,3,-2,-5]=>[-5,-2,3,-4,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-4,-3,2,5]=>[5,2,-3,-4,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-4,-3,2,-5]=>[-5,2,-3,-4,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-4,-3,-2,5]=>[5,-2,-3,-4,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,-4,-3,-2,-5]=>[-5,-2,-3,-4,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,4,3,5,2]=>[2,5,3,4,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,4,3,5,-2]=>[-2,5,3,4,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,4,3,-5,2]=>[2,-5,3,4,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,4,3,-5,-2]=>[-2,-5,3,4,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,4,-3,5,2]=>[2,5,-3,4,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,4,-3,5,-2]=>[-2,5,-3,4,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,4,-3,-5,2]=>[2,-5,-3,4,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,4,-3,-5,-2]=>[-2,-5,-3,4,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,-4,3,5,2]=>[2,5,3,-4,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-4,3,5,-2]=>[-2,5,3,-4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-4,3,-5,2]=>[2,-5,3,-4,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-4,3,-5,-2]=>[-2,-5,3,-4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-4,-3,5,2]=>[2,5,-3,-4,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-4,-3,5,-2]=>[-2,5,-3,-4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-4,-3,-5,2]=>[2,-5,-3,-4,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-4,-3,-5,-2]=>[-2,-5,-3,-4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[-1,4,3,5,2]=>[2,5,3,4,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,4,3,5,-2]=>[-2,5,3,4,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,4,3,-5,2]=>[2,-5,3,4,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,4,3,-5,-2]=>[-2,-5,3,4,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,4,-3,5,2]=>[2,5,-3,4,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,4,-3,5,-2]=>[-2,5,-3,4,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,4,-3,-5,2]=>[2,-5,-3,4,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,4,-3,-5,-2]=>[-2,-5,-3,4,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,-4,3,5,2]=>[2,5,3,-4,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-4,3,5,-2]=>[-2,5,3,-4,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-4,3,-5,2]=>[2,-5,3,-4,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-4,3,-5,-2]=>[-2,-5,3,-4,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-4,-3,5,2]=>[2,5,-3,-4,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-4,-3,5,-2]=>[-2,5,-3,-4,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-4,-3,-5,2]=>[2,-5,-3,-4,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-4,-3,-5,-2]=>[-2,-5,-3,-4,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,4,5,2,3]=>[3,2,5,4,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,4,5,2,-3]=>[-3,2,5,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,5,-2,3]=>[3,-2,5,4,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,4,5,-2,-3]=>[-3,-2,5,4,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,4,-5,2,3]=>[3,2,-5,4,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,4,-5,2,-3]=>[-3,2,-5,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,-5,-2,3]=>[3,-2,-5,4,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,4,-5,-2,-3]=>[-3,-2,-5,4,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,-4,5,2,3]=>[3,2,5,-4,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,5,2,-3]=>[-3,2,5,-4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,5,-2,3]=>[3,-2,5,-4,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-4,5,-2,-3]=>[-3,-2,5,-4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,-4,-5,2,3]=>[3,2,-5,-4,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,-5,2,-3]=>[-3,2,-5,-4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,-5,-2,3]=>[3,-2,-5,-4,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-4,-5,-2,-3]=>[-3,-2,-5,-4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[-1,4,5,2,3]=>[3,2,5,4,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,5,2,-3]=>[-3,2,5,4,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,5,-2,3]=>[3,-2,5,4,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,4,5,-2,-3]=>[-3,-2,5,4,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,4,-5,2,3]=>[3,2,-5,4,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,-5,2,-3]=>[-3,2,-5,4,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,-5,-2,3]=>[3,-2,-5,4,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,4,-5,-2,-3]=>[-3,-2,-5,4,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,-4,5,2,3]=>[3,2,5,-4,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,5,2,-3]=>[-3,2,5,-4,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,5,-2,3]=>[3,-2,5,-4,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-4,5,-2,-3]=>[-3,-2,5,-4,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-4,-5,2,3]=>[3,2,-5,-4,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,-5,2,-3]=>[-3,2,-5,-4,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,-5,-2,3]=>[3,-2,-5,-4,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-4,-5,-2,-3]=>[-3,-2,-5,-4,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,4,5,3,2]=>[2,3,5,4,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,4,5,3,-2]=>[-2,3,5,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,5,-3,2]=>[2,-3,5,4,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,4,5,-3,-2]=>[-2,-3,5,4,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,4,-5,3,2]=>[2,3,-5,4,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,4,-5,3,-2]=>[-2,3,-5,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,4,-5,-3,2]=>[2,-3,-5,4,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,4,-5,-3,-2]=>[-2,-3,-5,4,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,-4,5,3,2]=>[2,3,5,-4,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-4,5,3,-2]=>[-2,3,5,-4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,5,-3,2]=>[2,-3,5,-4,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-4,5,-3,-2]=>[-2,-3,5,-4,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,-4,-5,3,2]=>[2,3,-5,-4,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-4,-5,3,-2]=>[-2,3,-5,-4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-4,-5,-3,2]=>[2,-3,-5,-4,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-4,-5,-3,-2]=>[-2,-3,-5,-4,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[-1,4,5,3,2]=>[2,3,5,4,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,4,5,3,-2]=>[-2,3,5,4,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,5,-3,2]=>[2,-3,5,4,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,4,5,-3,-2]=>[-2,-3,5,4,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,4,-5,3,2]=>[2,3,-5,4,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,4,-5,3,-2]=>[-2,3,-5,4,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,4,-5,-3,2]=>[2,-3,-5,4,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,4,-5,-3,-2]=>[-2,-3,-5,4,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,-4,5,3,2]=>[2,3,5,-4,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-4,5,3,-2]=>[-2,3,5,-4,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,5,-3,2]=>[2,-3,5,-4,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-4,5,-3,-2]=>[-2,-3,5,-4,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-4,-5,3,2]=>[2,3,-5,-4,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-4,-5,3,-2]=>[-2,3,-5,-4,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-4,-5,-3,2]=>[2,-3,-5,-4,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-4,-5,-3,-2]=>[-2,-3,-5,-4,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[1,5,2,3,4]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,5,2,3,-4]=>[-4,3,2,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,5,2,-3,4]=>[4,-3,2,5,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,5,2,-3,-4]=>[-4,-3,2,5,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,5,-2,3,4]=>[4,3,-2,5,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-2,3,-4]=>[-4,3,-2,5,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-2,-3,4]=>[4,-3,-2,5,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,5,-2,-3,-4]=>[-4,-3,-2,5,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,-5,2,3,4]=>[4,3,2,-5,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,-5,2,3,-4]=>[-4,3,2,-5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-5,2,-3,4]=>[4,-3,2,-5,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-5,2,-3,-4]=>[-4,-3,2,-5,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,-5,-2,3,4]=>[4,3,-2,-5,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-2,3,-4]=>[-4,3,-2,-5,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-2,-3,4]=>[4,-3,-2,-5,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,-5,-2,-3,-4]=>[-4,-3,-2,-5,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[-1,5,2,3,4]=>[4,3,2,5,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,5,2,3,-4]=>[-4,3,2,5,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,5,2,-3,4]=>[4,-3,2,5,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,5,2,-3,-4]=>[-4,-3,2,5,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,5,-2,3,4]=>[4,3,-2,5,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-2,3,-4]=>[-4,3,-2,5,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-2,-3,4]=>[4,-3,-2,5,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,5,-2,-3,-4]=>[-4,-3,-2,5,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-1,-5,2,3,4]=>[4,3,2,-5,-1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-5,2,3,-4]=>[-4,3,2,-5,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-5,2,-3,4]=>[4,-3,2,-5,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-5,2,-3,-4]=>[-4,-3,2,-5,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-5,-2,3,4]=>[4,3,-2,-5,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-2,3,-4]=>[-4,3,-2,-5,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-2,-3,4]=>[4,-3,-2,-5,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,-5,-2,-3,-4]=>[-4,-3,-2,-5,-1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,5,2,4,3]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,5,2,4,-3]=>[-3,4,2,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,5,2,-4,3]=>[3,-4,2,5,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,5,2,-4,-3]=>[-3,-4,2,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,5,-2,4,3]=>[3,4,-2,5,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,5,-2,4,-3]=>[-3,4,-2,5,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-2,-4,