10044. Fast Maximum Clique Problem

Problem Description

Given a graph $G(V, E)$, a clique is a sub-graph $g(v, e)$, so that for all vertex pairs $v_1, v_2 \in v$, there exists an edge $(v_1, v_2) \in e$. Maximum clique is the clique that has maximum number of vertex.

Input Format

There will be only one test case. For each test:

The first line has one integer $n$, the number of vertex. ($1 \lt n \le 100$)

The following $n$ lines has $n$ 0 or 1 each, indicating whether an edge exists between $i$ (line number) and $j$ (column number).

Sample Input

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

Sample Output

4