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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001817
-----------------------------------------------------------------------------
Collection: Signed permutations
-----------------------------------------------------------------------------
Description: The number of flag weak exceedances of a signed permutation.
This is the number of negative entries plus twice the number of weak exceedances of the signed permutation.
-----------------------------------------------------------------------------
References: [1] Eu, S.-P., Fu, T.-S., Hsu, H.-C., Liao, H.-C. Signed Countings of types B and D permutations and $t,q$-Euler Numbers [[arXiv:1708.05518]]
-----------------------------------------------------------------------------
Code:
def statistic(pi):
neg = sum(1 for a in pi if a < 0)
wex = sum(1 for i, a in enumerate(pi, 1) if a >= i)
return 2*wex + neg
-----------------------------------------------------------------------------
Statistic values:
[1] => 2
[-1] => 1
[1,2] => 4
[1,-2] => 3
[-1,2] => 3
[-1,-2] => 2
[2,1] => 2
[2,-1] => 3
[-2,1] => 1
[-2,-1] => 2
[1,2,3] => 6
[1,2,-3] => 5
[1,-2,3] => 5
[1,-2,-3] => 4
[-1,2,3] => 5
[-1,2,-3] => 4
[-1,-2,3] => 4
[-1,-2,-3] => 3
[1,3,2] => 4
[1,3,-2] => 5
[1,-3,2] => 3
[1,-3,-2] => 4
[-1,3,2] => 3
[-1,3,-2] => 4
[-1,-3,2] => 2
[-1,-3,-2] => 3
[2,1,3] => 4
[2,1,-3] => 3
[2,-1,3] => 5
[2,-1,-3] => 4
[-2,1,3] => 3
[-2,1,-3] => 2
[-2,-1,3] => 4
[-2,-1,-3] => 3
[2,3,1] => 4
[2,3,-1] => 5
[2,-3,1] => 3
[2,-3,-1] => 4
[-2,3,1] => 3
[-2,3,-1] => 4
[-2,-3,1] => 2
[-2,-3,-1] => 3
[3,1,2] => 2
[3,1,-2] => 3
[3,-1,2] => 3
[3,-1,-2] => 4
[-3,1,2] => 1
[-3,1,-2] => 2
[-3,-1,2] => 2
[-3,-1,-2] => 3
[3,2,1] => 4
[3,2,-1] => 5
[3,-2,1] => 3
[3,-2,-1] => 4
[-3,2,1] => 3
[-3,2,-1] => 4
[-3,-2,1] => 2
[-3,-2,-1] => 3
[1,2,3,4] => 8
[1,2,3,-4] => 7
[1,2,-3,4] => 7
[1,2,-3,-4] => 6
[1,-2,3,4] => 7
[1,-2,3,-4] => 6
[1,-2,-3,4] => 6
[1,-2,-3,-4] => 5
[-1,2,3,4] => 7
[-1,2,3,-4] => 6
[-1,2,-3,4] => 6
[-1,2,-3,-4] => 5
[-1,-2,3,4] => 6
[-1,-2,3,-4] => 5
[-1,-2,-3,4] => 5
[-1,-2,-3,-4] => 4
[1,2,4,3] => 6
[1,2,4,-3] => 7
[1,2,-4,3] => 5
[1,2,-4,-3] => 6
[1,-2,4,3] => 5
[1,-2,4,-3] => 6
[1,-2,-4,3] => 4
[1,-2,-4,-3] => 5
[-1,2,4,3] => 5
[-1,2,4,-3] => 6
[-1,2,-4,3] => 4
[-1,2,-4,-3] => 5
[-1,-2,4,3] => 4
[-1,-2,4,-3] => 5
[-1,-2,-4,3] => 3
[-1,-2,-4,-3] => 4
[1,3,2,4] => 6
[1,3,2,-4] => 5
[1,3,-2,4] => 7
[1,3,-2,-4] => 6
[1,-3,2,4] => 5
[1,-3,2,-4] => 4
[1,-3,-2,4] => 6
[1,-3,-2,-4] => 5
[-1,3,2,4] => 5
[-1,3,2,-4] => 4
[-1,3,-2,4] => 6
[-1,3,-2,-4] => 5
[-1,-3,2,4] => 4
[-1,-3,2,-4] => 3
[-1,-3,-2,4] => 5
[-1,-3,-2,-4] => 4
[1,3,4,2] => 6
[1,3,4,-2] => 7
[1,3,-4,2] => 5
[1,3,-4,-2] => 6
[1,-3,4,2] => 5
[1,-3,4,-2] => 6
[1,-3,-4,2] => 4
[1,-3,-4,-2] => 5
[-1,3,4,2] => 5
[-1,3,4,-2] => 6
[-1,3,-4,2] => 4
[-1,3,-4,-2] => 5
[-1,-3,4,2] => 4
[-1,-3,4,-2] => 5
[-1,-3,-4,2] => 3
[-1,-3,-4,-2] => 4