3]=>[3,-4,-2,5,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,5,-2,-4,-3]=>[-3,-4,-2,5,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,-5,2,4,3]=>[3,4,2,-5,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,-5,2,4,-3]=>[-3,4,2,-5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-5,2,-4,3]=>[3,-4,2,-5,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-5,2,-4,-3]=>[-3,-4,2,-5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,-5,-2,4,3]=>[3,4,-2,-5,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-5,-2,4,-3]=>[-3,4,-2,-5,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-2,-4,3]=>[3,-4,-2,-5,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,-5,-2,-4,-3]=>[-3,-4,-2,-5,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[-1,5,2,4,3]=>[3,4,2,5,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,5,2,4,-3]=>[-3,4,2,5,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,5,2,-4,3]=>[3,-4,2,5,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,5,2,-4,-3]=>[-3,-4,2,5,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,5,-2,4,3]=>[3,4,-2,5,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,5,-2,4,-3]=>[-3,4,-2,5,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-2,-4,3]=>[3,-4,-2,5,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,5,-2,-4,-3]=>[-3,-4,-2,5,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,-5,2,4,3]=>[3,4,2,-5,-1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-5,2,4,-3]=>[-3,4,2,-5,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-5,2,-4,3]=>[3,-4,2,-5,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-5,2,-4,-3]=>[-3,-4,2,-5,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-5,-2,4,3]=>[3,4,-2,-5,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-5,-2,4,-3]=>[-3,4,-2,-5,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-2,-4,3]=>[3,-4,-2,-5,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,-5,-2,-4,-3]=>[-3,-4,-2,-5,-1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,5,3,2,4]=>[4,2,3,5,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,5,3,2,-4]=>[-4,2,3,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,5,3,-2,4]=>[4,-2,3,5,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,5,3,-2,-4]=>[-4,-2,3,5,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,5,-3,2,4]=>[4,2,-3,5,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-3,2,-4]=>[-4,2,-3,5,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-3,-2,4]=>[4,-2,-3,5,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,5,-3,-2,-4]=>[-4,-2,-3,5,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,-5,3,2,4]=>[4,2,3,-5,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-5,3,2,-4]=>[-4,2,3,-5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-5,3,-2,4]=>[4,-2,3,-5,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,-5,3,-2,-4]=>[-4,-2,3,-5,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,-5,-3,2,4]=>[4,2,-3,-5,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-3,2,-4]=>[-4,2,-3,-5,1]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-3,-2,4]=>[4,-2,-3,-5,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,-5,-3,-2,-4]=>[-4,-2,-3,-5,1]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[-1,5,3,2,4]=>[4,2,3,5,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,5,3,2,-4]=>[-4,2,3,5,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,5,3,-2,4]=>[4,-2,3,5,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,5,3,-2,-4]=>[-4,-2,3,5,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,5,-3,2,4]=>[4,2,-3,5,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-3,2,-4]=>[-4,2,-3,5,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-3,-2,4]=>[4,-2,-3,5,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,5,-3,-2,-4]=>[-4,-2,-3,5,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-1,-5,3,2,4]=>[4,2,3,-5,-1]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-5,3,2,-4]=>[-4,2,3,-5,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-5,3,-2,4]=>[4,-2,3,-5,-1]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-5,3,-2,-4]=>[-4,-2,3,-5,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-5,-3,2,4]=>[4,2,-3,-5,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-3,2,-4]=>[-4,2,-3,-5,-1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-3,-2,4]=>[4,-2,-3,-5,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,-5,-3,-2,-4]=>[-4,-2,-3,-5,-1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[1,5,3,4,2]=>[2,4,3,5,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,5,3,4,-2]=>[-2,4,3,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,5,3,-4,2]=>[2,-4,3,5,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,5,3,-4,-2]=>[-2,-4,3,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,5,-3,4,2]=>[2,4,-3,5,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,5,-3,4,-2]=>[-2,4,-3,5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-3,-4,2]=>[2,-4,-3,5,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,5,-3,-4,-2]=>[-2,-4,-3,5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,-5,3,4,2]=>[2,4,3,-5,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,-5,3,4,-2]=>[-2,4,3,-5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,-5,3,-4,2]=>[2,-4,3,-5,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-5,3,-4,-2]=>[-2,-4,3,-5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,-5,-3,4,2]=>[2,4,-3,-5,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-5,-3,4,-2]=>[-2,4,-3,-5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-3,-4,2]=>[2,-4,-3,-5,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,-5,-3,-4,-2]=>[-2,-4,-3,-5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[-1,5,3,4,2]=>[2,4,3,5,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,5,3,4,-2]=>[-2,4,3,5,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,5,3,-4,2]=>[2,-4,3,5,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,5,3,-4,-2]=>[-2,-4,3,5,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,5,-3,4,2]=>[2,4,-3,5,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,5,-3,4,-2]=>[-2,4,-3,5,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-3,-4,2]=>[2,-4,-3,5,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,5,-3,-4,-2]=>[-2,-4,-3,5,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-1,-5,3,4,2]=>[2,4,3,-5,-1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-5,3,4,-2]=>[-2,4,3,-5,-1]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-5,3,-4,2]=>[2,-4,3,-5,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-5,3,-4,-2]=>[-2,-4,3,-5,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-5,-3,4,2]=>[2,4,-3,-5,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-5,-3,4,-2]=>[-2,4,-3,-5,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-3,-4,2]=>[2,-4,-3,-5,-1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-1,-5,-3,-4,-2]=>[-2,-4,-3,-5,-1]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,5,4,2,3]=>[3,2,4,5,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,5,4,2,-3]=>[-3,2,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,5,4,-2,3]=>[3,-2,4,5,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,5,4,-2,-3]=>[-3,-2,4,5,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,5,-4,2,3]=>[3,2,-4,5,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-4,2,-3]=>[-3,2,-4,5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-4,-2,3]=>[3,-2,-4,5,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,5,-4,-2,-3]=>[-3,-2,-4,5,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,-5,4,2,3]=>[3,2,4,-5,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,-5,4,2,-3]=>[-3,2,4,-5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-5,4,-2,3]=>[3,-2,4,-5,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-5,4,-2,-3]=>[-3,-2,4,-5,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,-5,-4,2,3]=>[3,2,-4,-5,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-4,2,-3]=>[-3,2,-4,-5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-4,-2,3]=>[3,-2,-4,-5,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,-5,-4,-2,-3]=>[-3,-2,-4,-5,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[-1,5,4,2,3]=>[3,2,4,5,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,5,4,2,-3]=>[-3,2,4,5,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,5,4,-2,3]=>[3,-2,4,5,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,5,4,-2,-3]=>[-3,-2,4,5,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,5,-4,2,3]=>[3,2,-4,5,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-4,2,-3]=>[-3,2,-4,5,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-4,-2,3]=>[3,-2,-4,5,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,5,-4,-2,-3]=>[-3,-2,-4,5,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-1,-5,4,2,3]=>[3,2,4,-5,-1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-5,4,2,-3]=>[-3,2,4,-5,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-5,4,-2,3]=>[3,-2,4,-5,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-5,4,-2,-3]=>[-3,-2,4,-5,-1]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-1,-5,-4,2,3]=>[3,2,-4,-5,-1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-4,2,-3]=>[-3,2,-4,-5,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-4,-2,3]=>[3,-2,-4,-5,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,-5,-4,-2,-3]=>[-3,-2,-4,-5,-1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[1,5,4,3,2]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,5,4,3,-2]=>[-2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,5,4,-3,2]=>[2,-3,4,5,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,5,4,-3,-2]=>[-2,-3,4,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,5,-4,3,2]=>[2,3,-4,5,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,5,-4,3,-2]=>[-2,3,-4,5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,5,-4,-3,2]=>[2,-3,-4,5,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,5,-4,-3,-2]=>[-2,-3,-4,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,-5,4,3,2]=>[2,3,4,-5,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,-5,4,3,-2]=>[-2,3,4,-5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,-5,4,-3,2]=>[2,-3,4,-5,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,-5,4,-3,-2]=>[-2,-3,4,-5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,-5,-4,3,2]=>[2,3,-4,-5,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,-5,-4,3,-2]=>[-2,3,-4,-5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,-5,-4,-3,2]=>[2,-3,-4,-5,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,-5,-4,-3,-2]=>[-2,-3,-4,-5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[-1,5,4,3,2]=>[2,3,4,5,