*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000558
-----------------------------------------------------------------------------
Collection: Set partitions
-----------------------------------------------------------------------------
Description: The number of occurrences of the pattern {{1,2}} in a set partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def Klazar_occurrences(pi, pattern):
"""
Return the number of occurrences of pattern in pi.
EXAMPLES:
From Mansour 2013, page 86, Example 3.24
The set partition π = 135/26/4 contains four occurrences of
the pattern 12/3, namely, 13/6, 13/4, 15/6, and 35/6. On the other hand, the
set partition π avoids the pattern 12/34.
sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3]])
4
sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3,4]])
0
"""
pi = SetPartition(pi).standardization()
pattern = SetPartition(pattern).standardization()
count = 0
for s in Subsets(range(1,1+pi.size()), pattern.size()):
if pi.restriction(s).standardization() == pattern:
count += 1
return count
def statistic(pi):
return Klazar_occurrences(pi, [[1,2]])
-----------------------------------------------------------------------------
Statistic values:
{{1,2}} => 1
{{1},{2}} => 0
{{1,2,3}} => 3
{{1,2},{3}} => 1
{{1,3},{2}} => 1
{{1},{2,3}} => 1
{{1},{2},{3}} => 0
{{1,2,3,4}} => 6
{{1,2,3},{4}} => 3
{{1,2,4},{3}} => 3
{{1,2},{3,4}} => 2
{{1,2},{3},{4}} => 1
{{1,3,4},{2}} => 3
{{1,3},{2,4}} => 2
{{1,3},{2},{4}} => 1
{{1,4},{2,3}} => 2
{{1},{2,3,4}} => 3
{{1},{2,3},{4}} => 1
{{1,4},{2},{3}} => 1
{{1},{2,4},{3}} => 1
{{1},{2},{3,4}} => 1
{{1},{2},{3},{4}} => 0
{{1,2,3,4,5}} => 10
{{1,2,3,4},{5}} => 6
{{1,2,3,5},{4}} => 6
{{1,2,3},{4,5}} => 4
{{1,2,3},{4},{5}} => 3
{{1,2,4,5},{3}} => 6
{{1,2,4},{3,5}} => 4
{{1,2,4},{3},{5}} => 3
{{1,2,5},{3,4}} => 4
{{1,2},{3,4,5}} => 4
{{1,2},{3,4},{5}} => 2
{{1,2,5},{3},{4}} => 3
{{1,2},{3,5},{4}} => 2
{{1,2},{3},{4,5}} => 2
{{1,2},{3},{4},{5}} => 1
{{1,3,4,5},{2}} => 6
{{1,3,4},{2,5}} => 4
{{1,3,4},{2},{5}} => 3
{{1,3,5},{2,4}} => 4
{{1,3},{2,4,5}} => 4
{{1,3},{2,4},{5}} => 2
{{1,3,5},{2},{4}} => 3
{{1,3},{2,5},{4}} => 2
{{1,3},{2},{4,5}} => 2
{{1,3},{2},{4},{5}} => 1
{{1,4,5},{2,3}} => 4
{{1,4},{2,3,5}} => 4
{{1,4},{2,3},{5}} => 2
{{1,5},{2,3,4}} => 4
{{1},{2,3,4,5}} => 6
{{1},{2,3,4},{5}} => 3
{{1,5},{2,3},{4}} => 2
{{1},{2,3,5},{4}} => 3
{{1},{2,3},{4,5}} => 2
{{1},{2,3},{4},{5}} => 1
{{1,4,5},{2},{3}} => 3
{{1,4},{2,5},{3}} => 2
{{1,4},{2},{3,5}} => 2
{{1,4},{2},{3},{5}} => 1
{{1,5},{2,4},{3}} => 2
{{1},{2,4,5},{3}} => 3
{{1},{2,4},{3,5}} => 2
{{1},{2,4},{3},{5}} => 1
{{1,5},{2},{3,4}} => 2
{{1},{2,5},{3,4}} => 2
{{1},{2},{3,4,5}} => 3
{{1},{2},{3,4},{5}} => 1
{{1,5},{2},{3},{4}} => 1
{{1},{2,5},{3},{4}} => 1
{{1},{2},{3,5},{4}} => 1
{{1},{2},{3},{4,5}} => 1
{{1},{2},{3},{4},{5}} => 0
{{1,2,3,4,5,6}} => 15
{{1,2,3,4,5},{6}} => 10
{{1,2,3,4,6},{5}} => 10
{{1,2,3,4},{5,6}} => 7
{{1,2,3,4},{5},{6}} => 6
{{1,2,3,5,6},{4}} => 10
{{1,2,3,5},{4,6}} => 7
{{1,2,3,5},{4},{6}} => 6
{{1,2,3,6},{4,5}} => 7
{{1,2,3},{4,5,6}} => 6
{{1,2,3},{4,5},{6}} => 4
{{1,2,3,6},{4},{5}} => 6
{{1,2,3},{4,6},{5}} => 4
{{1,2,3},{4},{5,6}} => 4
{{1,2,3},{4},{5},{6}} => 3
{{1,2,4,5,6},{3}} => 10
{{1,2,4,5},{3,6}} => 7
{{1,2,4,5},{3},{6}} => 6
{{1,2,4,6},{3,5}} => 7
{{1,2,4},{3,5,6}} => 6
{{1,2,4},{3,5},{6}} => 4
{{1,2,4,6},{3},{5}} => 6
{{1,2,4},{3,6},{5}} => 4
{{1,2,4},{3},{5,6}} => 4
{{1,2,4},{3},{5},{6}} => 3
{{1,2,5,6},{3,4}} => 7
{{1,2,5},{3,4,6}} => 6
{{1,2,5},{3,4},{6}} => 4
{{1,2,6},{3,4,5}} => 6
{{1,2},{3,4,5,6}} => 7
{{1,2},{3,4,5},{6}} => 4
{{1,2,6},{3,4},{5}} => 4
{{1,2},{3,4,6},{5}} => 4
{{1,2},{3,4},{5,6}} => 3
{{1,2},{3,4},{5},{6}} => 2
{{1,2,5,6},{3},{4}} => 6
{{1,2,5},{3,6},{4}} => 4
{{1,2,5},{3},{4,6}} => 4
{{1,2,5},{3},{4},{6}} => 3
{{1,2,6},{3,5},{4}} => 4
{{1,2},{3,5,6},{4}} => 4
{{1,2},{3,5},{4,6}} => 3
{{1,2},{3,5},{4},{6}} => 2
{{1,2,6},{3},{4,5}} => 4
{{1,2},{3,6},{4,5}} => 3
{{1,2},{3},{4,5,6}} => 4
{{1,2},{3},{4,5},{6}} => 2
{{1,2,6},{3},{4},{5}} => 3
{{1,2},{3,6},{4},{5}} => 2
{{1,2},{3},{4,6},{5}} => 2
{{1,2},{3},{4},{5,6}} => 2
{{1,2},{3},{4},{5},{6}} => 1
{{1,3,4,5,6},{2}} => 10
{{1,3,4,5},{2,6}} => 7
{{1,3,4,5},{2},{6}} => 6
{{1,3,4,6},{2,5}} => 7
{{1,3,4},{2,5,6}} => 6
{{1,3,4},{2,5},{6}} => 4
{{1,3,4,6},{2},{5}} => 6
{{1,3,4},{2,6},{5}} => 4
{{1,3,4},{2},{5,6}} => 4
