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.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		int n = int.Parse(Console.ReadLine());
    string[] strings = new string[n];   
    for(int i = 0; i < n; i++)//それぞれの行
    {
    	strings[i] = Console.ReadLine();
    }
    int answer = -1;
    int answerMemo = 0;
    Queue<int> que = new Queue<int>();
    int[] vertexNums = new int[n];//各頂点の番号
    bool answerExist = true;

    for(int i = 0; i < n; i++)//全ての頂点
    {
      for(int j = 0; j < n; j++)
      {
        vertexNums[j] = -1;
      }
      vertexNums[i] = 1;
      answerMemo = 1;
      que.Enqueue(i);
      answerExist = true;

      while(que.Count > 0)
      {
        int topMemo = que.Peek();
        que.Dequeue();

        for(int j = 0; j < n; j++)
        {
          if(strings[topMemo][j] == '1')//辺でつながっている頂点ならば
          {
            //Console.WriteLine(i+" a"+j+" "+topMemo);
            if(vertexNums[j] == -1)
            {
              vertexNums[j] = vertexNums[topMemo]+1;
              answerMemo = vertexNums[topMemo]+1;
              que.Enqueue(j);
            }else if(vertexNums[j] != vertexNums[topMemo]-1 && vertexNums[j] != vertexNums[topMemo]+1)
            {
              //Console.WriteLine(i+" "+j);
              answerExist = false;
              while(que.Count > 0)
              {
                que.Dequeue();
              }
              break;
            }
          }
        }
      }

      if(answerExist) answer = Math.Max(answer, answerMemo);
    }

		Console.WriteLine(answer);
	}
}