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,5,4,3,-2]=>[-2,3,4,5,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,5,4,-3,2]=>[2,-3,4,5,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,5,4,-3,-2]=>[-2,-3,4,5,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,5,-4,3,2]=>[2,3,-4,5,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,5,-4,3,-2]=>[-2,3,-4,5,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,5,-4,-3,2]=>[2,-3,-4,5,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,5,-4,-3,-2]=>[-2,-3,-4,5,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-1,-5,4,3,2]=>[2,3,4,-5,-1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[-1,-5,4,3,-2]=>[-2,3,4,-5,-1]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[-1,-5,4,-3,2]=>[2,-3,4,-5,-1]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[-1,-5,4,-3,-2]=>[-2,-3,4,-5,-1]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-1,-5,-4,3,2]=>[2,3,-4,-5,-1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[-1,-5,-4,3,-2]=>[-2,3,-4,-5,-1]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-1,-5,-4,-3,2]=>[2,-3,-4,-5,-1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-1,-5,-4,-3,-2]=>[-2,-3,-4,-5,-1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[2,1,3,4,5]=>[5,4,3,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,1,3,4,-5]=>[-5,4,3,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,1,3,-4,5]=>[5,-4,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,1,3,-4,-5]=>[-5,-4,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,1,-3,4,5]=>[5,4,-3,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-3,4,-5]=>[-5,4,-3,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-3,-4,5]=>[5,-4,-3,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,1,-3,-4,-5]=>[-5,-4,-3,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,-1,3,4,5]=>[5,4,3,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[2,-1,3,4,-5]=>[-5,4,3,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[2,-1,3,-4,5]=>[5,-4,3,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[2,-1,3,-4,-5]=>[-5,-4,3,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[2,-1,-3,4,5]=>[5,4,-3,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-3,4,-5]=>[-5,4,-3,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-3,-4,5]=>[5,-4,-3,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[2,-1,-3,-4,-5]=>[-5,-4,-3,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[-2,1,3,4,5]=>[5,4,3,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,1,3,4,-5]=>[-5,4,3,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,1,3,-4,5]=>[5,-4,3,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,1,3,-4,-5]=>[-5,-4,3,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,1,-3,4,5]=>[5,4,-3,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-3,4,-5]=>[-5,4,-3,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-3,-4,5]=>[5,-4,-3,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-2,1,-3,-4,-5]=>[-5,-4,-3,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-2,-1,3,4,5]=>[5,4,3,-1,-2]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-2,-1,3,4,-5]=>[-5,4,3,-1,-2]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-2,-1,3,-4,5]=>[5,-4,3,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-2,-1,3,-4,-5]=>[-5,-4,3,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-2,-1,-3,4,5]=>[5,4,-3,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-3,4,-5]=>[-5,4,-3,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-3,-4,5]=>[5,-4,-3,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-2,-1,-3,-4,-5]=>[-5,-4,-3,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[2,1,3,5,4]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,1,3,5,-4]=>[-4,5,3,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,1,3,-5,4]=>[4,-5,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,1,3,-5,-4]=>[-4,-5,3,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,1,-3,5,4]=>[4,5,-3,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,1,-3,5,-4]=>[-4,5,-3,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-3,-5,4]=>[4,-5,-3,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,1,-3,-5,-4]=>[-4,-5,-3,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,-1,3,5,4]=>[4,5,3,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[2,-1,3,5,-4]=>[-4,5,3,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[2,-1,3,-5,4]=>[4,-5,3,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[2,-1,3,-5,-4]=>[-4,-5,3,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[2,-1,-3,5,4]=>[4,5,-3,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[2,-1,-3,5,-4]=>[-4,5,-3,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-3,-5,4]=>[4,-5,-3,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[2,-1,-3,-5,-4]=>[-4,-5,-3,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[-2,1,3,5,4]=>[4,5,3,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,1,3,5,-4]=>[-4,5,3,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,1,3,-5,4]=>[4,-5,3,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,1,3,-5,-4]=>[-4,-5,3,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,1,-3,5,4]=>[4,5,-3,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-2,1,-3,5,-4]=>[-4,5,-3,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-3,-5,4]=>[4,-5,-3,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-2,1,-3,-5,-4]=>[-4,-5,-3,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,-1,3,5,4]=>[4,5,3,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-2,-1,3,5,-4]=>[-4,5,3,-1,-2]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-2,-1,3,-5,4]=>[4,-5,3,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-2,-1,3,-5,-4]=>[-4,-5,3,-1,-2]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-2,-1,-3,5,4]=>[4,5,-3,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-2,-1,-3,5,-4]=>[-4,5,-3,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-3,-5,4]=>[4,-5,-3,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-2,-1,-3,-5,-4]=>[-4,-5,-3,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[2,1,4,3,5]=>[5,3,4,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,4,3,-5]=>[-5,3,4,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,4,-3,5]=>[5,-3,4,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,1,4,-3,-5]=>[-5,-3,4,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,1,-4,3,5]=>[5,3,-4,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-4,3,-5]=>[-5,3,-4,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-4,-3,5]=>[5,-3,-4,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,1,-4,-3,-5]=>[-5,-3,-4,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,-1,4,3,5]=>[5,3,4,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,4,3,-5]=>[-5,3,4,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,4,-3,5]=>[5,-3,4,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[2,-1,4,-3,-5]=>[-5,-3,4,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[2,-1,-4,3,5]=>[5,3,-4,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-4,3,-5]=>[-5,3,-4,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-4,-3,5]=>[5,-3,-4,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[2,-1,-4,-3,-5]=>[-5,-3,-4,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[-2,1,4,3,5]=>[5,3,4,1,-2]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,4,3,-5]=>[-5,3,4,1,-2]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,4,-3,5]=>[5,-3,4,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,1,4,-3,-5]=>[-5,-3,4,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,1,-4,3,5]=>[5,3,-4,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-4,3,-5]=>[-5,3,-4,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-4,-3,5]=>[5,-3,-4,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,1,-4,-3,-5]=>[-5,-3,-4,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,-1,4,3,5]=>[5,3,4,-1,-2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,4,3,-5]=>[-5,3,4,-1,-2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,4,-3,5]=>[5,-3,4,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-2,-1,4,-3,-5]=>[-5,-3,4,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-2,-1,-4,3,5]=>[5,3,-4,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-4,3,-5]=>[-5,3,-4,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-4,-3,5]=>[5,-3,-4,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-2,-1,-4,-3,-5]=>[-5,-3,-4,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[2,1,4,5,3]=>[3,5,4,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,1,4,5,-3]=>[-3,5,4,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,1,4,-5,3]=>[3,-5,4,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,1,4,-5,-3]=>[-3,-5,4,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,1,-4,5,3]=>[3,5,-4,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,1,-4,5,-3]=>[-3,5,-4,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-4,-5,3]=>[3,-5,-4,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,1,-4,-5,-3]=>[-3,-5,-4,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,-1,4,5,3]=>[3,5,4,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[2,-1,4,5,-3]=>[-3,5,4,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[2,-1,4,-5,3]=>[3,-5,4,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[2,-1,4,-5,-3]=>[-3,-5,4,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[2,-1,-4,5,3]=>[3,5,-4,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[2,-1,-4,5,-3]=>[-3,5,-4,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-4,-5,3]=>[3,-5,-4,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[2,-1,-4,-5,-3]=>[-3,-5,-4,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[-2,1,4,5,3]=>[3,5,4,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,1,4,5,-3]=>[-3,5,4,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,1,4,-5,3]=>[3,-5,4,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,1,4,-5,-3]=>[-3,-5,4,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,1,-4,5,3]=>[3,5,-4,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-2,1,-4,5,-3]=>[-3,5,-4,1,-2]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-4,-5,3]=>[3,-5,-4,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
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[-2,-1,4,5,3]=>[3,5,4,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
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[-2,-1,4,-5,3]=>[3,-5,4,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