[1,4,2,3] => 4
[1,4,2,-3] => 5
[1,4,-2,3] => 5
[1,4,-2,-3] => 6
[1,-4,2,3] => 3
[1,-4,2,-3] => 4
[1,-4,-2,3] => 4
[1,-4,-2,-3] => 5
[-1,4,2,3] => 3
[-1,4,2,-3] => 4
[-1,4,-2,3] => 4
[-1,4,-2,-3] => 5
[-1,-4,2,3] => 2
[-1,-4,2,-3] => 3
[-1,-4,-2,3] => 3
[-1,-4,-2,-3] => 4
[1,4,3,2] => 6
[1,4,3,-2] => 7
[1,4,-3,2] => 5
[1,4,-3,-2] => 6
[1,-4,3,2] => 5
[1,-4,3,-2] => 6
[1,-4,-3,2] => 4
[1,-4,-3,-2] => 5
[-1,4,3,2] => 5
[-1,4,3,-2] => 6
[-1,4,-3,2] => 4
[-1,4,-3,-2] => 5
[-1,-4,3,2] => 4
[-1,-4,3,-2] => 5
[-1,-4,-3,2] => 3
[-1,-4,-3,-2] => 4
[2,1,3,4] => 6
[2,1,3,-4] => 5
[2,1,-3,4] => 5
[2,1,-3,-4] => 4
[2,-1,3,4] => 7
[2,-1,3,-4] => 6
[2,-1,-3,4] => 6
[2,-1,-3,-4] => 5
[-2,1,3,4] => 5
[-2,1,3,-4] => 4
[-2,1,-3,4] => 4
[-2,1,-3,-4] => 3
[-2,-1,3,4] => 6
[-2,-1,3,-4] => 5
[-2,-1,-3,4] => 5
[-2,-1,-3,-4] => 4
[2,1,4,3] => 4
[2,1,4,-3] => 5
[2,1,-4,3] => 3
[2,1,-4,-3] => 4
[2,-1,4,3] => 5
[2,-1,4,-3] => 6
[2,-1,-4,3] => 4
[2,-1,-4,-3] => 5
[-2,1,4,3] => 3
[-2,1,4,-3] => 4
[-2,1,-4,3] => 2
[-2,1,-4,-3] => 3
[-2,-1,4,3] => 4
[-2,-1,4,-3] => 5
[-2,-1,-4,3] => 3
[-2,-1,-4,-3] => 4
[2,3,1,4] => 6
[2,3,1,-4] => 5
[2,3,-1,4] => 7
[2,3,-1,-4] => 6
[2,-3,1,4] => 5
[2,-3,1,-4] => 4
[2,-3,-1,4] => 6
[2,-3,-1,-4] => 5
[-2,3,1,4] => 5
[-2,3,1,-4] => 4
[-2,3,-1,4] => 6
[-2,3,-1,-4] => 5
[-2,-3,1,4] => 4
[-2,-3,1,-4] => 3
[-2,-3,-1,4] => 5
[-2,-3,-1,-4] => 4
[2,3,4,1] => 6
[2,3,4,-1] => 7
[2,3,-4,1] => 5
[2,3,-4,-1] => 6
[2,-3,4,1] => 5
[2,-3,4,-1] => 6
[2,-3,-4,1] => 4
[2,-3,-4,-1] => 5
[-2,3,4,1] => 5
[-2,3,4,-1] => 6
[-2,3,-4,1] => 4
[-2,3,-4,-1] => 5
[-2,-3,4,1] => 4
[-2,-3,4,-1] => 5
[-2,-3,-4,1] => 3
[-2,-3,-4,-1] => 4
[2,4,1,3] => 4
[2,4,1,-3] => 5
[2,4,-1,3] => 5
[2,4,-1,-3] => 6
[2,-4,1,3] => 3
[2,-4,1,-3] => 4
[2,-4,-1,3] => 4
[2,-4,-1,-3] => 5
[-2,4,1,3] => 3
[-2,4,1,-3] => 4
[-2,4,-1,3] => 4
[-2,4,-1,-3] => 5
[-2,-4,1,3] => 2
[-2,-4,1,-3] => 3
[-2,-4,-1,3] => 3
[-2,-4,-1,-3] => 4
[2,4,3,1] => 6
[2,4,3,-1] => 7
[2,4,-3,1] => 5
[2,4,-3,-1] => 6
[2,-4,3,1] => 5
[2,-4,3,-1] => 6
[2,-4,-3,1] => 4
[2,-4,-3,-1] => 5
[-2,4,3,1] => 5
[-2,4,3,-1] => 6
[-2,4,-3,1] => 4
[-2,4,-3,-1] => 5
[-2,-4,3,1] => 4
[-2,-4,3,-1] => 5
[-2,-4,-3,1] => 3
[-2,-4,-3,-1] => 4
[3,1,2,4] => 4
[3,1,2,-4] => 3
[3,1,-2,4] => 5
[3,1,-2,-4] => 4
[3,-1,2,4] => 5
[3,-1,2,-4] => 4
[3,-1,-2,4] => 6
[3,-1,-2,-4] => 5
[-3,1,2,4] => 3
[-3,1,2,-4] => 2
[-3,1,-2,4] => 4
[-3,1,-2,-4] => 3
[-3,-1,2,4] => 4
[-3,-1,2,-4] => 3
[-3,-1,-2,4] => 5
[-3,-1,-2,-4] => 4
[3,1,4,2] => 4
[3,1,4,-2] => 5
[3,1,-4,2] => 3
[3,1,-4,-2] => 4
[3,-1,4,2] => 5
[3,-1,4,-2] => 6
[3,-1,-4,2] => 4
[3,-1,-4,-2] => 5
[-3,1,4,2] => 3
[-3,1,4,-2] => 4
[-3,1,-4,2] => 2
[-3,1,-4,-2] => 3
[-3,-1,4,2] => 4
[-3,-1,4,-2] => 5
[-3,-1,-4,2] => 3
[-3,-1,-4,-2] => 4
[3,2,1,4] => 6
[3,2,1,-4] => 5
[3,2,-1,4] => 7
[3,2,-1,-4] => 6
[3,-2,1,4] => 5
[3,-2,1,-4] => 4
[3,-2,-1,4] => 6
[3,-2,-1,-4] => 5
[-3,2,1,4] => 5
[-3,2,1,-4] => 4
[-3,2,-1,4] => 6
[-3,2,-1,-4] => 5
