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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		List<int>[] E = new List<int>[N];
		for(int i=0;i<N;i++) E[i] = new List<int>();
		for(int i=0;i<N;i++){
			for(int j=0;j<N;j++){
				if(S[i][j] == '1') E[i].Add(j);
			}
		}
		int[] bw = new int[N];
		for(int i=0;i<N;i++) bw[i] = -1;
		var q = new Queue<int>();
		bw[0] = 0;
		q.Enqueue(0);
		while(q.Count > 0){
			var now = q.Dequeue();
			foreach(var nxt in E[now]){
				if(bw[nxt] == -1){
					bw[nxt] = bw[now] ^ 1;
					q.Enqueue(nxt);
				} else if(bw[nxt] == bw[now]){
					Console.WriteLine(-1);
					return;
				}
			}
		}
		
		int ma = 0;
		for(int i=0;i<N;i++){
			int[] dep = new int[N];
			for(int j=0;j<N;j++) dep[j] = -1;
			dep[i] = 0;
			q = new Queue<int>();
			q.Enqueue(i);
			while(q.Count > 0){
				var now = q.Dequeue();
				foreach(var nxt in E[now]){
					if(dep[nxt] == -1){
						dep[nxt] = dep[now] + 1;
						q.Enqueue(nxt);
					}
				}
			}
			//Console.WriteLine(String.Join(" ",dep));
			for(int j=0;j<N;j++){
				ma = Math.Max(dep[j] + 1, ma);
			}
		}
		
		Console.WriteLine(ma);
		
		
		
	}
	int N;
	String[] S;
	public Sol(){
		N = ri();
		S = new String[N];
		for(int i=0;i<N;i++){
			S[i] = rs();
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}