{{1,3,4},{2},{5},{6}} => 3
{{1,3,5,6},{2,4}} => 7
{{1,3,5},{2,4,6}} => 6
{{1,3,5},{2,4},{6}} => 4
{{1,3,6},{2,4,5}} => 6
{{1,3},{2,4,5,6}} => 7
{{1,3},{2,4,5},{6}} => 4
{{1,3,6},{2,4},{5}} => 4
{{1,3},{2,4,6},{5}} => 4
{{1,3},{2,4},{5,6}} => 3
{{1,3},{2,4},{5},{6}} => 2
{{1,3,5,6},{2},{4}} => 6
{{1,3,5},{2,6},{4}} => 4
{{1,3,5},{2},{4,6}} => 4
{{1,3,5},{2},{4},{6}} => 3
{{1,3,6},{2,5},{4}} => 4
{{1,3},{2,5,6},{4}} => 4
{{1,3},{2,5},{4,6}} => 3
{{1,3},{2,5},{4},{6}} => 2
{{1,3,6},{2},{4,5}} => 4
{{1,3},{2,6},{4,5}} => 3
{{1,3},{2},{4,5,6}} => 4
{{1,3},{2},{4,5},{6}} => 2
{{1,3,6},{2},{4},{5}} => 3
{{1,3},{2,6},{4},{5}} => 2
{{1,3},{2},{4,6},{5}} => 2
{{1,3},{2},{4},{5,6}} => 2
{{1,3},{2},{4},{5},{6}} => 1
{{1,4,5,6},{2,3}} => 7
{{1,4,5},{2,3,6}} => 6
{{1,4,5},{2,3},{6}} => 4
{{1,4,6},{2,3,5}} => 6
{{1,4},{2,3,5,6}} => 7
{{1,4},{2,3,5},{6}} => 4
{{1,4,6},{2,3},{5}} => 4
{{1,4},{2,3,6},{5}} => 4
{{1,4},{2,3},{5,6}} => 3
{{1,4},{2,3},{5},{6}} => 2
{{1,5,6},{2,3,4}} => 6
{{1,5},{2,3,4,6}} => 7
{{1,5},{2,3,4},{6}} => 4
{{1,6},{2,3,4,5}} => 7
{{1},{2,3,4,5,6}} => 10
{{1},{2,3,4,5},{6}} => 6
{{1,6},{2,3,4},{5}} => 4
{{1},{2,3,4,6},{5}} => 6
{{1},{2,3,4},{5,6}} => 4
{{1},{2,3,4},{5},{6}} => 3
{{1,5,6},{2,3},{4}} => 4
{{1,5},{2,3,6},{4}} => 4
{{1,5},{2,3},{4,6}} => 3
{{1,5},{2,3},{4},{6}} => 2
{{1,6},{2,3,5},{4}} => 4
{{1},{2,3,5,6},{4}} => 6
{{1},{2,3,5},{4,6}} => 4
{{1},{2,3,5},{4},{6}} => 3
{{1,6},{2,3},{4,5}} => 3
{{1},{2,3,6},{4,5}} => 4
{{1},{2,3},{4,5,6}} => 4
{{1},{2,3},{4,5},{6}} => 2
{{1,6},{2,3},{4},{5}} => 2
{{1},{2,3,6},{4},{5}} => 3
{{1},{2,3},{4,6},{5}} => 2
{{1},{2,3},{4},{5,6}} => 2
{{1},{2,3},{4},{5},{6}} => 1
{{1,4,5,6},{2},{3}} => 6
{{1,4,5},{2,6},{3}} => 4
{{1,4,5},{2},{3,6}} => 4
{{1,4,5},{2},{3},{6}} => 3
{{1,4,6},{2,5},{3}} => 4
{{1,4},{2,5,6},{3}} => 4
{{1,4},{2,5},{3,6}} => 3
{{1,4},{2,5},{3},{6}} => 2
{{1,4,6},{2},{3,5}} => 4
{{1,4},{2,6},{3,5}} => 3
{{1,4},{2},{3,5,6}} => 4
{{1,4},{2},{3,5},{6}} => 2
{{1,4,6},{2},{3},{5}} => 3
{{1,4},{2,6},{3},{5}} => 2
{{1,4},{2},{3,6},{5}} => 2
{{1,4},{2},{3},{5,6}} => 2
{{1,4},{2},{3},{5},{6}} => 1
{{1,5,6},{2,4},{3}} => 4
{{1,5},{2,4,6},{3}} => 4
{{1,5},{2,4},{3,6}} => 3
{{1,5},{2,4},{3},{6}} => 2
{{1,6},{2,4,5},{3}} => 4
{{1},{2,4,5,6},{3}} => 6
{{1},{2,4,5},{3,6}} => 4
{{1},{2,4,5},{3},{6}} => 3
{{1,6},{2,4},{3,5}} => 3
{{1},{2,4,6},{3,5}} => 4
{{1},{2,4},{3,5,6}} => 4
{{1},{2,4},{3,5},{6}} => 2
{{1,6},{2,4},{3},{5}} => 2
{{1},{2,4,6},{3},{5}} => 3
{{1},{2,4},{3,6},{5}} => 2
{{1},{2,4},{3},{5,6}} => 2
{{1},{2,4},{3},{5},{6}} => 1
{{1,5,6},{2},{3,4}} => 4
{{1,5},{2,6},{3,4}} => 3
{{1,5},{2},{3,4,6}} => 4
{{1,5},{2},{3,4},{6}} => 2
{{1,6},{2,5},{3,4}} => 3
{{1},{2,5,6},{3,4}} => 4
{{1},{2,5},{3,4,6}} => 4
{{1},{2,5},{3,4},{6}} => 2
{{1,6},{2},{3,4,5}} => 4
{{1},{2,6},{3,4,5}} => 4
{{1},{2},{3,4,5,6}} => 6
{{1},{2},{3,4,5},{6}} => 3
{{1,6},{2},{3,4},{5}} => 2
{{1},{2,6},{3,4},{5}} => 2
{{1},{2},{3,4,6},{5}} => 3
{{1},{2},{3,4},{5,6}} => 2
{{1},{2},{3,4},{5},{6}} => 1
{{1,5,6},{2},{3},{4}} => 3
{{1,5},{2,6},{3},{4}} => 2
{{1,5},{2},{3,6},{4}} => 2
{{1,5},{2},{3},{4,6}} => 2
{{1,5},{2},{3},{4},{6}} => 1
{{1,6},{2,5},{3},{4}} => 2
{{1},{2,5,6},{3},{4}} => 3
{{1},{2,5},{3,6},{4}} => 2
{{1},{2,5},{3},{4,6}} => 2
{{1},{2,5},{3},{4},{6}} => 1
{{1,6},{2},{3,5},{4}} => 2
{{1},{2,6},{3,5},{4}} => 2
{{1},{2},{3,5,6},{4}} => 3
{{1},{2},{3,5},{4,6}} => 2
{{1},{2},{3,5},{4},{6}} => 1
{{1,6},{2},{3},{4,5}} => 2
{{1},{2,6},{3},{4,5}} => 2
{{1},{2},{3,6},{4,5}} => 2
{{1},{2},{3},{4,5,6}} => 3
{{1},{2},{3},{4,5},{6}} => 1
{{1,6},{2},{3},{4},{5}} => 1
{{1},{2,6},{3},{4},{5}} => 1
{{1},{2},{3,6},{4},{5}} => 1
{{1},{2},{3},{4,6},{5}} => 1
{{1},{2},{3},{4},{5,6}} => 1
{{1},{2},{3},{4},{5},{6}} => 0
{{1,2,3,4,5,6,7}} => 21
{{1,2,3,4,5,6},{7}} => 15
{{1,2,3,4,5,7},{6}} => 15
{{1,2,3,4,5},{6,7}} => 11
{{1,2,3,4,5},{6},{7}} => 10
{{1,2,3,4,6,7},{5}} => 15
{{1,2,3,4,6},{5,7}} => 11
{{1,2,3,4,6},{5},{7}} => 10
{{1,2,3,4,7},{5,6}} => 11
{{1,2,3,4},{5,6,7}} => 9
{{1,2,3,4},{5,6},{7}} => 7
{{1,2,3,4,7},{5},{6}} => 10
{{1,2,3,4},{5,7},{6}} => 7
{{1,2,3,4},{5},{6,7}} => 7
{{1,2,3,4},{5},{6},{7}} => 6
{{1,2,3,5,6,7},{4}} => 15
{{1,2,3,5,6},{4,7}} => 11
{{1,2,3,5,6},{4},{7}} => 10
{{1,2,3,5,7},{4,6}} => 11
{{1,2,3,5},{4,6,7}} => 9
{{1,2,3,5},{4,6},{7}} => 7
{{1,2,3,5,7},{4},{6}} => 10
{{1,2,3,5},{4,7},{6}} => 7
