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.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int[,]A = new int[N,N];
		for(var i=0;i<N;i++){
			string s = Console.ReadLine();
			for(var j=0;j<N;j++){
				A[i,j] = int.Parse(s.Substring(j,1));
			}
		}
		int[]D = new int[N];
		for(var i=0;i<N;i++){
			D[i] = 999;
		}
		int d1 = 0;
		D[0] = 0;
		var list = new List<int>();
		list.Add(0);
		int max = 0;
		int maxi = -1;
		while(list.Count>0){
			var list2 = new List<int>(list);
			list.Clear();
			foreach(var j in list2){
				for(var k=0;k<N;k++){
					if(A[j,k]==1){
						if(D[j]+1 < D[k]){
							D[k] = D[j]+1;
							if(D[k] > max){
                              	max = D[k];
                              	maxi = k;
                            }							
							list.Add(k);
						}
					}
				}
			}
		}
		Console.Error.WriteLine(max+" "+maxi);
		max = 0;
		maxi = -1;
		bool flag = true;
		for(var h=0;h<N;h++){
			d1 = h;
		//d1 = maxi;
		for(var i=0;i<N;i++){
			D[i] = 999;
		}
		D[d1] = 0;
		list = new List<int>();
		list.Add(d1);
		while(list.Count>0){
			var list2 = new List<int>(list);
			list.Clear();
			foreach(var j in list2){
				for(var k=0;k<N;k++){
					if(A[j,k]==1){
						if(D[j]+1 < D[k]){
							D[k] = D[j]+1;
							if(D[k] > max){
                              	max = D[k];
                              	maxi = k;
                            }
							list.Add(k);
						} else if(D[j]==D[k]){
                          	flag = false;
                        }
					}
				}
			}
		}
		}
		Console.Error.WriteLine(max+" "+maxi);
      	if(flag){
			Console.WriteLine(max+1);
        } else {
          	Console.WriteLine("-1");
        }
	}
}