[-3,-2,1,4] => 4
[-3,-2,1,-4] => 3
[-3,-2,-1,4] => 5
[-3,-2,-1,-4] => 4
[3,2,4,1] => 6
[3,2,4,-1] => 7
[3,2,-4,1] => 5
[3,2,-4,-1] => 6
[3,-2,4,1] => 5
[3,-2,4,-1] => 6
[3,-2,-4,1] => 4
[3,-2,-4,-1] => 5
[-3,2,4,1] => 5
[-3,2,4,-1] => 6
[-3,2,-4,1] => 4
[-3,2,-4,-1] => 5
[-3,-2,4,1] => 4
[-3,-2,4,-1] => 5
[-3,-2,-4,1] => 3
[-3,-2,-4,-1] => 4
[3,4,1,2] => 4
[3,4,1,-2] => 5
[3,4,-1,2] => 5
[3,4,-1,-2] => 6
[3,-4,1,2] => 3
[3,-4,1,-2] => 4
[3,-4,-1,2] => 4
[3,-4,-1,-2] => 5
[-3,4,1,2] => 3
[-3,4,1,-2] => 4
[-3,4,-1,2] => 4
[-3,4,-1,-2] => 5
[-3,-4,1,2] => 2
[-3,-4,1,-2] => 3
[-3,-4,-1,2] => 3
[-3,-4,-1,-2] => 4
[3,4,2,1] => 4
[3,4,2,-1] => 5
[3,4,-2,1] => 5
[3,4,-2,-1] => 6
[3,-4,2,1] => 3
[3,-4,2,-1] => 4
[3,-4,-2,1] => 4
[3,-4,-2,-1] => 5
[-3,4,2,1] => 3
[-3,4,2,-1] => 4
[-3,4,-2,1] => 4
[-3,4,-2,-1] => 5
[-3,-4,2,1] => 2
[-3,-4,2,-1] => 3
[-3,-4,-2,1] => 3
[-3,-4,-2,-1] => 4
[4,1,2,3] => 2
[4,1,2,-3] => 3
[4,1,-2,3] => 3
[4,1,-2,-3] => 4
[4,-1,2,3] => 3
[4,-1,2,-3] => 4
[4,-1,-2,3] => 4
[4,-1,-2,-3] => 5
[-4,1,2,3] => 1
[-4,1,2,-3] => 2
[-4,1,-2,3] => 2
[-4,1,-2,-3] => 3
[-4,-1,2,3] => 2
[-4,-1,2,-3] => 3
[-4,-1,-2,3] => 3
[-4,-1,-2,-3] => 4
[4,1,3,2] => 4
[4,1,3,-2] => 5
[4,1,-3,2] => 3
[4,1,-3,-2] => 4
[4,-1,3,2] => 5
[4,-1,3,-2] => 6
[4,-1,-3,2] => 4
[4,-1,-3,-2] => 5
[-4,1,3,2] => 3
[-4,1,3,-2] => 4
[-4,1,-3,2] => 2
[-4,1,-3,-2] => 3
[-4,-1,3,2] => 4
[-4,-1,3,-2] => 5
[-4,-1,-3,2] => 3
[-4,-1,-3,-2] => 4
[4,2,1,3] => 4
[4,2,1,-3] => 5
[4,2,-1,3] => 5
[4,2,-1,-3] => 6
[4,-2,1,3] => 3
[4,-2,1,-3] => 4
[4,-2,-1,3] => 4
[4,-2,-1,-3] => 5
[-4,2,1,3] => 3
[-4,2,1,-3] => 4
[-4,2,-1,3] => 4
[-4,2,-1,-3] => 5
[-4,-2,1,3] => 2
[-4,-2,1,-3] => 3
[-4,-2,-1,3] => 3
[-4,-2,-1,-3] => 4
[4,2,3,1] => 6
[4,2,3,-1] => 7
[4,2,-3,1] => 5
[4,2,-3,-1] => 6
[4,-2,3,1] => 5
[4,-2,3,-1] => 6
[4,-2,-3,1] => 4
[4,-2,-3,-1] => 5
[-4,2,3,1] => 5
[-4,2,3,-1] => 6
[-4,2,-3,1] => 4
[-4,2,-3,-1] => 5
[-4,-2,3,1] => 4
[-4,-2,3,-1] => 5
[-4,-2,-3,1] => 3
[-4,-2,-3,-1] => 4
[4,3,1,2] => 4
[4,3,1,-2] => 5
[4,3,-1,2] => 5
[4,3,-1,-2] => 6
[4,-3,1,2] => 3
[4,-3,1,-2] => 4
[4,-3,-1,2] => 4
[4,-3,-1,-2] => 5
[-4,3,1,2] => 3
[-4,3,1,-2] => 4
[-4,3,-1,2] => 4
[-4,3,-1,-2] => 5
[-4,-3,1,2] => 2
[-4,-3,1,-2] => 3
[-4,-3,-1,2] => 3
[-4,-3,-1,-2] => 4
[4,3,2,1] => 4
[4,3,2,-1] => 5
[4,3,-2,1] => 5
[4,3,-2,-1] => 6
[4,-3,2,1] => 3
[4,-3,2,-1] => 4
[4,-3,-2,1] => 4
[4,-3,-2,-1] => 5
[-4,3,2,1] => 3
[-4,3,2,-1] => 4
[-4,3,-2,1] => 4
[-4,3,-2,-1] => 5
[-4,-3,2,1] => 2
[-4,-3,2,-1] => 3
[-4,-3,-2,1] => 3
[-4,-3,-2,-1] => 4
[1,2,3,4,5] => 10
[1,2,3,4,-5] => 9
[1,2,3,-4,5] => 9
[1,2,3,-4,-5] => 8
[1,2,-3,4,5] => 9
[1,2,-3,4,-5] => 8
[1,2,-3,-4,5] => 8
[1,2,-3,-4,-5] => 7
[1,-2,3,4,5] => 9
[1,-2,3,4,-5] => 8
[1,-2,3,-4,5] => 8
[1,-2,3,-4,-5] => 7
[1,-2,-3,4,5] => 8
[1,-2,-3,4,-5] => 7
[1,-2,-3,-4,5] => 7
[1,-2,-3,-4,-5] => 6
[-1,2,3,4,5] => 9
[-1,2,3,4,-5] => 8
[-1,2,3,-4,5] => 8
[-1,2,3,-4,-5] => 7
[-1,2,-3,4,5] => 8