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[-2,-1,-4,5,3]=>[3,5,-4,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-2,-1,-4,5,-3]=>[-3,5,-4,-1,-2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-4,-5,3]=>[3,-5,-4,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-2,-1,-4,-5,-3]=>[-3,-5,-4,-1,-2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[2,1,5,3,4]=>[4,3,5,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,5,3,-4]=>[-4,3,5,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,5,-3,4]=>[4,-3,5,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,1,5,-3,-4]=>[-4,-3,5,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,1,-5,3,4]=>[4,3,-5,1,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-5,3,-4]=>[-4,3,-5,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-5,-3,4]=>[4,-3,-5,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,1,-5,-3,-4]=>[-4,-3,-5,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,-1,5,3,4]=>[4,3,5,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,5,3,-4]=>[-4,3,5,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,5,-3,4]=>[4,-3,5,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[2,-1,5,-3,-4]=>[-4,-3,5,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[2,-1,-5,3,4]=>[4,3,-5,-1,2]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-5,3,-4]=>[-4,3,-5,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-5,-3,4]=>[4,-3,-5,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[2,-1,-5,-3,-4]=>[-4,-3,-5,-1,2]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[-2,1,5,3,4]=>[4,3,5,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,5,3,-4]=>[-4,3,5,1,-2]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,5,-3,4]=>[4,-3,5,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,1,5,-3,-4]=>[-4,-3,5,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,1,-5,3,4]=>[4,3,-5,1,-2]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-5,3,-4]=>[-4,3,-5,1,-2]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-5,-3,4]=>[4,-3,-5,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,1,-5,-3,-4]=>[-4,-3,-5,1,-2]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-2,-1,5,3,4]=>[4,3,5,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,5,3,-4]=>[-4,3,5,-1,-2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,5,-3,4]=>[4,-3,5,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-2,-1,5,-3,-4]=>[-4,-3,5,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-2,-1,-5,3,4]=>[4,3,-5,-1,-2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-5,3,-4]=>[-4,3,-5,-1,-2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-5,-3,4]=>[4,-3,-5,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-2,-1,-5,-3,-4]=>[-4,-3,-5,-1,-2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[2,1,5,4,3]=>[3,4,5,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,1,5,4,-3]=>[-3,4,5,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,5,-4,3]=>[3,-4,5,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,1,5,-4,-3]=>[-3,-4,5,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,1,-5,4,3]=>[3,4,-5,1,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[2,1,-5,4,-3]=>[-3,4,-5,1,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[2,1,-5,-4,3]=>[3,-4,-5,1,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[2,1,-5,-4,-3]=>[-3,-4,-5,1,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[2,-1,5,4,3]=>[3,4,5,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[2,-1,5,4,-3]=>[-3,4,5,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,5,-4,3]=>[3,-4,5,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[2,-1,5,-4,-3]=>[-3,-4,5,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[2,-1,-5,4,3]=>[3,4,-5,-1,2]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[2,-1,-5,4,-3]=>[-3,4,-5,-1,2]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[2,-1,-5,-4,3]=>[3,-4,-5,-1,2]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[2,-1,-5,-4,-3]=>[-3,-4,-5,-1,2]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[-2,1,5,4,3]=>[3,4,5,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-2,1,5,4,-3]=>[-3,4,5,1,-2]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,5,-4,3]=>[3,-4,5,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,1,5,-4,-3]=>[-3,-4,5,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,1,-5,4,3]=>[3,4,-5,1,-2]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-2,1,-5,4,-3]=>[-3,4,-5,1,-2]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-2,1,-5,-4,3]=>[3,-4,-5,1,-2]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-2,1,-5,-4,-3]=>[-3,-4,-5,1,-2]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-2,-1,5,4,3]=>[3,4,5,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
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[-2,-1,5,-4,3]=>[3,-4,5,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-2,-1,5,-4,-3]=>[-3,-4,5,-1,-2]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-2,-1,-5,4,3]=>[3,4,-5,-1,-2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-2,-1,-5,4,-3]=>[-3,4,-5,-1,-2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-2,-1,-5,-4,3]=>[3,-4,-5,-1,-2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
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[2,3,1,4,5]=>[5,4,1,3,2]=>[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]]
[2,3,1,4,-5]=>[-5,4,1,3,2]=>[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]]
[2,3,1,-4,5]=>[5,-4,1,3,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]
[2,3,1,-4,-5]=>[-5,-4,1,3,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]
[2,3,-1,4,5]=>[5,4,-1,3,2]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[2,3,-1,4,-5]=>[-5,4,-1,3,2]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[2,3,-1,-4,5]=>[5,-4,-1,3,2]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[2,3,-1,-4,-5]=>[-5,-4,-1,3,2]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[2,-3,1,4,5]=>[5,4,1,-3,2]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[2,-3,1,4,-5]=>[-5,4,1,-3,2]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[2,-3,1,-4,5]=>[5,-4,1,-3,2]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[2,-3,1,-4,-5]=>[-5,-4,1,-3,2]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[2,-3,-1,4,5]=>[5,4,-1,-3,2]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[2,-3,-1,4,-5]=>[-5,4,-1,-3,2]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[2,-3,-1,-4,5]=>[5,-4,-1,-3,2]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[2,-3,-1,-4,-5]=>[-5,-4,-1,-3,2]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[-2,3,1,4,-5]=>[-5,4,1,3,-2]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-2,3,1,-4,5]=>[5,-4,1,3,-2]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-2,3,1,-4,-5]=>[-5,-4,1,3,-2]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-2,3,-1,4,5]=>[5,4,-1,3,-2]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-2,3,-1,4,-5]=>[-5,4,-1,3,-2]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-2,3,-1,-4,5]=>[5,-4,-1,3,-2]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-2,3,-1,-4,-5]=>[-5,-4,-1,3,-2]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
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[-2,-3,1,4,-5]=>[-5,4,1,-3,-2]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-2,-3,1,-4,5]=>[5,-4,1,-3,-2]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-2,-3,1,-4,-5]=>[-5,-4,1,-3,-2]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[-2,-3,-1,4,5]=>[5,4,-1,-3,-2]=>[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]
[-2,-3,-1,4,-5]=>[-5,4,-1,-3,-2]=>[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]
[-2,-3,-1,-4,5]=>[5,-4,-1,-3,-2]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
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[2,3,1,5,4]=>[4,5,1,3,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]
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[2,3,1,-5,4]=>[4,-5,1,3,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]
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[2,3,-1,-5,4]=>[4,-5,-1,3,2]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
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[2,-3,1,-5,4]=>[4,-5,1,-3,2]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
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[2,-3,-1,5,4]=>[4,5,-1,-3,2]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[2,-3,-1,-5,4]=>[4,-5,-1,-3,2]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[-2,3,1,-5,4]=>[4,-5,1,3,-2]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
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[-2,3,-1,5,4]=>[4,5,-1,3,-2]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
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[-2,-3,1,5,4]=>[4,5,1,-3,-2]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
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[-2,-3,-1,5,4]=>[4,5,-1,-3,-2]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
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[2,-3,-4,-1,5]=>[5,-1,-4,-3,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
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[2,-3,5,1,4]=>[4,1,5,-3,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[2,-3,5,1,-4]=>[-4,1,5,-3,2]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[2,-3,5,-1,4]=>[4,-1,5,-3,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[2,-3,5,-1,-4]=>[-4,-1,5,-3,2]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[2,-3,-5,1,4]=>[4,1,-5,-3,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[2,-3,-5,1,-4]=>[-4,1,-5,-3,2]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[2,-3,-5,-1,4]=>[4,-1,-5,-3,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[2,-3,-5,-1,-4]=>[-4,-1,-5,-3,2]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[-2,3,5,1,4]=>[4,1,5,3,-2]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-2,3,5,1,-4]=>[-4,1,5,3,-2]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-2,3,5,-1,4]=>[4,-1,5,3,-2]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-2,3,5,-1,-4]=>[-4,-1,5,3,-2]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-2,3,-5,1,4]=>[4,1,-5,3,-2]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-2,3,-5,1,-4]=>[-4,1,-5,3,-2]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[-2,3,-5,-1,4]=>[4,-1,-5,3,-2]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-2,3,-5,-1,-4]=>[-4,-1,-5,3,-2]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-2,-3,5,1,4]=>[4,1,5,-3,-2]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-2,-3,5,1,-4]=>[-4,1,5,-3,-2]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-2,-3,5,-1,4]=>[4,-1,5,-3,-2]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