{{1,2,3,5},{4},{6,7}} => 7
{{1,2,3,5},{4},{6},{7}} => 6
{{1,2,3,6,7},{4,5}} => 11
{{1,2,3,6},{4,5,7}} => 9
{{1,2,3,6},{4,5},{7}} => 7
{{1,2,3,7},{4,5,6}} => 9
{{1,2,3},{4,5,6,7}} => 9
{{1,2,3},{4,5,6},{7}} => 6
{{1,2,3,7},{4,5},{6}} => 7
{{1,2,3},{4,5,7},{6}} => 6
{{1,2,3},{4,5},{6,7}} => 5
{{1,2,3},{4,5},{6},{7}} => 4
{{1,2,3,6,7},{4},{5}} => 10
{{1,2,3,6},{4,7},{5}} => 7
{{1,2,3,6},{4},{5,7}} => 7
{{1,2,3,6},{4},{5},{7}} => 6
{{1,2,3,7},{4,6},{5}} => 7
{{1,2,3},{4,6,7},{5}} => 6
{{1,2,3},{4,6},{5,7}} => 5
{{1,2,3},{4,6},{5},{7}} => 4
{{1,2,3,7},{4},{5,6}} => 7
{{1,2,3},{4,7},{5,6}} => 5
{{1,2,3},{4},{5,6,7}} => 6
{{1,2,3},{4},{5,6},{7}} => 4
{{1,2,3,7},{4},{5},{6}} => 6
{{1,2,3},{4,7},{5},{6}} => 4
{{1,2,3},{4},{5,7},{6}} => 4
{{1,2,3},{4},{5},{6,7}} => 4
{{1,2,3},{4},{5},{6},{7}} => 3
{{1,2,4,5,6,7},{3}} => 15
{{1,2,4,5,6},{3,7}} => 11
{{1,2,4,5,6},{3},{7}} => 10
{{1,2,4,5,7},{3,6}} => 11
{{1,2,4,5},{3,6,7}} => 9
{{1,2,4,5},{3,6},{7}} => 7
{{1,2,4,5,7},{3},{6}} => 10
{{1,2,4,5},{3,7},{6}} => 7
{{1,2,4,5},{3},{6,7}} => 7
{{1,2,4,5},{3},{6},{7}} => 6
{{1,2,4,6,7},{3,5}} => 11
{{1,2,4,6},{3,5,7}} => 9
{{1,2,4,6},{3,5},{7}} => 7
{{1,2,4,7},{3,5,6}} => 9
{{1,2,4},{3,5,6,7}} => 9
{{1,2,4},{3,5,6},{7}} => 6
{{1,2,4,7},{3,5},{6}} => 7
{{1,2,4},{3,5,7},{6}} => 6
{{1,2,4},{3,5},{6,7}} => 5
{{1,2,4},{3,5},{6},{7}} => 4
{{1,2,4,6,7},{3},{5}} => 10
{{1,2,4,6},{3,7},{5}} => 7
{{1,2,4,6},{3},{5,7}} => 7
{{1,2,4,6},{3},{5},{7}} => 6
{{1,2,4,7},{3,6},{5}} => 7
{{1,2,4},{3,6,7},{5}} => 6
{{1,2,4},{3,6},{5,7}} => 5
{{1,2,4},{3,6},{5},{7}} => 4
{{1,2,4,7},{3},{5,6}} => 7
{{1,2,4},{3,7},{5,6}} => 5
{{1,2,4},{3},{5,6,7}} => 6
{{1,2,4},{3},{5,6},{7}} => 4
{{1,2,4,7},{3},{5},{6}} => 6
{{1,2,4},{3,7},{5},{6}} => 4
{{1,2,4},{3},{5,7},{6}} => 4
{{1,2,4},{3},{5},{6,7}} => 4
{{1,2,4},{3},{5},{6},{7}} => 3
{{1,2,5,6,7},{3,4}} => 11
{{1,2,5,6},{3,4,7}} => 9
{{1,2,5,6},{3,4},{7}} => 7
{{1,2,5,7},{3,4,6}} => 9
{{1,2,5},{3,4,6,7}} => 9
{{1,2,5},{3,4,6},{7}} => 6
{{1,2,5,7},{3,4},{6}} => 7
{{1,2,5},{3,4,7},{6}} => 6
{{1,2,5},{3,4},{6,7}} => 5
{{1,2,5},{3,4},{6},{7}} => 4
{{1,2,6,7},{3,4,5}} => 9
{{1,2,6},{3,4,5,7}} => 9
{{1,2,6},{3,4,5},{7}} => 6
{{1,2,7},{3,4,5,6}} => 9
{{1,2},{3,4,5,6,7}} => 11
{{1,2},{3,4,5,6},{7}} => 7
{{1,2,7},{3,4,5},{6}} => 6
{{1,2},{3,4,5,7},{6}} => 7
{{1,2},{3,4,5},{6,7}} => 5
{{1,2},{3,4,5},{6},{7}} => 4
{{1,2,6,7},{3,4},{5}} => 7
{{1,2,6},{3,4,7},{5}} => 6
{{1,2,6},{3,4},{5,7}} => 5
{{1,2,6},{3,4},{5},{7}} => 4
{{1,2,7},{3,4,6},{5}} => 6
{{1,2},{3,4,6,7},{5}} => 7
{{1,2},{3,4,6},{5,7}} => 5
{{1,2},{3,4,6},{5},{7}} => 4
{{1,2,7},{3,4},{5,6}} => 5
{{1,2},{3,4,7},{5,6}} => 5
{{1,2},{3,4},{5,6,7}} => 5
{{1,2},{3,4},{5,6},{7}} => 3
{{1,2,7},{3,4},{5},{6}} => 4
{{1,2},{3,4,7},{5},{6}} => 4
{{1,2},{3,4},{5,7},{6}} => 3
{{1,2},{3,4},{5},{6,7}} => 3
{{1,2},{3,4},{5},{6},{7}} => 2
{{1,2,5,6,7},{3},{4}} => 10
{{1,2,5,6},{3,7},{4}} => 7
{{1,2,5,6},{3},{4,7}} => 7
{{1,2,5,6},{3},{4},{7}} => 6
{{1,2,5,7},{3,6},{4}} => 7
{{1,2,5},{3,6,7},{4}} => 6
{{1,2,5},{3,6},{4,7}} => 5
{{1,2,5},{3,6},{4},{7}} => 4
{{1,2,5,7},{3},{4,6}} => 7
{{1,2,5},{3,7},{4,6}} => 5
{{1,2,5},{3},{4,6,7}} => 6
{{1,2,5},{3},{4,6},{7}} => 4
{{1,2,5,7},{3},{4},{6}} => 6
{{1,2,5},{3,7},{4},{6}} => 4
{{1,2,5},{3},{4,7},{6}} => 4
{{1,2,5},{3},{4},{6,7}} => 4
{{1,2,5},{3},{4},{6},{7}} => 3
{{1,2,6,7},{3,5},{4}} => 7
{{1,2,6},{3,5,7},{4}} => 6
{{1,2,6},{3,5},{4,7}} => 5
{{1,2,6},{3,5},{4},{7}} => 4
{{1,2,7},{3,5,6},{4}} => 6
{{1,2},{3,5,6,7},{4}} => 7
{{1,2},{3,5,6},{4,7}} => 5
{{1,2},{3,5,6},{4},{7}} => 4
{{1,2,7},{3,5},{4,6}} => 5
{{1,2},{3,5,7},{4,6}} => 5
{{1,2},{3,5},{4,6,7}} => 5
{{1,2},{3,5},{4,6},{7}} => 3
{{1,2,7},{3,5},{4},{6}} => 4
{{1,2},{3,5,7},{4},{6}} => 4
{{1,2},{3,5},{4,7},{6}} => 3
{{1,2},{3,5},{4},{6,7}} => 3
{{1,2},{3,5},{4},{6},{7}} => 2
{{1,2,6,7},{3},{4,5}} => 7
{{1,2,6},{3,7},{4,5}} => 5
{{1,2,6},{3},{4,5,7}} => 6
{{1,2,6},{3},{4,5},{7}} => 4
{{1,2,7},{3,6},{4,5}} => 5
{{1,2},{3,6,7},{4,5}} => 5
{{1,2},{3,6},{4,5,7}} => 5
{{1,2},{3,6},{4,5},{7}} => 3
{{1,2,7},{3},{4,5,6}} => 6
{{1,2},{3,7},{4,5,6}} => 5
{{1,2},{3},{4,5,6,7}} => 7
{{1,2},{3},{4,5,6},{7}} => 4
{{1,2,7},{3},{4,5},{6}} => 4
{{1,2},{3,7},{4,5},{6}} => 3
{{1,2},{3},{4,5,7},{6}} => 4
{{1,2},{3},{4,5},{6,7}} => 3
{{1,2},{3},{4,5},{6},{7}} => 2
{{1,2,6,7},{3},{4},{5}} => 6
{{1,2,6},{3,7},{4},{5}} => 4