[-1,2,-3,4,-5] => 7
[-1,2,-3,-4,5] => 7
[-1,2,-3,-4,-5] => 6
[-1,-2,3,4,5] => 8
[-1,-2,3,4,-5] => 7
[-1,-2,3,-4,5] => 7
[-1,-2,3,-4,-5] => 6
[-1,-2,-3,4,5] => 7
[-1,-2,-3,4,-5] => 6
[-1,-2,-3,-4,5] => 6
[-1,-2,-3,-4,-5] => 5
[1,2,3,5,4] => 8
[1,2,3,5,-4] => 9
[1,2,3,-5,4] => 7
[1,2,3,-5,-4] => 8
[1,2,-3,5,4] => 7
[1,2,-3,5,-4] => 8
[1,2,-3,-5,4] => 6
[1,2,-3,-5,-4] => 7
[1,-2,3,5,4] => 7
[1,-2,3,5,-4] => 8
[1,-2,3,-5,4] => 6
[1,-2,3,-5,-4] => 7
[1,-2,-3,5,4] => 6
[1,-2,-3,5,-4] => 7
[1,-2,-3,-5,4] => 5
[1,-2,-3,-5,-4] => 6
[-1,2,3,5,4] => 7
[-1,2,3,5,-4] => 8
[-1,2,3,-5,4] => 6
[-1,2,3,-5,-4] => 7
[-1,2,-3,5,4] => 6
[-1,2,-3,5,-4] => 7
[-1,2,-3,-5,4] => 5
[-1,2,-3,-5,-4] => 6
[-1,-2,3,5,4] => 6
[-1,-2,3,5,-4] => 7
[-1,-2,3,-5,4] => 5
[-1,-2,3,-5,-4] => 6
[-1,-2,-3,5,4] => 5
[-1,-2,-3,5,-4] => 6
[-1,-2,-3,-5,4] => 4
[-1,-2,-3,-5,-4] => 5
[1,2,4,3,5] => 8
[1,2,4,3,-5] => 7
[1,2,4,-3,5] => 9
[1,2,4,-3,-5] => 8
[1,2,-4,3,5] => 7
[1,2,-4,3,-5] => 6
[1,2,-4,-3,5] => 8
[1,2,-4,-3,-5] => 7
[1,-2,4,3,5] => 7
[1,-2,4,3,-5] => 6
[1,-2,4,-3,5] => 8
[1,-2,4,-3,-5] => 7
[1,-2,-4,3,5] => 6
[1,-2,-4,3,-5] => 5
[1,-2,-4,-3,5] => 7
[1,-2,-4,-3,-5] => 6
[-1,2,4,3,5] => 7
[-1,2,4,3,-5] => 6
[-1,2,4,-3,5] => 8
[-1,2,4,-3,-5] => 7
[-1,2,-4,3,5] => 6
[-1,2,-4,3,-5] => 5
[-1,2,-4,-3,5] => 7
[-1,2,-4,-3,-5] => 6
[-1,-2,4,3,5] => 6
[-1,-2,4,3,-5] => 5
[-1,-2,4,-3,5] => 7
[-1,-2,4,-3,-5] => 6
[-1,-2,-4,3,5] => 5
[-1,-2,-4,3,-5] => 4
[-1,-2,-4,-3,5] => 6
[-1,-2,-4,-3,-5] => 5
[1,2,4,5,3] => 8
[1,2,4,5,-3] => 9
[1,2,4,-5,3] => 7
[1,2,4,-5,-3] => 8
[1,2,-4,5,3] => 7
[1,2,-4,5,-3] => 8
[1,2,-4,-5,3] => 6
[1,2,-4,-5,-3] => 7
[1,-2,4,5,3] => 7
[1,-2,4,5,-3] => 8
[1,-2,4,-5,3] => 6
[1,-2,4,-5,-3] => 7
[1,-2,-4,5,3] => 6
[1,-2,-4,5,-3] => 7
[1,-2,-4,-5,3] => 5
[1,-2,-4,-5,-3] => 6
[-1,2,4,5,3] => 7
[-1,2,4,5,-3] => 8
[-1,2,4,-5,3] => 6
[-1,2,4,-5,-3] => 7
[-1,2,-4,5,3] => 6
[-1,2,-4,5,-3] => 7
[-1,2,-4,-5,3] => 5
[-1,2,-4,-5,-3] => 6
[-1,-2,4,5,3] => 6
[-1,-2,4,5,-3] => 7
[-1,-2,4,-5,3] => 5
[-1,-2,4,-5,-3] => 6
[-1,-2,-4,5,3] => 5
[-1,-2,-4,5,-3] => 6
[-1,-2,-4,-5,3] => 4
[-1,-2,-4,-5,-3] => 5
[1,2,5,3,4] => 6
[1,2,5,3,-4] => 7
[1,2,5,-3,4] => 7
[1,2,5,-3,-4] => 8
[1,2,-5,3,4] => 5
[1,2,-5,3,-4] => 6
[1,2,-5,-3,4] => 6
[1,2,-5,-3,-4] => 7
[1,-2,5,3,4] => 5
[1,-2,5,3,-4] => 6
[1,-2,5,-3,4] => 6
[1,-2,5,-3,-4] => 7
[1,-2,-5,3,4] => 4
[1,-2,-5,3,-4] => 5
[1,-2,-5,-3,4] => 5
[1,-2,-5,-3,-4] => 6
[-1,2,5,3,4] => 5
[-1,2,5,3,-4] => 6
[-1,2,5,-3,4] => 6
[-1,2,5,-3,-4] => 7
[-1,2,-5,3,4] => 4
[-1,2,-5,3,-4] => 5
[-1,2,-5,-3,4] => 5
[-1,2,-5,-3,-4] => 6
[-1,-2,5,3,4] => 4
[-1,-2,5,3,-4] => 5
[-1,-2,5,-3,4] => 5
[-1,-2,5,-3,-4] => 6
[-1,-2,-5,3,4] => 3
[-1,-2,-5,3,-4] => 4
[-1,-2,-5,-3,4] => 4
[-1,-2,-5,-3,-4] => 5
[1,2,5,4,3] => 8
[1,2,5,4,-3] => 9
[1,2,5,-4,3] => 7
[1,2,5,-4,-3] => 8
[1,2,-5,4,3] => 7
[1,2,-5,4,-3] => 8
[1,2,-5,-4,3] => 6
[1,2,-5,-4,-3] => 7
[1,-2,5,4,3] => 7
[1,-2,5,4,-3] => 8