[-2,-3,5,-1,-4]=>[-4,-1,5,-3,-2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[-2,-3,-5,1,4]=>[4,1,-5,-3,-2]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-2,-3,-5,1,-4]=>[-4,1,-5,-3,-2]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-2,-3,-5,-1,4]=>[4,-1,-5,-3,-2]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
[-2,-3,-5,-1,-4]=>[-4,-1,-5,-3,-2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[2,3,5,4,1]=>[1,4,5,3,2]=>[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]]
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[2,3,5,-4,1]=>[1,-4,5,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[2,3,5,-4,-1]=>[-1,-4,5,3,2]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[2,3,-5,4,1]=>[1,4,-5,3,2]=>[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]]
[2,3,-5,4,-1]=>[-1,4,-5,3,2]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[2,3,-5,-4,1]=>[1,-4,-5,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[2,3,-5,-4,-1]=>[-1,-4,-5,3,2]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[2,-3,5,4,1]=>[1,4,5,-3,2]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[2,-3,5,4,-1]=>[-1,4,5,-3,2]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[2,-3,5,-4,1]=>[1,-4,5,-3,2]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[2,-3,5,-4,-1]=>[-1,-4,5,-3,2]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[2,-3,-5,4,1]=>[1,4,-5,-3,2]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[2,-3,-5,4,-1]=>[-1,4,-5,-3,2]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[2,-3,-5,-4,1]=>[1,-4,-5,-3,2]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[2,-3,-5,-4,-1]=>[-1,-4,-5,-3,2]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[-2,3,5,4,1]=>[1,4,5,3,-2]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-2,3,5,4,-1]=>[-1,4,5,3,-2]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[-2,3,5,-4,1]=>[1,-4,5,3,-2]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-2,3,5,-4,-1]=>[-1,-4,5,3,-2]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-2,3,-5,4,1]=>[1,4,-5,3,-2]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
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[-2,-3,5,4,1]=>[1,4,5,-3,-2]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[-2,-3,-5,-4,1]=>[1,-4,-5,-3,-2]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
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[2,4,1,3,-5]=>[-5,3,1,4,2]=>[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]]
[2,4,1,-3,5]=>[5,-3,1,4,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]
[2,4,1,-3,-5]=>[-5,-3,1,4,2]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]
[2,4,-1,3,5]=>[5,3,-1,4,2]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
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[2,4,-1,-3,5]=>[5,-3,-1,4,2]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
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[2,-4,1,-3,5]=>[5,-3,1,-4,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
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[2,-4,-1,-3,5]=>[5,-3,-1,-4,2]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[2,-4,-1,-3,-5]=>[-5,-3,-1,-4,2]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
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[-2,4,1,-3,5]=>[5,-3,1,4,-2]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-2,4,1,-3,-5]=>[-5,-3,1,4,-2]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-2,4,-1,3,5]=>[5,3,-1,4,-2]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[-2,4,-1,3,-5]=>[-5,3,-1,4,-2]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[-2,4,-1,-3,5]=>[5,-3,-1,4,-2]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-2,4,-1,-3,-5]=>[-5,-3,-1,4,-2]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
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[-2,-4,1,3,-5]=>[-5,3,1,-4,-2]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[-2,-4,1,-3,5]=>[5,-3,1,-4,-2]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[-2,-4,1,-3,-5]=>[-5,-3,1,-4,-2]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
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[-2,-4,-1,-3,5]=>[5,-3,-1,-4,-2]=>[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]
[-2,-4,-1,-3,-5]=>[-5,-3,-1,-4,-2]=>[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]
[2,4,1,5,3]=>[3,5,1,4,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
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[2,4,1,-5,3]=>[3,-5,1,4,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[2,4,1,-5,-3]=>[-3,-5,1,4,2]=>[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]]
[2,4,-1,5,3]=>[3,5,-1,4,2]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[2,4,-1,5,-3]=>[-3,5,-1,4,2]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[2,4,-1,-5,3]=>[3,-5,-1,4,2]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[2,4,-1,-5,-3]=>[-3,-5,-1,4,2]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
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[2,-4,1,-5,3]=>[3,-5,1,-4,2]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
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[2,-4,-1,5,3]=>[3,5,-1,-4,2]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[2,-4,-1,-5,3]=>[3,-5,-1,-4,2]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[-2,4,-1,5,3]=>[3,5,-1,4,-2]=>[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]
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[2,4,3,-1,-5]=>[-5,-1,3,4,2]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
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[-2,4,3,-1,5]=>[5,-1,3,4,-2]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[-2,4,3,-1,-5]=>[-5,-1,3,4,-2]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[-2,4,-3,1,5]=>[5,1,-3,4,-2]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[-2,4,-3,1,-5]=>[-5,1,-3,4,-2]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
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[-2,-4,3,1,5]=>[5,1,3,-4,-2]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-2,-4,3,1,-5]=>[-5,1,3,-4,-2]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-2,-4,3,-1,5]=>[5,-1,3,-4,-2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[-2,-4,3,-1,-5]=>[-5,-1,3,-4,-2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
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[-2,-4,-3,-1,5]=>[5,-1,-3,-4,-2]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]
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[2,-4,3,-5,-1]=>[-1,-5,3,-4,2]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[2,-4,-3,5,1]=>[1,5,-3,-4,2]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
[2,-4,-3,5,-1]=>[-1,5,-3,-4,2]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
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[-2,4,3,-5,-1]=>[-1,-5,3,4,-2]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]
[-2,4,-3,5,1]=>[1,5,-3,4,-2]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
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[2,-4,5,-1,3]=>[3,-1,5,-4,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
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[2,-4,-5,1,-3]=>[-3,1,-5,-4,2]=>[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]
[2,-4,-5,-1,3]=>[3,-1,-5,-4,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
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[-2,4,5,-1,3]=>[3,-1,5,4,-2]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]
[-2,4,5,-1,-3]=>[-3,-1,5,4,-2]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
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[-2,5,-1,4,3]=>[3,4,-1,5,-2]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
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[2,5,3,-1,4]=>[4,-1,3,5,2]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
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[3,-1,2,-5,4]=>[4,-5,2,-1,3]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[3,-1,2,-5,-4]=>[-4,-5,2,-1,3]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[3,-1,-2,5,4]=>[4,5,-2,-1,3]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[3,-1,-2,5,-4]=>[-4,5,-2,-1,3]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[3,-1,-2,-5,4]=>[4,-5,-2,-1,3]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[3,-1,-2,-5,-4]=>[-4,-5,-2,-1,3]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[-3,1,2,5,4]=>[4,5,2,1,-3]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-3,1,2,5,-4]=>[-4,5,2,1,-3]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-3,1,2,-5,4]=>[4,-5,2,1,-3]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[-3,1,2,-5,-4]=>[-4,-5,2,1,-3]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[-3,1,-2,5,4]=>[4,5,-2,1,-3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-3,1,-2,5,-4]=>[-4,5,-2,1,-3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,1,-2,-5,4]=>[4,-5,-2,1,-3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-3,1,-2,-5,-4]=>[-4,-5,-2,1,-3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,-1,2,5,4]=>[4,5,2,-1,-3]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-3,-1,2,5,-4]=>[-4,5,2,-1,-3]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-3,-1,2,-5,4]=>[4,-5,2,-1,-3]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-3,-1,2,-5,-4]=>[-4,-5,2,-1,-3]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-3,-1,-2,5,4]=>[4,5,-2,-1,-3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[-3,-1,-2,5,-4]=>[-4,5,-2,-1,-3]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[-3,-1,-2,-5,4]=>[4,-5,-2,-1,-3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[-3,-1,-2,-5,-4]=>[-4,-5,-2,-1,-3]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[3,1,4,2,5]=>[5,2,4,1,3]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,4,2,-5]=>[-5,2,4,1,3]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,4,-2,5]=>[5,-2,4,1,3]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[3,1,4,-2,-5]=>[-5,-2,4,1,3]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[3,1,-4,2,5]=>[5,2,-4,1,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,-4,2,-5]=>[-5,2,-4,1,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,-4,-2,5]=>[5,-2,-4,1,3]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[3,1,-4,-2,-5]=>[-5,-2,-4,1,3]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[3,-1,4,2,5]=>[5,2,4,-1,3]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,4,2,-5]=>[-5,2,4,-1,3]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,4,-2,5]=>[5,-2,4,-1,3]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[3,-1,4,-2,-5]=>[-5,-2,4,-1,3]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[3,-1,-4,2,5]=>[5,2,-4,-1,3]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,-4,2,-5]=>[-5,2,-4,-1,3]