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 static System.Console;
using System.Collections;
using System.Collections.Generic;
using System.ComponentModel.Design;
using System.Linq;
using System.Xml;
using System.Diagnostics;
using System.IO;
using System.Threading;

namespace ConsoleApplication1
{
    internal class Program
    {
        static readonly int MAX_N = 205;
        private static readonly int INF = 1 << 29;
        private static List<int>[] G;
        private static int[,] d;
        private static int[] color;
        
        public static void Main(string[] args)
        {
            G = new List<int>[MAX_N];
            d = new int[MAX_N, MAX_N];
            color = new int[MAX_N];
            int N = int.Parse(ReadLine());
            for (int i = 0; i < N; i++)
            {
              	G[i] = new List<int>();
                for (int j = 0; j < N; j++)
                {
                    d[i,j] = i==j ? 0 : INF;
                }
            }
            
            for (int i=0; i < N; i++)
            {
                var list = ReadLine().ToCharArray().Select(x => x - '0').ToList(); 
                for (int j = 0; j < N; j++)
                {
                    if (list[j] == 1)
                    {
                        G[i].Add(j);
                        d[i, j] = 1;
                    }
                }
            }
        
        
            //２部判定
            if (! dfs(0, 1))
            {
                WriteLine(-1);
                return;
            }
            
            // ワーシャル・フロイド法
            for(int k=0;k<N;k++)
             for(int i=0;i<N;i++)
               for (int j=0;j<N;j++)
                 d[i,j] = Math.Min(d[i,j], d[i,k] + d[k,j]);
            int ans = 0;
            for (int i=0;i<N;i++)
              for (int j=0;j<N;j++)
                ans = Math.Max(ans, d[i,j]);
            WriteLine(ans+1);
        }
        
        public static bool dfs(int node, int c)
        {
            color[node] = c;
            foreach (int v in G[node])
            {
                if (color[v] == c) return false;
                if (color[v] == 0 && !dfs(v, -c)) return false;
            }
            
            return true;
        }
    }
    
    
}