[1,-2,5,-4,3] => 6
[1,-2,5,-4,-3] => 7
[1,-2,-5,4,3] => 6
[1,-2,-5,4,-3] => 7
[1,-2,-5,-4,3] => 5
[1,-2,-5,-4,-3] => 6
[-1,2,5,4,3] => 7
[-1,2,5,4,-3] => 8
[-1,2,5,-4,3] => 6
[-1,2,5,-4,-3] => 7
[-1,2,-5,4,3] => 6
[-1,2,-5,4,-3] => 7
[-1,2,-5,-4,3] => 5
[-1,2,-5,-4,-3] => 6
[-1,-2,5,4,3] => 6
[-1,-2,5,4,-3] => 7
[-1,-2,5,-4,3] => 5
[-1,-2,5,-4,-3] => 6
[-1,-2,-5,4,3] => 5
[-1,-2,-5,4,-3] => 6
[-1,-2,-5,-4,3] => 4
[-1,-2,-5,-4,-3] => 5
[1,3,2,4,5] => 8
[1,3,2,4,-5] => 7
[1,3,2,-4,5] => 7
[1,3,2,-4,-5] => 6
[1,3,-2,4,5] => 9
[1,3,-2,4,-5] => 8
[1,3,-2,-4,5] => 8
[1,3,-2,-4,-5] => 7
[1,-3,2,4,5] => 7
[1,-3,2,4,-5] => 6
[1,-3,2,-4,5] => 6
[1,-3,2,-4,-5] => 5
[1,-3,-2,4,5] => 8
[1,-3,-2,4,-5] => 7
[1,-3,-2,-4,5] => 7
[1,-3,-2,-4,-5] => 6
[-1,3,2,4,5] => 7
[-1,3,2,4,-5] => 6
[-1,3,2,-4,5] => 6
[-1,3,2,-4,-5] => 5
[-1,3,-2,4,5] => 8
[-1,3,-2,4,-5] => 7
[-1,3,-2,-4,5] => 7
[-1,3,-2,-4,-5] => 6
[-1,-3,2,4,5] => 6
[-1,-3,2,4,-5] => 5
[-1,-3,2,-4,5] => 5
[-1,-3,2,-4,-5] => 4
[-1,-3,-2,4,5] => 7
[-1,-3,-2,4,-5] => 6
[-1,-3,-2,-4,5] => 6
[-1,-3,-2,-4,-5] => 5
[1,3,2,5,4] => 6
[1,3,2,5,-4] => 7
[1,3,2,-5,4] => 5
[1,3,2,-5,-4] => 6
[1,3,-2,5,4] => 7
[1,3,-2,5,-4] => 8
[1,3,-2,-5,4] => 6
[1,3,-2,-5,-4] => 7
[1,-3,2,5,4] => 5
[1,-3,2,5,-4] => 6
[1,-3,2,-5,4] => 4
[1,-3,2,-5,-4] => 5
[1,-3,-2,5,4] => 6
[1,-3,-2,5,-4] => 7
[1,-3,-2,-5,4] => 5
[1,-3,-2,-5,-4] => 6
[-1,3,2,5,4] => 5
[-1,3,2,5,-4] => 6
[-1,3,2,-5,4] => 4
[-1,3,2,-5,-4] => 5
[-1,3,-2,5,4] => 6
[-1,3,-2,5,-4] => 7
[-1,3,-2,-5,4] => 5
[-1,3,-2,-5,-4] => 6
[-1,-3,2,5,4] => 4
[-1,-3,2,5,-4] => 5
[-1,-3,2,-5,4] => 3
[-1,-3,2,-5,-4] => 4
[-1,-3,-2,5,4] => 5
[-1,-3,-2,5,-4] => 6
[-1,-3,-2,-5,4] => 4
[-1,-3,-2,-5,-4] => 5
[1,3,4,2,5] => 8
[1,3,4,2,-5] => 7
[1,3,4,-2,5] => 9
[1,3,4,-2,-5] => 8
[1,3,-4,2,5] => 7
[1,3,-4,2,-5] => 6
[1,3,-4,-2,5] => 8
[1,3,-4,-2,-5] => 7
[1,-3,4,2,5] => 7
[1,-3,4,2,-5] => 6
[1,-3,4,-2,5] => 8
[1,-3,4,-2,-5] => 7
[1,-3,-4,2,5] => 6
[1,-3,-4,2,-5] => 5
[1,-3,-4,-2,5] => 7
[1,-3,-4,-2,-5] => 6
[-1,3,4,2,5] => 7
[-1,3,4,2,-5] => 6
[-1,3,4,-2,5] => 8
[-1,3,4,-2,-5] => 7
[-1,3,-4,2,5] => 6
[-1,3,-4,2,-5] => 5
[-1,3,-4,-2,5] => 7
[-1,3,-4,-2,-5] => 6
[-1,-3,4,2,5] => 6
[-1,-3,4,2,-5] => 5
[-1,-3,4,-2,5] => 7
[-1,-3,4,-2,-5] => 6
[-1,-3,-4,2,5] => 5
[-1,-3,-4,2,-5] => 4
[-1,-3,-4,-2,5] => 6
[-1,-3,-4,-2,-5] => 5
[1,3,4,5,2] => 8
[1,3,4,5,-2] => 9
[1,3,4,-5,2] => 7
[1,3,4,-5,-2] => 8
[1,3,-4,5,2] => 7
[1,3,-4,5,-2] => 8
[1,3,-4,-5,2] => 6
[1,3,-4,-5,-2] => 7
[1,-3,4,5,2] => 7
[1,-3,4,5,-2] => 8
[1,-3,4,-5,2] => 6
[1,-3,4,-5,-2] => 7
[1,-3,-4,5,2] => 6
[1,-3,-4,5,-2] => 7
[1,-3,-4,-5,2] => 5
[1,-3,-4,-5,-2] => 6
[-1,3,4,5,2] => 7
[-1,3,4,5,-2] => 8
[-1,3,4,-5,2] => 6
[-1,3,4,-5,-2] => 7
[-1,3,-4,5,2] => 6
[-1,3,-4,5,-2] => 7
[-1,3,-4,-5,2] => 5
[-1,3,-4,-5,-2] => 6
[-1,-3,4,5,2] => 6
[-1,-3,4,5,-2] => 7
[-1,-3,4,-5,2] => 5
[-1,-3,4,-5,-2] => 6
[-1,-3,-4,5,2] => 5
[-1,-3,-4,5,-2] => 6
[-1,-3,-4,-5,2] => 4