{{1,2,6},{3},{4,7},{5}} => 4
{{1,2,6},{3},{4},{5,7}} => 4
{{1,2,6},{3},{4},{5},{7}} => 3
{{1,2,7},{3,6},{4},{5}} => 4
{{1,2},{3,6,7},{4},{5}} => 4
{{1,2},{3,6},{4,7},{5}} => 3
{{1,2},{3,6},{4},{5,7}} => 3
{{1,2},{3,6},{4},{5},{7}} => 2
{{1,2,7},{3},{4,6},{5}} => 4
{{1,2},{3,7},{4,6},{5}} => 3
{{1,2},{3},{4,6,7},{5}} => 4
{{1,2},{3},{4,6},{5,7}} => 3
{{1,2},{3},{4,6},{5},{7}} => 2
{{1,2,7},{3},{4},{5,6}} => 4
{{1,2},{3,7},{4},{5,6}} => 3
{{1,2},{3},{4,7},{5,6}} => 3
{{1,2},{3},{4},{5,6,7}} => 4
{{1,2},{3},{4},{5,6},{7}} => 2
{{1,2,7},{3},{4},{5},{6}} => 3
{{1,2},{3,7},{4},{5},{6}} => 2
{{1,2},{3},{4,7},{5},{6}} => 2
{{1,2},{3},{4},{5,7},{6}} => 2
{{1,2},{3},{4},{5},{6,7}} => 2
{{1,2},{3},{4},{5},{6},{7}} => 1
{{1,3,4,5,6,7},{2}} => 15
{{1,3,4,5,6},{2,7}} => 11
{{1,3,4,5,6},{2},{7}} => 10
{{1,3,4,5,7},{2,6}} => 11
{{1,3,4,5},{2,6,7}} => 9
{{1,3,4,5},{2,6},{7}} => 7
{{1,3,4,5,7},{2},{6}} => 10
{{1,3,4,5},{2,7},{6}} => 7
{{1,3,4,5},{2},{6,7}} => 7
{{1,3,4,5},{2},{6},{7}} => 6
{{1,3,4,6,7},{2,5}} => 11
{{1,3,4,6},{2,5,7}} => 9
{{1,3,4,6},{2,5},{7}} => 7
{{1,3,4,7},{2,5,6}} => 9
{{1,3,4},{2,5,6,7}} => 9
{{1,3,4},{2,5,6},{7}} => 6
{{1,3,4,7},{2,5},{6}} => 7
{{1,3,4},{2,5,7},{6}} => 6
{{1,3,4},{2,5},{6,7}} => 5
{{1,3,4},{2,5},{6},{7}} => 4
{{1,3,4,6,7},{2},{5}} => 10
{{1,3,4,6},{2,7},{5}} => 7
{{1,3,4,6},{2},{5,7}} => 7
{{1,3,4,6},{2},{5},{7}} => 6
{{1,3,4,7},{2,6},{5}} => 7
{{1,3,4},{2,6,7},{5}} => 6
{{1,3,4},{2,6},{5,7}} => 5
{{1,3,4},{2,6},{5},{7}} => 4
{{1,3,4,7},{2},{5,6}} => 7
{{1,3,4},{2,7},{5,6}} => 5
{{1,3,4},{2},{5,6,7}} => 6
{{1,3,4},{2},{5,6},{7}} => 4
{{1,3,4,7},{2},{5},{6}} => 6
{{1,3,4},{2,7},{5},{6}} => 4
{{1,3,4},{2},{5,7},{6}} => 4
{{1,3,4},{2},{5},{6,7}} => 4
{{1,3,4},{2},{5},{6},{7}} => 3
{{1,3,5,6,7},{2,4}} => 11
{{1,3,5,6},{2,4,7}} => 9
{{1,3,5,6},{2,4},{7}} => 7
{{1,3,5,7},{2,4,6}} => 9
{{1,3,5},{2,4,6,7}} => 9
{{1,3,5},{2,4,6},{7}} => 6
{{1,3,5,7},{2,4},{6}} => 7
{{1,3,5},{2,4,7},{6}} => 6
{{1,3,5},{2,4},{6,7}} => 5
{{1,3,5},{2,4},{6},{7}} => 4
{{1,3,6,7},{2,4,5}} => 9
{{1,3,6},{2,4,5,7}} => 9
{{1,3,6},{2,4,5},{7}} => 6
{{1,3,7},{2,4,5,6}} => 9
{{1,3},{2,4,5,6,7}} => 11
{{1,3},{2,4,5,6},{7}} => 7
{{1,3,7},{2,4,5},{6}} => 6
{{1,3},{2,4,5,7},{6}} => 7
{{1,3},{2,4,5},{6,7}} => 5
{{1,3},{2,4,5},{6},{7}} => 4
{{1,3,6,7},{2,4},{5}} => 7
{{1,3,6},{2,4,7},{5}} => 6
{{1,3,6},{2,4},{5,7}} => 5
{{1,3,6},{2,4},{5},{7}} => 4
{{1,3,7},{2,4,6},{5}} => 6
{{1,3},{2,4,6,7},{5}} => 7
{{1,3},{2,4,6},{5,7}} => 5
{{1,3},{2,4,6},{5},{7}} => 4
{{1,3,7},{2,4},{5,6}} => 5
{{1,3},{2,4,7},{5,6}} => 5
{{1,3},{2,4},{5,6,7}} => 5
{{1,3},{2,4},{5,6},{7}} => 3
{{1,3,7},{2,4},{5},{6}} => 4
{{1,3},{2,4,7},{5},{6}} => 4
{{1,3},{2,4},{5,7},{6}} => 3
{{1,3},{2,4},{5},{6,7}} => 3
{{1,3},{2,4},{5},{6},{7}} => 2
{{1,3,5,6,7},{2},{4}} => 10
{{1,3,5,6},{2,7},{4}} => 7
{{1,3,5,6},{2},{4,7}} => 7
{{1,3,5,6},{2},{4},{7}} => 6
{{1,3,5,7},{2,6},{4}} => 7
{{1,3,5},{2,6,7},{4}} => 6
{{1,3,5},{2,6},{4,7}} => 5
{{1,3,5},{2,6},{4},{7}} => 4
{{1,3,5,7},{2},{4,6}} => 7
{{1,3,5},{2,7},{4,6}} => 5
{{1,3,5},{2},{4,6,7}} => 6
{{1,3,5},{2},{4,6},{7}} => 4
{{1,3,5,7},{2},{4},{6}} => 6
{{1,3,5},{2,7},{4},{6}} => 4
{{1,3,5},{2},{4,7},{6}} => 4
{{1,3,5},{2},{4},{6,7}} => 4
{{1,3,5},{2},{4},{6},{7}} => 3
{{1,3,6,7},{2,5},{4}} => 7
{{1,3,6},{2,5,7},{4}} => 6
{{1,3,6},{2,5},{4,7}} => 5
{{1,3,6},{2,5},{4},{7}} => 4
{{1,3,7},{2,5,6},{4}} => 6
{{1,3},{2,5,6,7},{4}} => 7
{{1,3},{2,5,6},{4,7}} => 5
{{1,3},{2,5,6},{4},{7}} => 4
{{1,3,7},{2,5},{4,6}} => 5
{{1,3},{2,5,7},{4,6}} => 5
{{1,3},{2,5},{4,6,7}} => 5
{{1,3},{2,5},{4,6},{7}} => 3
{{1,3,7},{2,5},{4},{6}} => 4
{{1,3},{2,5,7},{4},{6}} => 4
{{1,3},{2,5},{4,7},{6}} => 3
{{1,3},{2,5},{4},{6,7}} => 3
{{1,3},{2,5},{4},{6},{7}} => 2
{{1,3,6,7},{2},{4,5}} => 7
{{1,3,6},{2,7},{4,5}} => 5
{{1,3,6},{2},{4,5,7}} => 6
{{1,3,6},{2},{4,5},{7}} => 4
{{1,3,7},{2,6},{4,5}} => 5
{{1,3},{2,6,7},{4,5}} => 5
{{1,3},{2,6},{4,5,7}} => 5
{{1,3},{2,6},{4,5},{7}} => 3
{{1,3,7},{2},{4,5,6}} => 6
{{1,3},{2,7},{4,5,6}} => 5
{{1,3},{2},{4,5,6,7}} => 7
{{1,3},{2},{4,5,6},{7}} => 4
{{1,3,7},{2},{4,5},{6}} => 4
{{1,3},{2,7},{4,5},{6}} => 3
{{1,3},{2},{4,5,7},{6}} => 4
{{1,3},{2},{4,5},{6,7}} => 3
{{1,3},{2},{4,5},{6},{7}} => 2
{{1,3,6,7},{2},{4},{5}} => 6
{{1,3,6},{2,7},{4},{5}} => 4
{{1,3,6},{2},{4,7},{5}} => 4
{{1,3,6},{2},{4},{5,7}} => 4
{{1,3,6},{2},{4},{5},{7}} => 3
