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: Wrong Answer)

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

namespace AtCoder.Abc
{
    class QuestionB
    {
        public static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            bool[,] flags = new bool[n, n];
            bool hasOdd = false;
            int result = 0;
            for (int i = 0; i < n; i++)
            {
                int count = 0;
                string input = Console.ReadLine();
                for(int j = 0; j < n; j++)
                {
                    if (input[j] == '1')
                    {
                        flags[i, j] = true;
                        count++;
                    }
                    else
                    {
                        flags[i, j] = false;
                    }
                }
                if(count % 2 == 1)
                {
                    hasOdd = true;
                    result++;
                }
            }

            if(hasOdd == false)
            {
                Console.WriteLine(-1);
            }
            else
            {
                Console.WriteLine(result);
            }
        }
    }
}