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;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static StreamReader sr;

        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)998244353;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var N = Sarray()[0];
            var Sij = new string[N];
            for (var i = 0; i < N; ++i)
                Sij[i] = ReadLine();
            var ans = 0L;
            for (var i = 0; i < N; ++i)
            {
                var q = new Queue<long>();
                var no = Enumerable.Repeat(-1, (int)N).ToArray();
                q.Enqueue(i);
                no[i] = 0;
                while (q.Any())
                {
                    var r = q.Dequeue();
                    for (var j = 0; j < N; ++j)
                    {
                        if ('0' == Sij[r][j]) continue;
                        if (-1 == no[j])
                        {
                            no[j] = no[r] + 1;
                            q.Enqueue(j);
                        }
                        if (Abs(no[j] - no[r]) != 1)
                        {
                            WriteLine(-1);
                            return;
                        }
                    }
                }
                ans = Max(ans, no.Max());
            }
            WriteLine(ans + 1);
            //Out.Flush();
        }
    }
}