{{1,3,7},{2,6},{4},{5}} => 4
{{1,3},{2,6,7},{4},{5}} => 4
{{1,3},{2,6},{4,7},{5}} => 3
{{1,3},{2,6},{4},{5,7}} => 3
{{1,3},{2,6},{4},{5},{7}} => 2
{{1,3,7},{2},{4,6},{5}} => 4
{{1,3},{2,7},{4,6},{5}} => 3
{{1,3},{2},{4,6,7},{5}} => 4
{{1,3},{2},{4,6},{5,7}} => 3
{{1,3},{2},{4,6},{5},{7}} => 2
{{1,3,7},{2},{4},{5,6}} => 4
{{1,3},{2,7},{4},{5,6}} => 3
{{1,3},{2},{4,7},{5,6}} => 3
{{1,3},{2},{4},{5,6,7}} => 4
{{1,3},{2},{4},{5,6},{7}} => 2
{{1,3,7},{2},{4},{5},{6}} => 3
{{1,3},{2,7},{4},{5},{6}} => 2
{{1,3},{2},{4,7},{5},{6}} => 2
{{1,3},{2},{4},{5,7},{6}} => 2
{{1,3},{2},{4},{5},{6,7}} => 2
{{1,3},{2},{4},{5},{6},{7}} => 1
{{1,4,5,6,7},{2,3}} => 11
{{1,4,5,6},{2,3,7}} => 9
{{1,4,5,6},{2,3},{7}} => 7
{{1,4,5,7},{2,3,6}} => 9
{{1,4,5},{2,3,6,7}} => 9
{{1,4,5},{2,3,6},{7}} => 6
{{1,4,5,7},{2,3},{6}} => 7
{{1,4,5},{2,3,7},{6}} => 6
{{1,4,5},{2,3},{6,7}} => 5
{{1,4,5},{2,3},{6},{7}} => 4
{{1,4,6,7},{2,3,5}} => 9
{{1,4,6},{2,3,5,7}} => 9
{{1,4,6},{2,3,5},{7}} => 6
{{1,4,7},{2,3,5,6}} => 9
{{1,4},{2,3,5,6,7}} => 11
{{1,4},{2,3,5,6},{7}} => 7
{{1,4,7},{2,3,5},{6}} => 6
{{1,4},{2,3,5,7},{6}} => 7
{{1,4},{2,3,5},{6,7}} => 5
{{1,4},{2,3,5},{6},{7}} => 4
{{1,4,6,7},{2,3},{5}} => 7
{{1,4,6},{2,3,7},{5}} => 6
{{1,4,6},{2,3},{5,7}} => 5
{{1,4,6},{2,3},{5},{7}} => 4
{{1,4,7},{2,3,6},{5}} => 6
{{1,4},{2,3,6,7},{5}} => 7
{{1,4},{2,3,6},{5,7}} => 5
{{1,4},{2,3,6},{5},{7}} => 4
{{1,4,7},{2,3},{5,6}} => 5
{{1,4},{2,3,7},{5,6}} => 5
{{1,4},{2,3},{5,6,7}} => 5
{{1,4},{2,3},{5,6},{7}} => 3
{{1,4,7},{2,3},{5},{6}} => 4
{{1,4},{2,3,7},{5},{6}} => 4
{{1,4},{2,3},{5,7},{6}} => 3
{{1,4},{2,3},{5},{6,7}} => 3
{{1,4},{2,3},{5},{6},{7}} => 2
{{1,5,6,7},{2,3,4}} => 9
{{1,5,6},{2,3,4,7}} => 9
{{1,5,6},{2,3,4},{7}} => 6
{{1,5,7},{2,3,4,6}} => 9
{{1,5},{2,3,4,6,7}} => 11
{{1,5},{2,3,4,6},{7}} => 7
{{1,5,7},{2,3,4},{6}} => 6
{{1,5},{2,3,4,7},{6}} => 7
{{1,5},{2,3,4},{6,7}} => 5
{{1,5},{2,3,4},{6},{7}} => 4
{{1,6,7},{2,3,4,5}} => 9
{{1,6},{2,3,4,5,7}} => 11
{{1,6},{2,3,4,5},{7}} => 7
{{1,7},{2,3,4,5,6}} => 11
{{1},{2,3,4,5,6,7}} => 15
{{1},{2,3,4,5,6},{7}} => 10
{{1,7},{2,3,4,5},{6}} => 7
{{1},{2,3,4,5,7},{6}} => 10
{{1},{2,3,4,5},{6,7}} => 7
{{1},{2,3,4,5},{6},{7}} => 6
{{1,6,7},{2,3,4},{5}} => 6
{{1,6},{2,3,4,7},{5}} => 7
{{1,6},{2,3,4},{5,7}} => 5
{{1,6},{2,3,4},{5},{7}} => 4
{{1,7},{2,3,4,6},{5}} => 7
{{1},{2,3,4,6,7},{5}} => 10
{{1},{2,3,4,6},{5,7}} => 7
{{1},{2,3,4,6},{5},{7}} => 6
{{1,7},{2,3,4},{5,6}} => 5
{{1},{2,3,4,7},{5,6}} => 7
{{1},{2,3,4},{5,6,7}} => 6
{{1},{2,3,4},{5,6},{7}} => 4
{{1,7},{2,3,4},{5},{6}} => 4
{{1},{2,3,4,7},{5},{6}} => 6
{{1},{2,3,4},{5,7},{6}} => 4
{{1},{2,3,4},{5},{6,7}} => 4
{{1},{2,3,4},{5},{6},{7}} => 3
{{1,5,6,7},{2,3},{4}} => 7
{{1,5,6},{2,3,7},{4}} => 6
{{1,5,6},{2,3},{4,7}} => 5
{{1,5,6},{2,3},{4},{7}} => 4
{{1,5,7},{2,3,6},{4}} => 6
{{1,5},{2,3,6,7},{4}} => 7
{{1,5},{2,3,6},{4,7}} => 5
{{1,5},{2,3,6},{4},{7}} => 4
{{1,5,7},{2,3},{4,6}} => 5
{{1,5},{2,3,7},{4,6}} => 5
{{1,5},{2,3},{4,6,7}} => 5
{{1,5},{2,3},{4,6},{7}} => 3
{{1,5,7},{2,3},{4},{6}} => 4
{{1,5},{2,3,7},{4},{6}} => 4
{{1,5},{2,3},{4,7},{6}} => 3
{{1,5},{2,3},{4},{6,7}} => 3
{{1,5},{2,3},{4},{6},{7}} => 2
{{1,6,7},{2,3,5},{4}} => 6
{{1,6},{2,3,5,7},{4}} => 7
{{1,6},{2,3,5},{4,7}} => 5
{{1,6},{2,3,5},{4},{7}} => 4
{{1,7},{2,3,5,6},{4}} => 7
{{1},{2,3,5,6,7},{4}} => 10
{{1},{2,3,5,6},{4,7}} => 7
{{1},{2,3,5,6},{4},{7}} => 6
{{1,7},{2,3,5},{4,6}} => 5
{{1},{2,3,5,7},{4,6}} => 7
{{1},{2,3,5},{4,6,7}} => 6
{{1},{2,3,5},{4,6},{7}} => 4
{{1,7},{2,3,5},{4},{6}} => 4
{{1},{2,3,5,7},{4},{6}} => 6
{{1},{2,3,5},{4,7},{6}} => 4
{{1},{2,3,5},{4},{6,7}} => 4
{{1},{2,3,5},{4},{6},{7}} => 3
{{1,6,7},{2,3},{4,5}} => 5
{{1,6},{2,3,7},{4,5}} => 5
{{1,6},{2,3},{4,5,7}} => 5
{{1,6},{2,3},{4,5},{7}} => 3
{{1,7},{2,3,6},{4,5}} => 5
{{1},{2,3,6,7},{4,5}} => 7
{{1},{2,3,6},{4,5,7}} => 6
{{1},{2,3,6},{4,5},{7}} => 4
{{1,7},{2,3},{4,5,6}} => 5
{{1},{2,3,7},{4,5,6}} => 6
{{1},{2,3},{4,5,6,7}} => 7
{{1},{2,3},{4,5,6},{7}} => 4
{{1,7},{2,3},{4,5},{6}} => 3
{{1},{2,3,7},{4,5},{6}} => 4
{{1},{2,3},{4,5,7},{6}} => 4
{{1},{2,3},{4,5},{6,7}} => 3
{{1},{2,3},{4,5},{6},{7}} => 2
{{1,6,7},{2,3},{4},{5}} => 4
{{1,6},{2,3,7},{4},{5}} => 4
{{1,6},{2,3},{4,7},{5}} => 3
{{1,6},{2,3},{4},{5,7}} => 3
{{1,6},{2,3},{4},{5},{7}} => 2
{{1,7},{2,3,6},{4},{5}} => 4
{{1},{2,3,6,7},{4},{5}} => 6
{{1},{2,3,6},{4,7},{5}} => 4