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,-4,-2,5]=>[5,-2,-4,-1,3]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[3,-1,-4,-2,-5]=>[-5,-2,-4,-1,3]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[-3,1,4,2,5]=>[5,2,4,1,-3]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,4,2,-5]=>[-5,2,4,1,-3]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,4,-2,5]=>[5,-2,4,1,-3]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-3,1,4,-2,-5]=>[-5,-2,4,1,-3]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-3,1,-4,2,5]=>[5,2,-4,1,-3]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,-4,2,-5]=>[-5,2,-4,1,-3]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,-4,-2,5]=>[5,-2,-4,1,-3]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-3,1,-4,-2,-5]=>[-5,-2,-4,1,-3]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-3,-1,4,2,5]=>[5,2,4,-1,-3]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,4,2,-5]=>[-5,2,4,-1,-3]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,4,-2,5]=>[5,-2,4,-1,-3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[-3,-1,4,-2,-5]=>[-5,-2,4,-1,-3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[-3,-1,-4,2,5]=>[5,2,-4,-1,-3]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,-4,2,-5]=>[-5,2,-4,-1,-3]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,-4,-2,5]=>[5,-2,-4,-1,-3]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[-3,-1,-4,-2,-5]=>[-5,-2,-4,-1,-3]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[3,1,4,5,2]=>[2,5,4,1,3]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[3,1,4,5,-2]=>[-2,5,4,1,3]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[3,1,4,-5,2]=>[2,-5,4,1,3]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[3,1,4,-5,-2]=>[-2,-5,4,1,3]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[3,1,-4,5,2]=>[2,5,-4,1,3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[3,1,-4,5,-2]=>[-2,5,-4,1,3]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,1,-4,-5,2]=>[2,-5,-4,1,3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[3,1,-4,-5,-2]=>[-2,-5,-4,1,3]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,-1,4,5,2]=>[2,5,4,-1,3]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[3,-1,4,5,-2]=>[-2,5,4,-1,3]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[3,-1,4,-5,2]=>[2,-5,4,-1,3]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[3,-1,4,-5,-2]=>[-2,-5,4,-1,3]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[3,-1,-4,5,2]=>[2,5,-4,-1,3]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[3,-1,-4,5,-2]=>[-2,5,-4,-1,3]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[3,-1,-4,-5,2]=>[2,-5,-4,-1,3]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[3,-1,-4,-5,-2]=>[-2,-5,-4,-1,3]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
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[-3,1,4,5,-2]=>[-2,5,4,1,-3]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-3,1,4,-5,2]=>[2,-5,4,1,-3]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-3,1,4,-5,-2]=>[-2,-5,4,1,-3]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-3,1,-4,5,2]=>[2,5,-4,1,-3]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-3,1,-4,5,-2]=>[-2,5,-4,1,-3]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,1,-4,-5,2]=>[2,-5,-4,1,-3]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-3,1,-4,-5,-2]=>[-2,-5,-4,1,-3]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,-1,4,5,2]=>[2,5,4,-1,-3]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-3,-1,4,5,-2]=>[-2,5,4,-1,-3]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]
[-3,-1,4,-5,2]=>[2,-5,4,-1,-3]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-3,-1,4,-5,-2]=>[-2,-5,4,-1,-3]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]
[-3,-1,-4,5,2]=>[2,5,-4,-1,-3]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-3,-1,-4,5,-2]=>[-2,5,-4,-1,-3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,-4,-5,2]=>[2,-5,-4,-1,-3]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-3,-1,-4,-5,-2]=>[-2,-5,-4,-1,-3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[3,1,5,2,4]=>[4,2,5,1,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,5,2,-4]=>[-4,2,5,1,3]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,5,-2,4]=>[4,-2,5,1,3]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[3,1,5,-2,-4]=>[-4,-2,5,1,3]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[3,1,-5,2,4]=>[4,2,-5,1,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,-5,2,-4]=>[-4,2,-5,1,3]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,-5,-2,4]=>[4,-2,-5,1,3]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[3,1,-5,-2,-4]=>[-4,-2,-5,1,3]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[3,-1,5,2,4]=>[4,2,5,-1,3]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,5,2,-4]=>[-4,2,5,-1,3]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,5,-2,4]=>[4,-2,5,-1,3]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[3,-1,5,-2,-4]=>[-4,-2,5,-1,3]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[3,-1,-5,2,4]=>[4,2,-5,-1,3]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,-5,2,-4]=>[-4,2,-5,-1,3]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[3,-1,-5,-2,4]=>[4,-2,-5,-1,3]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[3,-1,-5,-2,-4]=>[-4,-2,-5,-1,3]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[-3,1,5,2,4]=>[4,2,5,1,-3]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,5,2,-4]=>[-4,2,5,1,-3]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,5,-2,4]=>[4,-2,5,1,-3]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-3,1,5,-2,-4]=>[-4,-2,5,1,-3]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-3,1,-5,2,4]=>[4,2,-5,1,-3]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,-5,2,-4]=>[-4,2,-5,1,-3]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-3,1,-5,-2,4]=>[4,-2,-5,1,-3]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-3,1,-5,-2,-4]=>[-4,-2,-5,1,-3]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-3,-1,5,2,4]=>[4,2,5,-1,-3]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
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[-3,-1,5,-2,4]=>[4,-2,5,-1,-3]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[-3,-1,5,-2,-4]=>[-4,-2,5,-1,-3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[-3,-1,-5,2,4]=>[4,2,-5,-1,-3]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,-5,2,-4]=>[-4,2,-5,-1,-3]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,-5,-2,4]=>[4,-2,-5,-1,-3]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[-3,-1,-5,-2,-4]=>[-4,-2,-5,-1,-3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[3,1,5,4,2]=>[2,4,5,1,3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[3,1,5,4,-2]=>[-2,4,5,1,3]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,1,5,-4,2]=>[2,-4,5,1,3]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[3,1,5,-4,-2]=>[-2,-4,5,1,3]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[3,1,-5,4,2]=>[2,4,-5,1,3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[3,1,-5,4,-2]=>[-2,4,-5,1,3]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,1,-5,-4,2]=>[2,-4,-5,1,3]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[3,1,-5,-4,-2]=>[-2,-4,-5,1,3]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[3,-1,5,4,2]=>[2,4,5,-1,3]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[3,-1,5,4,-2]=>[-2,4,5,-1,3]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[3,-1,5,-4,2]=>[2,-4,5,-1,3]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[3,-1,5,-4,-2]=>[-2,-4,5,-1,3]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[3,-1,-5,4,2]=>[2,4,-5,-1,3]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[3,-1,-5,4,-2]=>[-2,4,-5,-1,3]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[3,-1,-5,-4,2]=>[2,-4,-5,-1,3]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[3,-1,-5,-4,-2]=>[-2,-4,-5,-1,3]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[-3,1,5,4,2]=>[2,4,5,1,-3]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-3,1,5,4,-2]=>[-2,4,5,1,-3]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,1,5,-4,2]=>[2,-4,5,1,-3]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-3,1,5,-4,-2]=>[-2,-4,5,1,-3]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-3,1,-5,4,2]=>[2,4,-5,1,-3]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[-3,1,-5,4,-2]=>[-2,4,-5,1,-3]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,1,-5,-4,2]=>[2,-4,-5,1,-3]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-3,1,-5,-4,-2]=>[-2,-4,-5,1,-3]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-3,-1,5,4,2]=>[2,4,5,-1,-3]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-3,-1,5,4,-2]=>[-2,4,5,-1,-3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,5,-4,2]=>[2,-4,5,-1,-3]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-3,-1,5,-4,-2]=>[-2,-4,5,-1,-3]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]
[-3,-1,-5,4,2]=>[2,4,-5,-1,-3]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-3,-1,-5,4,-2]=>[-2,4,-5,-1,-3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[-3,-1,-5,-4,2]=>[2,-4,-5,-1,-3]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-3,-1,-5,-4,-2]=>[-2,-4,-5,-1,-3]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]
[3,2,1,4,5]=>[5,4,1,2,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[3,2,1,4,-5]=>[-5,4,1,2,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[3,2,1,-4,5]=>[5,-4,1,2,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[3,2,1,-4,-5]=>[-5,-4,1,2,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[3,2,-1,4,5]=>[5,4,-1,2,3]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,2,-1,4,-5]=>[-5,4,-1,2,3]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,2,-1,-4,5]=>[5,-4,-1,2,3]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[3,2,-1,-4,-5]=>[-5,-4,-1,2,3]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[3,-2,1,4,5]=>[5,4,1,-2,3]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[3,-2,1,4,-5]=>[-5,4,1,-2,3]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[3,-2,1,-4,5]=>[5,-4,1,-2,3]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[3,-2,1,-4,-5]=>[-5,-4,1,-2,3]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[3,-2,-1,4,5]=>[5,4,-1,-2,3]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[3,-2,-1,4,-5]=>[-5,4,-1,-2,3]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[3,-2,-1,-4,5]=>[5,-4,-1,-2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[3,-2,-1,-4,-5]=>[-5,-4,-1,-2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[-3,2,1,4,-5]=>[-5,4,1,2,-3]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-3,2,1,-4,5]=>[5,-4,1,2,-3]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-3,2,1,-4,-5]=>[-5,-4,1,2,-3]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[-3,2,-1,4,5]=>[5,4,-1,2,-3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,2,-1,4,-5]=>[-5,4,-1,2,-3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,2,-1,-4,5]=>[5,-4,-1,2,-3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-3,2,-1,-4,-5]=>[-5,-4,-1,2,-3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-3,-2,1,4,5]=>[5,4,1,-2,-3]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-3,-2,1,4,-5]=>[-5,4,1,-2,-3]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-3,-2,1,-4,5]=>[5,-4,1,-2,-3]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[-3,-2,1,-4,-5]=>[-5,-4,1,-2,-3]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