[-1,-3,-4,-5,-2] => 5
[1,3,5,2,4] => 6
[1,3,5,2,-4] => 7
[1,3,5,-2,4] => 7
[1,3,5,-2,-4] => 8
[1,3,-5,2,4] => 5
[1,3,-5,2,-4] => 6
[1,3,-5,-2,4] => 6
[1,3,-5,-2,-4] => 7
[1,-3,5,2,4] => 5
[1,-3,5,2,-4] => 6
[1,-3,5,-2,4] => 6
[1,-3,5,-2,-4] => 7
[1,-3,-5,2,4] => 4
[1,-3,-5,2,-4] => 5
[1,-3,-5,-2,4] => 5
[1,-3,-5,-2,-4] => 6
[-1,3,5,2,4] => 5
[-1,3,5,2,-4] => 6
[-1,3,5,-2,4] => 6
[-1,3,5,-2,-4] => 7
[-1,3,-5,2,4] => 4
[-1,3,-5,2,-4] => 5
[-1,3,-5,-2,4] => 5
[-1,3,-5,-2,-4] => 6
[-1,-3,5,2,4] => 4
[-1,-3,5,2,-4] => 5
[-1,-3,5,-2,4] => 5
[-1,-3,5,-2,-4] => 6
[-1,-3,-5,2,4] => 3
[-1,-3,-5,2,-4] => 4
[-1,-3,-5,-2,4] => 4
[-1,-3,-5,-2,-4] => 5
[1,3,5,4,2] => 8
[1,3,5,4,-2] => 9
[1,3,5,-4,2] => 7
[1,3,5,-4,-2] => 8
[1,3,-5,4,2] => 7
[1,3,-5,4,-2] => 8
[1,3,-5,-4,2] => 6
[1,3,-5,-4,-2] => 7
[1,-3,5,4,2] => 7
[1,-3,5,4,-2] => 8
[1,-3,5,-4,2] => 6
[1,-3,5,-4,-2] => 7
[1,-3,-5,4,2] => 6
[1,-3,-5,4,-2] => 7
[1,-3,-5,-4,2] => 5
[1,-3,-5,-4,-2] => 6
[-1,3,5,4,2] => 7
[-1,3,5,4,-2] => 8
[-1,3,5,-4,2] => 6
[-1,3,5,-4,-2] => 7
[-1,3,-5,4,2] => 6
[-1,3,-5,4,-2] => 7
[-1,3,-5,-4,2] => 5
[-1,3,-5,-4,-2] => 6
[-1,-3,5,4,2] => 6
[-1,-3,5,4,-2] => 7
[-1,-3,5,-4,2] => 5
[-1,-3,5,-4,-2] => 6
[-1,-3,-5,4,2] => 5
[-1,-3,-5,4,-2] => 6
[-1,-3,-5,-4,2] => 4
[-1,-3,-5,-4,-2] => 5
[1,4,2,3,5] => 6
[1,4,2,3,-5] => 5
[1,4,2,-3,5] => 7
[1,4,2,-3,-5] => 6
[1,4,-2,3,5] => 7
[1,4,-2,3,-5] => 6
[1,4,-2,-3,5] => 8
[1,4,-2,-3,-5] => 7
[1,-4,2,3,5] => 5
[1,-4,2,3,-5] => 4
[1,-4,2,-3,5] => 6
[1,-4,2,-3,-5] => 5
[1,-4,-2,3,5] => 6
[1,-4,-2,3,-5] => 5
[1,-4,-2,-3,5] => 7
[1,-4,-2,-3,-5] => 6
[-1,4,2,3,5] => 5
[-1,4,2,3,-5] => 4
[-1,4,2,-3,5] => 6
[-1,4,2,-3,-5] => 5
[-1,4,-2,3,5] => 6
[-1,4,-2,3,-5] => 5
[-1,4,-2,-3,5] => 7
[-1,4,-2,-3,-5] => 6
[-1,-4,2,3,5] => 4
[-1,-4,2,3,-5] => 3
[-1,-4,2,-3,5] => 5
[-1,-4,2,-3,-5] => 4
[-1,-4,-2,3,5] => 5
[-1,-4,-2,3,-5] => 4
[-1,-4,-2,-3,5] => 6
[-1,-4,-2,-3,-5] => 5
[1,4,2,5,3] => 6
[1,4,2,5,-3] => 7
[1,4,2,-5,3] => 5
[1,4,2,-5,-3] => 6
[1,4,-2,5,3] => 7
[1,4,-2,5,-3] => 8
[1,4,-2,-5,3] => 6
[1,4,-2,-5,-3] => 7
[1,-4,2,5,3] => 5
[1,-4,2,5,-3] => 6
[1,-4,2,-5,3] => 4
[1,-4,2,-5,-3] => 5
[1,-4,-2,5,3] => 6
[1,-4,-2,5,-3] => 7
[1,-4,-2,-5,3] => 5
[1,-4,-2,-5,-3] => 6
[-1,4,2,5,3] => 5
[-1,4,2,5,-3] => 6
[-1,4,2,-5,3] => 4
[-1,4,2,-5,-3] => 5
[-1,4,-2,5,3] => 6
[-1,4,-2,5,-3] => 7
[-1,4,-2,-5,3] => 5
[-1,4,-2,-5,-3] => 6
[-1,-4,2,5,3] => 4
[-1,-4,2,5,-3] => 5
[-1,-4,2,-5,3] => 3
[-1,-4,2,-5,-3] => 4
[-1,-4,-2,5,3] => 5
[-1,-4,-2,5,-3] => 6
[-1,-4,-2,-5,3] => 4
[-1,-4,-2,-5,-3] => 5
[1,4,3,2,5] => 8
[1,4,3,2,-5] => 7
[1,4,3,-2,5] => 9
[1,4,3,-2,-5] => 8
[1,4,-3,2,5] => 7
[1,4,-3,2,-5] => 6
[1,4,-3,-2,5] => 8
[1,4,-3,-2,-5] => 7
[1,-4,3,2,5] => 7
[1,-4,3,2,-5] => 6
[1,-4,3,-2,5] => 8
[1,-4,3,-2,-5] => 7
[1,-4,-3,2,5] => 6
[1,-4,-3,2,-5] => 5
[1,-4,-3,-2,5] => 7
[1,-4,-3,-2,-5] => 6
[-1,4,3,2,5] => 7
[-1,4,3,2,-5] => 6
[-1,4,3,-2,5] => 8
[-1,4,3,-2,-5] => 7
[-1,4,-3,2,5] => 6