{{1},{2,3,6},{4},{5,7}} => 4
{{1},{2,3,6},{4},{5},{7}} => 3
{{1,7},{2,3},{4,6},{5}} => 3
{{1},{2,3,7},{4,6},{5}} => 4
{{1},{2,3},{4,6,7},{5}} => 4
{{1},{2,3},{4,6},{5,7}} => 3
{{1},{2,3},{4,6},{5},{7}} => 2
{{1,7},{2,3},{4},{5,6}} => 3
{{1},{2,3,7},{4},{5,6}} => 4
{{1},{2,3},{4,7},{5,6}} => 3
{{1},{2,3},{4},{5,6,7}} => 4
{{1},{2,3},{4},{5,6},{7}} => 2
{{1,7},{2,3},{4},{5},{6}} => 2
{{1},{2,3,7},{4},{5},{6}} => 3
{{1},{2,3},{4,7},{5},{6}} => 2
{{1},{2,3},{4},{5,7},{6}} => 2
{{1},{2,3},{4},{5},{6,7}} => 2
{{1},{2,3},{4},{5},{6},{7}} => 1
{{1,4,5,6,7},{2},{3}} => 10
{{1,4,5,6},{2,7},{3}} => 7
{{1,4,5,6},{2},{3,7}} => 7
{{1,4,5,6},{2},{3},{7}} => 6
{{1,4,5,7},{2,6},{3}} => 7
{{1,4,5},{2,6,7},{3}} => 6
{{1,4,5},{2,6},{3,7}} => 5
{{1,4,5},{2,6},{3},{7}} => 4
{{1,4,5,7},{2},{3,6}} => 7
{{1,4,5},{2,7},{3,6}} => 5
{{1,4,5},{2},{3,6,7}} => 6
{{1,4,5},{2},{3,6},{7}} => 4
{{1,4,5,7},{2},{3},{6}} => 6
{{1,4,5},{2,7},{3},{6}} => 4
{{1,4,5},{2},{3,7},{6}} => 4
{{1,4,5},{2},{3},{6,7}} => 4
{{1,4,5},{2},{3},{6},{7}} => 3
{{1,4,6,7},{2,5},{3}} => 7
{{1,4,6},{2,5,7},{3}} => 6
{{1,4,6},{2,5},{3,7}} => 5
{{1,4,6},{2,5},{3},{7}} => 4
{{1,4,7},{2,5,6},{3}} => 6
{{1,4},{2,5,6,7},{3}} => 7
{{1,4},{2,5,6},{3,7}} => 5
{{1,4},{2,5,6},{3},{7}} => 4
{{1,4,7},{2,5},{3,6}} => 5
{{1,4},{2,5,7},{3,6}} => 5
{{1,4},{2,5},{3,6,7}} => 5
{{1,4},{2,5},{3,6},{7}} => 3
{{1,4,7},{2,5},{3},{6}} => 4
{{1,4},{2,5,7},{3},{6}} => 4
{{1,4},{2,5},{3,7},{6}} => 3
{{1,4},{2,5},{3},{6,7}} => 3
{{1,4},{2,5},{3},{6},{7}} => 2
{{1,4,6,7},{2},{3,5}} => 7
{{1,4,6},{2,7},{3,5}} => 5
{{1,4,6},{2},{3,5,7}} => 6
{{1,4,6},{2},{3,5},{7}} => 4
{{1,4,7},{2,6},{3,5}} => 5
{{1,4},{2,6,7},{3,5}} => 5
{{1,4},{2,6},{3,5,7}} => 5
{{1,4},{2,6},{3,5},{7}} => 3
{{1,4,7},{2},{3,5,6}} => 6
{{1,4},{2,7},{3,5,6}} => 5
{{1,4},{2},{3,5,6,7}} => 7
{{1,4},{2},{3,5,6},{7}} => 4
{{1,4,7},{2},{3,5},{6}} => 4
{{1,4},{2,7},{3,5},{6}} => 3
{{1,4},{2},{3,5,7},{6}} => 4
{{1,4},{2},{3,5},{6,7}} => 3
{{1,4},{2},{3,5},{6},{7}} => 2
{{1,4,6,7},{2},{3},{5}} => 6
{{1,4,6},{2,7},{3},{5}} => 4
{{1,4,6},{2},{3,7},{5}} => 4
{{1,4,6},{2},{3},{5,7}} => 4
{{1,4,6},{2},{3},{5},{7}} => 3
{{1,4,7},{2,6},{3},{5}} => 4
{{1,4},{2,6,7},{3},{5}} => 4
{{1,4},{2,6},{3,7},{5}} => 3
{{1,4},{2,6},{3},{5,7}} => 3
{{1,4},{2,6},{3},{5},{7}} => 2
{{1,4,7},{2},{3,6},{5}} => 4
{{1,4},{2,7},{3,6},{5}} => 3
{{1,4},{2},{3,6,7},{5}} => 4
{{1,4},{2},{3,6},{5,7}} => 3
{{1,4},{2},{3,6},{5},{7}} => 2
{{1,4,7},{2},{3},{5,6}} => 4
{{1,4},{2,7},{3},{5,6}} => 3
{{1,4},{2},{3,7},{5,6}} => 3
{{1,4},{2},{3},{5,6,7}} => 4
{{1,4},{2},{3},{5,6},{7}} => 2
{{1,4,7},{2},{3},{5},{6}} => 3
{{1,4},{2,7},{3},{5},{6}} => 2
{{1,4},{2},{3,7},{5},{6}} => 2
{{1,4},{2},{3},{5,7},{6}} => 2
{{1,4},{2},{3},{5},{6,7}} => 2
{{1,4},{2},{3},{5},{6},{7}} => 1
{{1,5,6,7},{2,4},{3}} => 7
{{1,5,6},{2,4,7},{3}} => 6
{{1,5,6},{2,4},{3,7}} => 5
{{1,5,6},{2,4},{3},{7}} => 4
{{1,5,7},{2,4,6},{3}} => 6
{{1,5},{2,4,6,7},{3}} => 7
{{1,5},{2,4,6},{3,7}} => 5
{{1,5},{2,4,6},{3},{7}} => 4
{{1,5,7},{2,4},{3,6}} => 5
{{1,5},{2,4,7},{3,6}} => 5
{{1,5},{2,4},{3,6,7}} => 5
{{1,5},{2,4},{3,6},{7}} => 3
{{1,5,7},{2,4},{3},{6}} => 4
{{1,5},{2,4,7},{3},{6}} => 4
{{1,5},{2,4},{3,7},{6}} => 3
{{1,5},{2,4},{3},{6,7}} => 3
{{1,5},{2,4},{3},{6},{7}} => 2
{{1,6,7},{2,4,5},{3}} => 6
{{1,6},{2,4,5,7},{3}} => 7
{{1,6},{2,4,5},{3,7}} => 5
{{1,6},{2,4,5},{3},{7}} => 4
{{1,7},{2,4,5,6},{3}} => 7
{{1},{2,4,5,6,7},{3}} => 10
{{1},{2,4,5,6},{3,7}} => 7
{{1},{2,4,5,6},{3},{7}} => 6
{{1,7},{2,4,5},{3,6}} => 5
{{1},{2,4,5,7},{3,6}} => 7
{{1},{2,4,5},{3,6,7}} => 6
{{1},{2,4,5},{3,6},{7}} => 4
{{1,7},{2,4,5},{3},{6}} => 4
{{1},{2,4,5,7},{3},{6}} => 6
{{1},{2,4,5},{3,7},{6}} => 4
{{1},{2,4,5},{3},{6,7}} => 4
{{1},{2,4,5},{3},{6},{7}} => 3
{{1,6,7},{2,4},{3,5}} => 5
{{1,6},{2,4,7},{3,5}} => 5
{{1,6},{2,4},{3,5,7}} => 5
{{1,6},{2,4},{3,5},{7}} => 3
{{1,7},{2,4,6},{3,5}} => 5
{{1},{2,4,6,7},{3,5}} => 7
{{1},{2,4,6},{3,5,7}} => 6
{{1},{2,4,6},{3,5},{7}} => 4
{{1,7},{2,4},{3,5,6}} => 5
{{1},{2,4,7},{3,5,6}} => 6
{{1},{2,4},{3,5,6,7}} => 7
{{1},{2,4},{3,5,6},{7}} => 4
{{1,7},{2,4},{3,5},{6}} => 3
{{1},{2,4,7},{3,5},{6}} => 4
{{1},{2,4},{3,5,7},{6}} => 4
{{1},{2,4},{3,5},{6,7}} => 3
{{1},{2,4},{3,5},{6},{7}} => 2
{{1,6,7},{2,4},{3},{5}} => 4
{{1,6},{2,4,7},{3},{5}} => 4
{{1,6},{2,4},{3,7},{5}} => 3
{{1,6},{2,4},{3},{5,7}} => 3
{{1,6},{2,4},{3},{5},{7}} => 2
