TORONTO KIDS COMPUTER CLUB | Aurora Saturday 14:30 Python Practice 22.06.18.
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Aurora Saturday 14:30 Python Practice 22.06.18.

23 Jun Aurora Saturday 14:30 Python Practice 22.06.18.

Question: 

A company’s network is composed of N computers. System administrators gathered information on the traffic between nodes, and carefully divided the network into two subnetworks in order to minimize traffic between parts.

Jack hacked into the company’s network and decided to reassign computers to maximize the traffic between two subnetworks.

The traffic data are given in the form of matrix C, where Cij is the amount of data sent between ith and jth nodes (Cij = Cji, Cii = 0). The goal is to divide the network nodes into the two disjointed subsets A and B so as to maximize the sum ∑Cij (i∈A,j∈B).

Input

The first line of input contains a number of nodes N (2 <= N <= 20). The following N lines, containing N space-separated integers each, represent the traffic matrix C (0 <= Cij <= 10000).

Output

Output must contain a single integer — the maximum traffic between the subnetworks.

Sample Input

3
0 50 30
50 0 40
30 40 0

Sample Output

90

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