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[-3,-2,-1,-4,5]=>[5,-4,-1,-2,-3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[-3,-2,-1,-4,-5]=>[-5,-4,-1,-2,-3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[3,2,1,5,4]=>[4,5,1,2,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[3,2,1,5,-4]=>[-4,5,1,2,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[3,2,1,-5,4]=>[4,-5,1,2,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[3,2,1,-5,-4]=>[-4,-5,1,2,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[3,2,-1,5,4]=>[4,5,-1,2,3]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[3,2,-1,5,-4]=>[-4,5,-1,2,3]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,2,-1,-5,4]=>[4,-5,-1,2,3]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[3,2,-1,-5,-4]=>[-4,-5,-1,2,3]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[3,-2,1,5,4]=>[4,5,1,-2,3]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[3,-2,1,5,-4]=>[-4,5,1,-2,3]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[3,-2,1,-5,4]=>[4,-5,1,-2,3]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[3,-2,1,-5,-4]=>[-4,-5,1,-2,3]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[3,-2,-1,5,4]=>[4,5,-1,-2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[3,-2,-1,5,-4]=>[-4,5,-1,-2,3]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[3,-2,-1,-5,4]=>[4,-5,-1,-2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[-3,2,1,-5,-4]=>[-4,-5,1,2,-3]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[-3,2,-1,5,4]=>[4,5,-1,2,-3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
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[-3,2,-1,-5,-4]=>[-4,-5,-1,2,-3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
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[-3,2,5,-4,1]=>[1,-4,5,2,-3]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[-3,2,5,-4,-1]=>[-1,-4,5,2,-3]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-3,2,-5,4,1]=>[1,4,-5,2,-3]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[-3,2,-5,4,-1]=>[-1,4,-5,2,-3]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[-3,2,-5,-4,1]=>[1,-4,-5,2,-3]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
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[-3,-2,5,4,1]=>[1,4,5,-2,-3]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
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[-3,-2,5,-4,1]=>[1,-4,5,-2,-3]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
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[3,4,1,-2,5]=>[5,-2,1,4,3]=>[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]
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[3,-4,1,-2,5]=>[5,-2,1,-4,3]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
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[3,-4,-1,-2,5]=>[5,-2,-1,-4,3]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
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[-3,4,1,-2,-5]=>[-5,-2,1,4,-3]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
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[-3,4,-1,-2,5]=>[5,-2,-1,4,-3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[-3,4,-1,-2,-5]=>[-5,-2,-1,4,-3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[-3,-4,1,2,5]=>[5,2,1,-4,-3]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
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[-3,-4,1,-2,5]=>[5,-2,1,-4,-3]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
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[3,-4,-5,-1,-2]=>[-2,-1,-5,-4,3]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
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[-3,4,5,1,-2]=>[-2,1,5,4,-3]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[-3,4,5,-1,2]=>[2,-1,5,4,-3]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]
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[-3,4,-5,1,-2]=>[-2,1,-5,4,-3]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[-3,4,-5,-1,2]=>[2,-1,-5,4,-3]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]
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[-3,-4,5,1,2]=>[2,1,5,-4,-3]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[-3,-4,5,1,-2]=>[-2,1,5,-4,-3]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[-3,-4,5,-1,2]=>[2,-1,5,-4,-3]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
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[3,4,5,2,1]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
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[3,4,-5,-2,-1]=>[-1,-2,-5,4,3]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
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[-3,-4,5,2,1]=>[1,2,5,-4,-3]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[-4,1,3,2,5]=>[5,2,3,1,-4]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-4,1,3,2,-5]=>[-5,2,3,1,-4]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[-4,1,3,-2,5]=>[5,-2,3,1,-4]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-4,1,3,-2,-5]=>[-5,-2,3,1,-4]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[-4,1,-3,2,5]=>[5,2,-3,1,-4]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-4,1,-3,2,-5]=>[-5,2,-3,1,-4]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[-4,1,-3,-2,5]=>[5,-2,-3,1,-4]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[-4,1,-3,-2,-5]=>[-5,-2,-3,1,-4]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[-4,-1,3,2,5]=>[5,2,3,-1,-4]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-4,-1,3,2,-5]=>[-5,2,3,-1,-4]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[-4,-1,3,-2,5]=>[5,-2,3,-1,-4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[-4,-1,3,-2,-5]=>[-5,-2,3,-1,-4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[-4,-1,-3,2,5]=>[5,2,-3,-1,-4]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[-4,-1,-3,2,-5]=>[-5,2,-3,-1,-4]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[-4,-1,-3,-2,5]=>[5,-2,-3,-1,-4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
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[4,1,3,5,2]=>[2,5,3,1,4]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[4,1,3,5,-2]=>[-2,5,3,1,4]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]
[4,1,3,-5,2]=>[2,-5,3,1,4]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[4,1,3,-5,-2]=>[-2,-5,3,1,4]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]
[4,1,-3,5,2]=>[2,5,-3,1,4]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[4,1,-3,5,-2]=>[-2,5,-3,1,4]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[4,1,-3,-5,2]=>[2,-5,-3,1,4]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[4,1,-3,-5,-2]=>[-2,-5,-3,1,4]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[4,-1,3,5,2]=>[2,5,3,-1,4]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[4,-1,3,5,-2]=>[-2,5,3,-1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[4,-1,3,-5,2]=>[2,-5,3,-1,4]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[4,-1,3,-5,-2]=>[-2,-5,3,-1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[4,-1,-3,5,2]=>[2,5,-3,-1,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[4,-1,-3,5,-2]=>[-2,5,-3,-1,4]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[4,-1,-3,-5,2]=>[2,-5,-3,-1,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[4,-1,-3,-5,-2]=>[-2,-5,-3,-1,4]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
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[-4,1,3,5,-2]=>[-2,5,3,1,-4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-4,1,3,-5,2]=>[2,-5,3,1,-4]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[-4,1,3,-5,-2]=>[-2,-5,3,1,-4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[-4,1,-3,5,2]=>[2,5,-3,1,-4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-4,1,-3,5,-2]=>[-2,5,-3,1,-4]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[-4,1,-3,-5,2]=>[2,-5,-3,1,-4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[-4,1,-3,-5,-2]=>[-2,-5,-3,1,-4]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[-4,-1,3,5,2]=>[2,5,3,-1,-4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-4,-1,3,5,-2]=>[-2,5,3,-1,-4]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]
[-4,-1,3,-5,2]=>[2,-5,3,-1,-4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[-4,-1,3,-5,-2]=>[-2,-5,3,-1,-4]=>[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]
[-4,-1,-3,5,2]=>[2,5,-3,-1,-4]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
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[-4,-1,-3,-5,2]=>[2,-5,-3,-1,-4]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
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[4,1,5,2,3]=>[3,2,5,1,4]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
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[4,1,5,-2,3]=>[3,-2,5,1,4]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[4,1,5,-2,-3]=>[-3,-2,5,1,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[4,1,-5,2,3]=>[3,2,-5,1,4]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[4,1,-5,2,-3]=>[-3,2,-5,1,4]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[4,1,-5,-2,3]=>[3,-2,-5,1,4]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[4,1,-5,-2,-3]=>[-3,-2,-5,1,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[4,-1,5,2,3]=>[3,2,5,-1,4]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[4,-1,5,2,-3]=>[-3,2,5,-1,4]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[4,-1,5,-2,3]=>[3,-2,5,-1,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
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[4,-1,-5,2,-3]=>[-3,2,-5,-1,4]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[4,-1,-5,-2,3]=>[3,-2,-5,-1,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
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[-4,1,5,-2,3]=>[3,-2,5,1,-4]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-4,1,5,-2,-3]=>[-3,-2,5,1,-4]=>[4,5,2,1,3]=>[[[.,[.,.]],.],[.,.]]