{{1,7},{2,4,6},{3},{5}} => 4
{{1},{2,4,6,7},{3},{5}} => 6
{{1},{2,4,6},{3,7},{5}} => 4
{{1},{2,4,6},{3},{5,7}} => 4
{{1},{2,4,6},{3},{5},{7}} => 3
{{1,7},{2,4},{3,6},{5}} => 3
{{1},{2,4,7},{3,6},{5}} => 4
{{1},{2,4},{3,6,7},{5}} => 4
{{1},{2,4},{3,6},{5,7}} => 3
{{1},{2,4},{3,6},{5},{7}} => 2
{{1,7},{2,4},{3},{5,6}} => 3
{{1},{2,4,7},{3},{5,6}} => 4
{{1},{2,4},{3,7},{5,6}} => 3
{{1},{2,4},{3},{5,6,7}} => 4
{{1},{2,4},{3},{5,6},{7}} => 2
{{1,7},{2,4},{3},{5},{6}} => 2
{{1},{2,4,7},{3},{5},{6}} => 3
{{1},{2,4},{3,7},{5},{6}} => 2
{{1},{2,4},{3},{5,7},{6}} => 2
{{1},{2,4},{3},{5},{6,7}} => 2
{{1},{2,4},{3},{5},{6},{7}} => 1
{{1,5,6,7},{2},{3,4}} => 7
{{1,5,6},{2,7},{3,4}} => 5
{{1,5,6},{2},{3,4,7}} => 6
{{1,5,6},{2},{3,4},{7}} => 4
{{1,5,7},{2,6},{3,4}} => 5
{{1,5},{2,6,7},{3,4}} => 5
{{1,5},{2,6},{3,4,7}} => 5
{{1,5},{2,6},{3,4},{7}} => 3
{{1,5,7},{2},{3,4,6}} => 6
{{1,5},{2,7},{3,4,6}} => 5
{{1,5},{2},{3,4,6,7}} => 7
{{1,5},{2},{3,4,6},{7}} => 4
{{1,5,7},{2},{3,4},{6}} => 4
{{1,5},{2,7},{3,4},{6}} => 3
{{1,5},{2},{3,4,7},{6}} => 4
{{1,5},{2},{3,4},{6,7}} => 3
{{1,5},{2},{3,4},{6},{7}} => 2
{{1,6,7},{2,5},{3,4}} => 5
{{1,6},{2,5,7},{3,4}} => 5
{{1,6},{2,5},{3,4,7}} => 5
{{1,6},{2,5},{3,4},{7}} => 3
{{1,7},{2,5,6},{3,4}} => 5
{{1},{2,5,6,7},{3,4}} => 7
{{1},{2,5,6},{3,4,7}} => 6
{{1},{2,5,6},{3,4},{7}} => 4
{{1,7},{2,5},{3,4,6}} => 5
{{1},{2,5,7},{3,4,6}} => 6
{{1},{2,5},{3,4,6,7}} => 7
{{1},{2,5},{3,4,6},{7}} => 4
{{1,7},{2,5},{3,4},{6}} => 3
{{1},{2,5,7},{3,4},{6}} => 4
{{1},{2,5},{3,4,7},{6}} => 4
{{1},{2,5},{3,4},{6,7}} => 3
{{1},{2,5},{3,4},{6},{7}} => 2
{{1,6,7},{2},{3,4,5}} => 6
{{1,6},{2,7},{3,4,5}} => 5
{{1,6},{2},{3,4,5,7}} => 7
{{1,6},{2},{3,4,5},{7}} => 4
{{1,7},{2,6},{3,4,5}} => 5
{{1},{2,6,7},{3,4,5}} => 6
{{1},{2,6},{3,4,5,7}} => 7
{{1},{2,6},{3,4,5},{7}} => 4
{{1,7},{2},{3,4,5,6}} => 7
{{1},{2,7},{3,4,5,6}} => 7
{{1},{2},{3,4,5,6,7}} => 10
{{1},{2},{3,4,5,6},{7}} => 6
{{1,7},{2},{3,4,5},{6}} => 4
{{1},{2,7},{3,4,5},{6}} => 4
{{1},{2},{3,4,5,7},{6}} => 6
{{1},{2},{3,4,5},{6,7}} => 4
{{1},{2},{3,4,5},{6},{7}} => 3
{{1,6,7},{2},{3,4},{5}} => 4
{{1,6},{2,7},{3,4},{5}} => 3
{{1,6},{2},{3,4,7},{5}} => 4
{{1,6},{2},{3,4},{5,7}} => 3
{{1,6},{2},{3,4},{5},{7}} => 2
{{1,7},{2,6},{3,4},{5}} => 3
{{1},{2,6,7},{3,4},{5}} => 4
{{1},{2,6},{3,4,7},{5}} => 4
{{1},{2,6},{3,4},{5,7}} => 3
{{1},{2,6},{3,4},{5},{7}} => 2
{{1,7},{2},{3,4,6},{5}} => 4
{{1},{2,7},{3,4,6},{5}} => 4
{{1},{2},{3,4,6,7},{5}} => 6
{{1},{2},{3,4,6},{5,7}} => 4
{{1},{2},{3,4,6},{5},{7}} => 3
{{1,7},{2},{3,4},{5,6}} => 3
{{1},{2,7},{3,4},{5,6}} => 3
{{1},{2},{3,4,7},{5,6}} => 4
{{1},{2},{3,4},{5,6,7}} => 4
{{1},{2},{3,4},{5,6},{7}} => 2
{{1,7},{2},{3,4},{5},{6}} => 2
{{1},{2,7},{3,4},{5},{6}} => 2
{{1},{2},{3,4,7},{5},{6}} => 3
{{1},{2},{3,4},{5,7},{6}} => 2
{{1},{2},{3,4},{5},{6,7}} => 2
{{1},{2},{3,4},{5},{6},{7}} => 1
{{1,5,6,7},{2},{3},{4}} => 6
{{1,5,6},{2,7},{3},{4}} => 4
{{1,5,6},{2},{3,7},{4}} => 4
{{1,5,6},{2},{3},{4,7}} => 4
{{1,5,6},{2},{3},{4},{7}} => 3
{{1,5,7},{2,6},{3},{4}} => 4
{{1,5},{2,6,7},{3},{4}} => 4
{{1,5},{2,6},{3,7},{4}} => 3
{{1,5},{2,6},{3},{4,7}} => 3
{{1,5},{2,6},{3},{4},{7}} => 2
{{1,5,7},{2},{3,6},{4}} => 4
{{1,5},{2,7},{3,6},{4}} => 3
{{1,5},{2},{3,6,7},{4}} => 4
{{1,5},{2},{3,6},{4,7}} => 3
{{1,5},{2},{3,6},{4},{7}} => 2
{{1,5,7},{2},{3},{4,6}} => 4
{{1,5},{2,7},{3},{4,6}} => 3
{{1,5},{2},{3,7},{4,6}} => 3
{{1,5},{2},{3},{4,6,7}} => 4
{{1,5},{2},{3},{4,6},{7}} => 2
{{1,5,7},{2},{3},{4},{6}} => 3
{{1,5},{2,7},{3},{4},{6}} => 2
{{1,5},{2},{3,7},{4},{6}} => 2
{{1,5},{2},{3},{4,7},{6}} => 2
{{1,5},{2},{3},{4},{6,7}} => 2
{{1,5},{2},{3},{4},{6},{7}} => 1
{{1,6,7},{2,5},{3},{4}} => 4
{{1,6},{2,5,7},{3},{4}} => 4
{{1,6},{2,5},{3,7},{4}} => 3
{{1,6},{2,5},{3},{4,7}} => 3
{{1,6},{2,5},{3},{4},{7}} => 2
{{1,7},{2,5,6},{3},{4}} => 4
{{1},{2,5,6,7},{3},{4}} => 6
{{1},{2,5,6},{3,7},{4}} => 4
{{1},{2,5,6},{3},{4,7}} => 4
{{1},{2,5,6},{3},{4},{7}} => 3
{{1,7},{2,5},{3,6},{4}} => 3
{{1},{2,5,7},{3,6},{4}} => 4
{{1},{2,5},{3,6,7},{4}} => 4
{{1},{2,5},{3,6},{4,7}} => 3
{{1},{2,5},{3,6},{4},{7}} => 2
{{1,7},{2,5},{3},{4,6}} => 3
{{1},{2,5,7},{3},{4,6}} => 4
{{1},{2,5},{3,7},{4,6}} => 3
{{1},{2,5},{3},{4,6,7}} => 4
{{1},{2,5},{3},{4,6},{7}} => 2
{{1,7},{2,5},{3},{4},{6}} => 2
{{1},{2,5,7},{3},{4},{6}} => 3
{{1},{2,5},{3,7},{4},{6}} => 2
