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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: St000053
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: The number of valleys of the Dyck path.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(r):
return r.number_of_valleys()
-----------------------------------------------------------------------------
Statistic values:
[1,0] => 0
[1,0,1,0] => 1
[1,1,0,0] => 0
[1,0,1,0,1,0] => 2
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 1
[1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0] => 2
[1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
-----------------------------------------------------------------------------
Created: Mar 25, 2013 at 17:36 by Jessica Striker
-----------------------------------------------------------------------------
Last Updated: Feb 17, 2015 at 17:43 by Martin Rubey