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[-4,-1,5,-2,3]=>[3,-2,5,-1,-4]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[-4,-1,5,-2,-3]=>[-3,-2,5,-1,-4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
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[-4,-1,-5,2,-3]=>[-3,2,-5,-1,-4]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
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[-4,-1,-5,-2,-3]=>[-3,-2,-5,-1,-4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[4,1,5,3,2]=>[2,3,5,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
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[4,1,5,-3,2]=>[2,-3,5,1,4]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[4,1,5,-3,-2]=>[-2,-3,5,1,4]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[4,1,-5,3,2]=>[2,3,-5,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[4,1,-5,3,-2]=>[-2,3,-5,1,4]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[4,1,-5,-3,2]=>[2,-3,-5,1,4]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[4,1,-5,-3,-2]=>[-2,-3,-5,1,4]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[4,-1,5,3,2]=>[2,3,5,-1,4]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[4,-1,5,3,-2]=>[-2,3,5,-1,4]=>[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]
[4,-1,5,-3,2]=>[2,-3,5,-1,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
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[4,-1,-5,3,2]=>[2,3,-5,-1,4]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
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[4,-1,-5,-3,2]=>[2,-3,-5,-1,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
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[-4,1,5,3,-2]=>[-2,3,5,1,-4]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[-4,1,5,-3,2]=>[2,-3,5,1,-4]=>[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]
[-4,1,5,-3,-2]=>[-2,-3,5,1,-4]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]
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[4,2,1,-3,5]=>[5,-3,1,2,4]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[4,2,1,-3,-5]=>[-5,-3,1,2,4]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
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[4,2,-1,3,-5]=>[-5,3,-1,2,4]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[4,2,-1,-3,5]=>[5,-3,-1,2,4]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
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[4,-2,1,-3,5]=>[5,-3,1,-2,4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[4,-2,1,-3,-5]=>[-5,-3,1,-2,4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
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[4,-2,-1,-3,5]=>[5,-3,-1,-2,4]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[4,-2,-1,-3,-5]=>[-5,-3,-1,-2,4]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
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[-4,2,1,-3,5]=>[5,-3,1,2,-4]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[-4,2,1,-3,-5]=>[-5,-3,1,2,-4]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
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[-4,2,-1,3,-5]=>[-5,3,-1,2,-4]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
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[-4,-2,1,-3,5]=>[5,-3,1,-2,-4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
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[4,2,1,-5,-3]=>[-3,-5,1,2,4]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[4,2,-1,5,3]=>[3,5,-1,2,4]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
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[-4,2,1,-5,3]=>[3,-5,1,2,-4]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
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[-4,2,-1,5,3]=>[3,5,-1,2,-4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
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[-4,3,1,-2,5]=>[5,-2,1,3,-4]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[-4,3,1,-2,-5]=>[-5,-2,1,3,-4]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[-4,3,-1,2,5]=>[5,2,-1,3,-4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[-4,3,-1,2,-5]=>[-5,2,-1,3,-4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[-4,3,-1,-2,5]=>[5,-2,-1,3,-4]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[-4,3,-1,-2,-5]=>[-5,-2,-1,3,-4]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[-4,-3,1,2,5]=>[5,2,1,-3,-4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-4,-3,1,2,-5]=>[-5,2,1,-3,-4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[-4,-3,1,-2,5]=>[5,-2,1,-3,-4]=>[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]
[-4,-3,1,-2,-5]=>[-5,-2,1,-3,-4]=>[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]
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[4,3,-1,5,2]=>[2,5,-1,3,4]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
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[4,-3,1,5,2]=>[2,5,1,-3,4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
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[4,-3,1,-5,2]=>[2,-5,1,-3,4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
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[4,-3,-1,5,2]=>[2,5,-1,-3,4]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
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[4,-3,-1,-5,2]=>[2,-5,-1,-3,4]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
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[-4,3,1,-5,2]=>[2,-5,1,3,-4]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
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[-4,3,-1,5,2]=>[2,5,-1,3,-4]=>[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]
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[-4,-3,1,-5,2]=>[2,-5,1,-3,-4]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
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[-5,4,3,-2,-1]=>[-1,-2,3,4,-5]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[-5,4,-3,2,1]=>[1,2,-3,4,-5]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
[-5,4,-3,2,-1]=>[-1,2,-3,4,-5]=>[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]]
[-5,4,-3,-2,1]=>[1,-2,-3,4,-5]=>[1,5,4,2,3]=>[.,[[[.,.],.],[.,.]]]
[-5,4,-3,-2,-1]=>[-1,-2,-3,4,-5]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[-5,-4,3,2,1]=>[1,2,3,-4,-5]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[-5,-4,3,2,-1]=>[-1,2,3,-4,-5]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[-5,-4,3,-2,1]=>[1,-2,3,-4,-5]=>[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]]
[-5,-4,3,-2,-1]=>[-1,-2,3,-4,-5]=>[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]]
[-5,-4,-3,2,1]=>[1,2,-3,-4,-5]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[-5,-4,-3,2,-1]=>[-1,2,-3,-4,-5]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[-5,-4,-3,-2,1]=>[1,-2,-3,-4,-5]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[-5,-4,-3,-2,-1]=>[-1,-2,-3,-4,-5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
Map
reverse
Description
The reversal of a signed permutation.
Map
standardize
Description
Return the standardization of the signed permutation, where 1 is the smallest and -1 the largest element.
Let $\pi\in\mathfrak H_n$ be a signed permutation. Assuming the order $1 < \dots < n < -n < \dots < -1$, this map returns the permutation in $\mathfrak S_n$ which is order isomorphic to $\pi(1),\dots,\pi(n)$.
Let $\pi\in\mathfrak H_n$ be a signed permutation. Assuming the order $1 < \dots < n < -n < \dots < -1$, this map returns the permutation in $\mathfrak S_n$ which is order isomorphic to $\pi(1),\dots,\pi(n)$.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
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