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++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <functional>
#include <map>

#define M 605

int dis[M][M], color[M];

using namespace std;

bool bfs(int s, int n)
{
	queue<int> q;
	q.push(s);
	color[s] = 1;
	while (!q.empty())
	{
		int from = q.front();
		q.pop();
		for (int i = 1; i <= n; i++)
		{
			if (dis[from][i] != (int)1e9 && color[i] == -1)
			{
				q.push(i);
				color[i] = !color[from];									//染成不同的颜色   
			}
			if (dis[from][i] != (int)1e9 && color[from] == color[i])		//颜色有相同，则不是二分图   
				return false;
		}
	}
	return true;
}

int main()
{
	int n;
	cin >> n;

	for (int i = 1; i <= n; i++)
	{
		string s;
		cin >> s;
		for (int j = 0; j < n; j++)
		{
			if (s[j] == '1')
				dis[i][j + 1] = 1;
			else
				dis[i][j + 1] = (int)1e9;
		}
	}

	memset(color, -1, sizeof(color));

	bool flag = false;
	for (int i = 1; i <= n; i++)
		if (color[i] == -1 && !bfs(i, n))
		{
			cout << -1 << endl;
			return 0;
		}

	for (int k = 1; k <= n; k++)
		for (int i = 1; i <= n; i++)
			for (int j = 1; j <= n; j++)
				dis[i][j] = min(dis[i][j], dis[i][k] + dis[k][j]);

	int maxl = -1;
	for (int i = 1; i <= n; i++)
		for (int j = i + 1; j <= n; j++)
		{
			if (dis[i][j] == 1e9)
			{
				cout << -1 << endl;
				return 0;
			}
			maxl = max(maxl, dis[i][j]);
		}

	cout << maxl + 1 << endl;

	return 0;
}