Problem:
Score : 500 points

Problem Statement

Given is a connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the edges are described by a grid of characters S.
If S_{i,j} is 1, there is an edge connecting Vertex i and j; otherwise, there is no such edge.

Determine whether it is possible to divide the vertices into non-empty sets V_1, \dots, V_k such that the following condition is satisfied. If the answer is yes, find the maximum possible number of sets, k, in such a division.

Every edge connects two vertices belonging to two "adjacent" sets. More formally, for every edge (i,j), there exists 1\leq t\leq k-1 such that i\in V_t,j\in V_{t+1} or i\in V_{t+1},j\in V_t holds.

Constraints

2 \leq N \leq 200

S_{i,j} is 0 or 1.

S_{i,i} is 0.

S_{i,j}=S_{j,i}

The given graph is connected.

N is an integer.

Input

Input is given from Standard Input in the following format:

N
S_{1,1}...S_{1,N}
:
S_{N,1}...S_{N,N}

Output

If it is impossible to divide the vertices into sets so that the condition is satisfied, print -1.
Otherwise, print the maximum possible number of sets, k, in a division that satisfies the condition.

Sample Input 1

2
01
10

Sample Output 1

2

We can put Vertex 1 in V_1 and Vertex 2 in V_2.

Sample Input 2

3
011
101
110

Sample Output 2

-1

Sample Input 3

6
010110
101001
010100
101000
100000
010000

Sample Output 3

4

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <utility>
#include <map>
#include <vector>
#include <algorithm>
#include <queue>
#include <math.h>
#include <stack>
#include <set>
#include <deque>
#include <cmath>
#include <cassert>

using namespace std;
typedef long long ll;
ll mod = 1e9+7;
#define rep(i,n) for(int i = 0; i < (n); ++i)

int dfs(int a, vector<vector<int>> &g, int pre_color, vector<int> &color, int cnt) {
    if (color[a] == -1) {
        color[a] = (pre_color == 1) ? 2 : 1;
    }
    //cout << cnt << endl;
    int tmp_cnt = cnt;
    for (auto v: g[a]) {
        int exp_color = pre_color;
        if (color[v] == -1) {
            tmp_cnt = dfs(v, g, color[a], color, cnt + 1);
            if (tmp_cnt == -1) {
                return -1;
            }
        }
        else if (color[v] != exp_color) {
            return -1;
        }
    }
    //cout << cnt << endl;
    return tmp_cnt;
}

int main() {
    int n;
    cin >> n;
    vector<vector<int>> g(n);
    rep(i, n) rep(j, n) {
        char c;
        cin >> c;
        if (c == '1') {
            g[i].push_back(j);
        }
    }
    int ans = -1;
    rep(i, n) {
        vector<int> color(n, -1);
        int cnt = dfs(i, g, 1, color, 1);
        //cout << cnt << endl;
        if (cnt != -1) {
            //for (auto c: color) {
            //    cout << c << " ";
            //}
            //cout << endl;
            ans = max(ans, cnt);
        }
    }
    cout << ans << endl;
    return 0;
}