{{1},{2,5},{3},{4,7},{6}} => 2
{{1},{2,5},{3},{4},{6,7}} => 2
{{1},{2,5},{3},{4},{6},{7}} => 1
{{1,6,7},{2},{3,5},{4}} => 4
{{1,6},{2,7},{3,5},{4}} => 3
{{1,6},{2},{3,5,7},{4}} => 4
{{1,6},{2},{3,5},{4,7}} => 3
{{1,6},{2},{3,5},{4},{7}} => 2
{{1,7},{2,6},{3,5},{4}} => 3
{{1},{2,6,7},{3,5},{4}} => 4
{{1},{2,6},{3,5,7},{4}} => 4
{{1},{2,6},{3,5},{4,7}} => 3
{{1},{2,6},{3,5},{4},{7}} => 2
{{1,7},{2},{3,5,6},{4}} => 4
{{1},{2,7},{3,5,6},{4}} => 4
{{1},{2},{3,5,6,7},{4}} => 6
{{1},{2},{3,5,6},{4,7}} => 4
{{1},{2},{3,5,6},{4},{7}} => 3
{{1,7},{2},{3,5},{4,6}} => 3
{{1},{2,7},{3,5},{4,6}} => 3
{{1},{2},{3,5,7},{4,6}} => 4
{{1},{2},{3,5},{4,6,7}} => 4
{{1},{2},{3,5},{4,6},{7}} => 2
{{1,7},{2},{3,5},{4},{6}} => 2
{{1},{2,7},{3,5},{4},{6}} => 2
{{1},{2},{3,5,7},{4},{6}} => 3
{{1},{2},{3,5},{4,7},{6}} => 2
{{1},{2},{3,5},{4},{6,7}} => 2
{{1},{2},{3,5},{4},{6},{7}} => 1
{{1,6,7},{2},{3},{4,5}} => 4
{{1,6},{2,7},{3},{4,5}} => 3
{{1,6},{2},{3,7},{4,5}} => 3
{{1,6},{2},{3},{4,5,7}} => 4
{{1,6},{2},{3},{4,5},{7}} => 2
{{1,7},{2,6},{3},{4,5}} => 3
{{1},{2,6,7},{3},{4,5}} => 4
{{1},{2,6},{3,7},{4,5}} => 3
{{1},{2,6},{3},{4,5,7}} => 4
{{1},{2,6},{3},{4,5},{7}} => 2
{{1,7},{2},{3,6},{4,5}} => 3
{{1},{2,7},{3,6},{4,5}} => 3
{{1},{2},{3,6,7},{4,5}} => 4
{{1},{2},{3,6},{4,5,7}} => 4
{{1},{2},{3,6},{4,5},{7}} => 2
{{1,7},{2},{3},{4,5,6}} => 4
{{1},{2,7},{3},{4,5,6}} => 4
{{1},{2},{3,7},{4,5,6}} => 4
{{1},{2},{3},{4,5,6,7}} => 6
{{1},{2},{3},{4,5,6},{7}} => 3
{{1,7},{2},{3},{4,5},{6}} => 2
{{1},{2,7},{3},{4,5},{6}} => 2
{{1},{2},{3,7},{4,5},{6}} => 2
{{1},{2},{3},{4,5,7},{6}} => 3
{{1},{2},{3},{4,5},{6,7}} => 2
{{1},{2},{3},{4,5},{6},{7}} => 1
{{1,6,7},{2},{3},{4},{5}} => 3
{{1,6},{2,7},{3},{4},{5}} => 2
{{1,6},{2},{3,7},{4},{5}} => 2
{{1,6},{2},{3},{4,7},{5}} => 2
{{1,6},{2},{3},{4},{5,7}} => 2
{{1,6},{2},{3},{4},{5},{7}} => 1
{{1,7},{2,6},{3},{4},{5}} => 2
{{1},{2,6,7},{3},{4},{5}} => 3
{{1},{2,6},{3,7},{4},{5}} => 2
{{1},{2,6},{3},{4,7},{5}} => 2
{{1},{2,6},{3},{4},{5,7}} => 2
{{1},{2,6},{3},{4},{5},{7}} => 1
{{1,7},{2},{3,6},{4},{5}} => 2
{{1},{2,7},{3,6},{4},{5}} => 2
{{1},{2},{3,6,7},{4},{5}} => 3
{{1},{2},{3,6},{4,7},{5}} => 2
{{1},{2},{3,6},{4},{5,7}} => 2
{{1},{2},{3,6},{4},{5},{7}} => 1
{{1,7},{2},{3},{4,6},{5}} => 2
{{1},{2,7},{3},{4,6},{5}} => 2
{{1},{2},{3,7},{4,6},{5}} => 2
{{1},{2},{3},{4,6,7},{5}} => 3
{{1},{2},{3},{4,6},{5,7}} => 2
{{1},{2},{3},{4,6},{5},{7}} => 1
{{1,7},{2},{3},{4},{5,6}} => 2
{{1},{2,7},{3},{4},{5,6}} => 2
{{1},{2},{3,7},{4},{5,6}} => 2
{{1},{2},{3},{4,7},{5,6}} => 2
{{1},{2},{3},{4},{5,6,7}} => 3
{{1},{2},{3},{4},{5,6},{7}} => 1
{{1,7},{2},{3},{4},{5},{6}} => 1
{{1},{2,7},{3},{4},{5},{6}} => 1
{{1},{2},{3,7},{4},{5},{6}} => 1
{{1},{2},{3},{4,7},{5},{6}} => 1
{{1},{2},{3},{4},{5,7},{6}} => 1
{{1},{2},{3},{4},{5},{6,7}} => 1
{{1},{2},{3},{4},{5},{6},{7}} => 0
{{1},{2},{3,4,5,6,7,8}} => 15
{{1},{2,4,5,6,7,8},{3}} => 15
{{1},{2,3,5,6,7,8},{4}} => 15
{{1},{2,3,4,6,7,8},{5}} => 15
{{1},{2,3,4,5,7,8},{6}} => 15
{{1},{2,3,4,5,6,7},{8}} => 15
{{1},{2,3,4,5,6,8},{7}} => 15
{{1},{2,3,4,5,6,7,8}} => 21
{{1,2},{3,4,5,6,7,8}} => 16
{{1,4,5,6,7,8},{2},{3}} => 15
{{1,3,5,6,7,8},{2},{4}} => 15
{{1,3,4,5,6,7,8},{2}} => 21
{{1,4,5,6,7,8},{2,3}} => 16
{{1,2,4,5,6,7,8},{3}} => 21
{{1,2,5,6,7,8},{3,4}} => 16
{{1,2,3,5,6,7,8},{4}} => 21
{{1,2,3,6,7,8},{4,5}} => 16
{{1,2,3,4,6,7,8},{5}} => 21
{{1,2,3,4,5,6},{7,8}} => 16
{{1,2,3,4,7,8},{5,6}} => 16
{{1,2,3,4,5,7,8},{6}} => 21
{{1,2,3,4,5,6,7},{8}} => 21
{{1,8},{2,3,4,5,6,7}} => 16
{{1,2,3,4,5,8},{6,7}} => 16
{{1,2,3,4,5,6,8},{7}} => 21
{{1,2,3,4,5,6,7,8}} => 28
{{1,3,5,6,7,8},{2,4}} => 16
{{1,3,4,6,7,8},{2,5}} => 16
{{1,2,4,6,7,8},{3,5}} => 16
{{1,3,4,5,7,8},{2,6}} => 16
{{1,2,4,5,7,8},{3,6}} => 16
{{1,2,3,5,7,8},{4,6}} => 16
{{1,3,4,5,6,8},{2,7}} => 16
{{1,2,4,5,6,8},{3,7}} => 16
{{1,2,3,5,6,8},{4,7}} => 16
{{1,2,3,4,6,8},{5,7}} => 16
{{1,3,4,5,6,7},{2,8}} => 16
{{1,2,4,5,6,7},{3,8}} => 16
{{1,2,3,5,6,7},{4,8}} => 16
{{1,2,3,4,6,7},{5,8}} => 16
{{1,2,3,4,5,7},{6,8}} => 16
{{1,3},{2,4,5,6,7,8}} => 16
{{1,4},{2,3,5,6,7,8}} => 16
{{1,5},{2,3,4,6,7,8}} => 16
{{1,6},{2,3,4,5,7,8}} => 16
{{1,7},{2,3,4,5,6,8}} => 16
-----------------------------------------------------------------------------
Created: Aug 05, 2016 at 09:31 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Aug 05, 2016 at 09:31 by Martin Rubey