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ADABANKET - Ada and Banquet

Ada the Ladybug is planning two banquets. It is not an easy process since she has many friends. At first, she had a plan to invite all of her friends but the banquet hall is not big enough. Ada wants to make two banquets and invite all friends to only one of them (also note that the number of invited friends to one banquet can't be equal to N due to capacity).

Each friend knows some other friends (and this property is always symmetrical). A friend will get one dissatisfaction for each of her friends who will not be invited to same banquet. Can you find the minimal total dissatisfaction?

Input

The first line contains an integer 2 ≤ N ≤ 900, the number of friends.

Each of next N lines contain N integers Ai, j (either 0 or 1), where 1 means the ith friend is friend of jth.

Note, that the matrix will be symmetrical.

Insect is not friend with himself (well .. at least in the representation).

Important note (after new studies) is, that as brain connections of insect are not so complicated as those of humans, so the process of making friends is slightly different. Two insects have exactly 10% chance of being friends, so also the adjacency matrix will be generated (very) pseudo-randomly with 10% chance for each edge. Anyway it will be also assured, that the friendship graph will be connected.

Output

Output the minimum total dissatisfaction.

Example Input

2
0 1
1 0

Example Output

2

Example Input

5
0 1 0 0 1
1 0 0 1 0
0 0 0 1 0
0 1 1 0 0
1 0 0 0 0

Example Output

2

Example Input

10
0 0 0 0 0 0 1 1 0 1
0 0 0 0 0 1 0 0 1 0
0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 1
1 0 0 0 1 0 0 0 1 0

Example Output

2

Example Input

30
0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0
0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0
1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0
0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0
1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0

Example Output

4

Example Input

80
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Example Output

6
Submit solution!
Added by:Morass
Date:2017-11-21
Time limit:2s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
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2020-06-19 10:04:46
Just a four Liner sol :-)
2019-02-24 11:28:30
@mehmetin Hint - try your AC code for my problem DISGRAPH.
2019-02-23 10:57:39 mehmetin
My AC code, assuming N-1 people goes to one banquet, gives 4 for the case below (taken from DISGRAPH), whereas it should be 2, if the group is split into two halves. Can someone explain this?

8
0 1 1 0 0 0 0 0
1 0 1 1 0 0 0 0
1 1 0 1 0 0 0 0
0 1 1 0 1 0 0 0
0 0 0 1 0 1 1 0
0 0 0 0 1 0 1 1
0 0 0 0 1 1 0 1
0 0 0 0 0 1 1 0


Last edit: 2019-02-23 11:03:58
2017-12-15 15:58:03
And maximum satisfaction 8-))
2017-11-30 14:01:52
@gestapo871: It means that probability of every edge ~10% (while remaining connected)
2017-11-30 09:45:26
What does the important note mean ? Can someone give full explanation ?
2017-11-27 23:53:53
No, the "banquet" is simply the right form of what I wanted to say ;-)
2017-11-27 22:01:28 Simes
Good point, and now I've also heard of a blanket hall. Perhaps @Morass can enlighten us?

Last edit: 2017-11-27 22:01:48
2017-11-27 20:53:09
Not like we've heard of ladybugs investigating the minimal total dissatisfaction of their friends ;) BTW. http://www.cotswoldwoollenweavers.co.uk/blankethall.html
2017-11-27 18:15:26 Simes
More likely "banquet", I never heard of a blanketing hall.
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