[-1,4,-3,2,-5] => 5
[-1,4,-3,-2,5] => 7
[-1,4,-3,-2,-5] => 6
[-1,-4,3,2,5] => 6
[-1,-4,3,2,-5] => 5
[-1,-4,3,-2,5] => 7
[-1,-4,3,-2,-5] => 6
[-1,-4,-3,2,5] => 5
[-1,-4,-3,2,-5] => 4
[-1,-4,-3,-2,5] => 6
[-1,-4,-3,-2,-5] => 5
[1,4,3,5,2] => 8
[1,4,3,5,-2] => 9
[1,4,3,-5,2] => 7
[1,4,3,-5,-2] => 8
[1,4,-3,5,2] => 7
[1,4,-3,5,-2] => 8
[1,4,-3,-5,2] => 6
[1,4,-3,-5,-2] => 7
[1,-4,3,5,2] => 7
[1,-4,3,5,-2] => 8
[1,-4,3,-5,2] => 6
[1,-4,3,-5,-2] => 7
[1,-4,-3,5,2] => 6
[1,-4,-3,5,-2] => 7
[1,-4,-3,-5,2] => 5
[1,-4,-3,-5,-2] => 6
[-1,4,3,5,2] => 7
[-1,4,3,5,-2] => 8
[-1,4,3,-5,2] => 6
[-1,4,3,-5,-2] => 7
[-1,4,-3,5,2] => 6
[-1,4,-3,5,-2] => 7
[-1,4,-3,-5,2] => 5
[-1,4,-3,-5,-2] => 6
[-1,-4,3,5,2] => 6
[-1,-4,3,5,-2] => 7
[-1,-4,3,-5,2] => 5
[-1,-4,3,-5,-2] => 6
[-1,-4,-3,5,2] => 5
[-1,-4,-3,5,-2] => 6
[-1,-4,-3,-5,2] => 4
[-1,-4,-3,-5,-2] => 5
[1,4,5,2,3] => 6
[1,4,5,2,-3] => 7
[1,4,5,-2,3] => 7
[1,4,5,-2,-3] => 8
[1,4,-5,2,3] => 5
[1,4,-5,2,-3] => 6
[1,4,-5,-2,3] => 6
[1,4,-5,-2,-3] => 7
[1,-4,5,2,3] => 5
[1,-4,5,2,-3] => 6
[1,-4,5,-2,3] => 6
[1,-4,5,-2,-3] => 7
[1,-4,-5,2,3] => 4
[1,-4,-5,2,-3] => 5
[1,-4,-5,-2,3] => 5
[1,-4,-5,-2,-3] => 6
[-1,4,5,2,3] => 5
[-1,4,5,2,-3] => 6
[-1,4,5,-2,3] => 6
[-1,4,5,-2,-3] => 7
[-1,4,-5,2,3] => 4
[-1,4,-5,2,-3] => 5
[-1,4,-5,-2,3] => 5
[-1,4,-5,-2,-3] => 6
[-1,-4,5,2,3] => 4
[-1,-4,5,2,-3] => 5
[-1,-4,5,-2,3] => 5
[-1,-4,5,-2,-3] => 6
[-1,-4,-5,2,3] => 3
[-1,-4,-5,2,-3] => 4
[-1,-4,-5,-2,3] => 4
[-1,-4,-5,-2,-3] => 5
[1,4,5,3,2] => 6
[1,4,5,3,-2] => 7
[1,4,5,-3,2] => 7
[1,4,5,-3,-2] => 8
[1,4,-5,3,2] => 5
[1,4,-5,3,-2] => 6
[1,4,-5,-3,2] => 6
[1,4,-5,-3,-2] => 7
[1,-4,5,3,2] => 5
[1,-4,5,3,-2] => 6
[1,-4,5,-3,2] => 6
[1,-4,5,-3,-2] => 7
[1,-4,-5,3,2] => 4
[1,-4,-5,3,-2] => 5
[1,-4,-5,-3,2] => 5
[1,-4,-5,-3,-2] => 6
[-1,4,5,3,2] => 5
[-1,4,5,3,-2] => 6
[-1,4,5,-3,2] => 6
[-1,4,5,-3,-2] => 7
[-1,4,-5,3,2] => 4
[-1,4,-5,3,-2] => 5
[-1,4,-5,-3,2] => 5
[-1,4,-5,-3,-2] => 6
[-1,-4,5,3,2] => 4
[-1,-4,5,3,-2] => 5
[-1,-4,5,-3,2] => 5
[-1,-4,5,-3,-2] => 6
[-1,-4,-5,3,2] => 3
[-1,-4,-5,3,-2] => 4
[-1,-4,-5,-3,2] => 4
[-1,-4,-5,-3,-2] => 5
[1,5,2,3,4] => 4
[1,5,2,3,-4] => 5
[1,5,2,-3,4] => 5
[1,5,2,-3,-4] => 6
[1,5,-2,3,4] => 5
[1,5,-2,3,-4] => 6
[1,5,-2,-3,4] => 6
[1,5,-2,-3,-4] => 7
[1,-5,2,3,4] => 3
[1,-5,2,3,-4] => 4
[1,-5,2,-3,4] => 4
[1,-5,2,-3,-4] => 5
[1,-5,-2,3,4] => 4
[1,-5,-2,3,-4] => 5
[1,-5,-2,-3,4] => 5
[1,-5,-2,-3,-4] => 6
[-1,5,2,3,4] => 3
[-1,5,2,3,-4] => 4
[-1,5,2,-3,4] => 4
[-1,5,2,-3,-4] => 5
[-1,5,-2,3,4] => 4
[-1,5,-2,3,-4] => 5
[-1,5,-2,-3,4] => 5
[-1,5,-2,-3,-4] => 6
[-1,-5,2,3,4] => 2
[-1,-5,2,3,-4] => 3
[-1,-5,2,-3,4] => 3
[-1,-5,2,-3,-4] => 4
[-1,-5,-2,3,4] => 3
[-1,-5,-2,3,-4] => 4
[-1,-5,-2,-3,4] => 4
[-1,-5,-2,-3,-4] => 5
[1,5,2,4,3] => 6
[1,5,2,4,-3] => 7
[1,5,2,-4,3] => 5
[1,5,2,-4,-3] => 6
[1,5,-2,4,3] => 7
[1,5,-2,4,-3] => 8
[1,5,-2,-4,3] => 6
[1,5,-2,-4,-3] => 7
[1,-5,2,4,3] => 5
[1,-5,2,4,-3] => 6
[1,-5,2,-4,3] => 4
