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;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace B
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var n = int.Parse(Console.ReadLine());

            var graph = new List<int>[n].Select(x => new List<int>()).ToArray();
            var start = 0;
            var min = graph.Length;
            for (var i = 0; i < graph.Length; i++)
            {
                var s = Console.ReadLine().Trim();
                var tmp = 0;
                for (var j = i + 1; j < s.Length; j++)
                {
                    if (s[j] == '1')
                    {
                        tmp++;
                        graph[i].Add(j);
                        graph[j].Add(i);
                    }
                }
                if (tmp < min && tmp != 0)
                {
                    min = tmp;
                    start = i;
                }
            }
            var queue = new Queue<int>();
            queue.Enqueue(start);
            var depths = Enumerable.Repeat(-1, graph.Length).ToArray();
            depths[start] = 0;
            while (queue.Any())
            {
                var current = queue.Dequeue();
                foreach (var next in graph[current])
                {
                    if (depths[next] != -1)
                    {
                        if (depths[current] % 2 == depths[next] % 2)
                        {
                            Console.WriteLine(-1);
                            return;
                        }
                        continue;
                    }
                    depths[next] = depths[current] + 1;
                    queue.Enqueue(next);
                }
            }
            Console.WriteLine(depths.Max() + 1);
        }
    }
}