[1,-5,2,-4,-3] => 5
[1,-5,-2,4,3] => 6
[1,-5,-2,4,-3] => 7
[1,-5,-2,-4,3] => 5
[1,-5,-2,-4,-3] => 6
[-1,5,2,4,3] => 5
[-1,5,2,4,-3] => 6
[-1,5,2,-4,3] => 4
[-1,5,2,-4,-3] => 5
[-1,5,-2,4,3] => 6
[-1,5,-2,4,-3] => 7
[-1,5,-2,-4,3] => 5
[-1,5,-2,-4,-3] => 6
[-1,-5,2,4,3] => 4
[-1,-5,2,4,-3] => 5
[-1,-5,2,-4,3] => 3
[-1,-5,2,-4,-3] => 4
[-1,-5,-2,4,3] => 5
[-1,-5,-2,4,-3] => 6
[-1,-5,-2,-4,3] => 4
[-1,-5,-2,-4,-3] => 5
[1,5,3,2,4] => 6
[1,5,3,2,-4] => 7
[1,5,3,-2,4] => 7
[1,5,3,-2,-4] => 8
[1,5,-3,2,4] => 5
[1,5,-3,2,-4] => 6
[1,5,-3,-2,4] => 6
[1,5,-3,-2,-4] => 7
[1,-5,3,2,4] => 5
[1,-5,3,2,-4] => 6
[1,-5,3,-2,4] => 6
[1,-5,3,-2,-4] => 7
[1,-5,-3,2,4] => 4
[1,-5,-3,2,-4] => 5
[1,-5,-3,-2,4] => 5
[1,-5,-3,-2,-4] => 6
[-1,5,3,2,4] => 5
[-1,5,3,2,-4] => 6
[-1,5,3,-2,4] => 6
[-1,5,3,-2,-4] => 7
[-1,5,-3,2,4] => 4
[-1,5,-3,2,-4] => 5
[-1,5,-3,-2,4] => 5
[-1,5,-3,-2,-4] => 6
[-1,-5,3,2,4] => 4
[-1,-5,3,2,-4] => 5
[-1,-5,3,-2,4] => 5
[-1,-5,3,-2,-4] => 6
[-1,-5,-3,2,4] => 3
[-1,-5,-3,2,-4] => 4
[-1,-5,-3,-2,4] => 4
[-1,-5,-3,-2,-4] => 5
[1,5,3,4,2] => 8
[1,5,3,4,-2] => 9
[1,5,3,-4,2] => 7
[1,5,3,-4,-2] => 8
[1,5,-3,4,2] => 7
[1,5,-3,4,-2] => 8
[1,5,-3,-4,2] => 6
[1,5,-3,-4,-2] => 7
[1,-5,3,4,2] => 7
[1,-5,3,4,-2] => 8
[1,-5,3,-4,2] => 6
[1,-5,3,-4,-2] => 7
[1,-5,-3,4,2] => 6
[1,-5,-3,4,-2] => 7
[1,-5,-3,-4,2] => 5
[1,-5,-3,-4,-2] => 6
[-1,5,3,4,2] => 7
[-1,5,3,4,-2] => 8
[-1,5,3,-4,2] => 6
[-1,5,3,-4,-2] => 7
[-1,5,-3,4,2] => 6
[-1,5,-3,4,-2] => 7
[-1,5,-3,-4,2] => 5
[-1,5,-3,-4,-2] => 6
[-1,-5,3,4,2] => 6
[-1,-5,3,4,-2] => 7
[-1,-5,3,-4,2] => 5
[-1,-5,3,-4,-2] => 6
[-1,-5,-3,4,2] => 5
[-1,-5,-3,4,-2] => 6
[-1,-5,-3,-4,2] => 4
[-1,-5,-3,-4,-2] => 5
[1,5,4,2,3] => 6
[1,5,4,2,-3] => 7
[1,5,4,-2,3] => 7
[1,5,4,-2,-3] => 8
[1,5,-4,2,3] => 5
[1,5,-4,2,-3] => 6
[1,5,-4,-2,3] => 6
[1,5,-4,-2,-3] => 7
[1,-5,4,2,3] => 5
[1,-5,4,2,-3] => 6
[1,-5,4,-2,3] => 6
[1,-5,4,-2,-3] => 7
[1,-5,-4,2,3] => 4
[1,-5,-4,2,-3] => 5
[1,-5,-4,-2,3] => 5
[1,-5,-4,-2,-3] => 6
[-1,5,4,2,3] => 5
[-1,5,4,2,-3] => 6
[-1,5,4,-2,3] => 6
[-1,5,4,-2,-3] => 7
[-1,5,-4,2,3] => 4
[-1,5,-4,2,-3] => 5
[-1,5,-4,-2,3] => 5
[-1,5,-4,-2,-3] => 6
[-1,-5,4,2,3] => 4
[-1,-5,4,2,-3] => 5
[-1,-5,4,-2,3] => 5
[-1,-5,4,-2,-3] => 6
[-1,-5,-4,2,3] => 3
[-1,-5,-4,2,-3] => 4
[-1,-5,-4,-2,3] => 4
[-1,-5,-4,-2,-3] => 5
[1,5,4,3,2] => 6
[1,5,4,3,-2] => 7
[1,5,4,-3,2] => 7
[1,5,4,-3,-2] => 8
[1,5,-4,3,2] => 5
[1,5,-4,3,-2] => 6
[1,5,-4,-3,2] => 6
[1,5,-4,-3,-2] => 7
[1,-5,4,3,2] => 5
[1,-5,4,3,-2] => 6
[1,-5,4,-3,2] => 6
[1,-5,4,-3,-2] => 7
[1,-5,-4,3,2] => 4
[1,-5,-4,3,-2] => 5
[1,-5,-4,-3,2] => 5
[1,-5,-4,-3,-2] => 6
[-1,5,4,3,2] => 5
[-1,5,4,3,-2] => 6
[-1,5,4,-3,2] => 6
[-1,5,4,-3,-2] => 7
[-1,5,-4,3,2] => 4
[-1,5,-4,3,-2] => 5
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Created: Jul 20, 2022 at 05:57 by Martin Rubey
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Last Updated: Jul 20, 2022 at 05:57 by Martin Rubey