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;
using System.Diagnostics;

static class CodeJam
{
    static int[] Distances(List<int>[] edges, int i)
    {
        int N = edges.Length;
        int[] d = Enumerable.Repeat(int.MaxValue, N).ToArray();
        var q = new Queue<int>();
        d[i] = 0;
        q.Enqueue(i);
        while (q.Count > 0)
        {
            int a = q.Dequeue();
            foreach (int b in edges[a])
            {
                if (d[a] + 1 < d[b])
                {
                    d[b] = d[a] + 1;
                    q.Enqueue(b);
                }
            }
        }
        return d;
    }

    static int Farthest(int[] d)
    {
        int max = 0;
        for (int j = 1; j < d.Length; ++j)
        {
            if (d[j] > d[max]) { max = j; }
        }
        return max;
    }

    static int Solve(List<int>[] edges)
    {
        int N = edges.Length;
        int[] colors = new int[N];
        var q = new Queue<int>();
        colors[0] = 1;
        q.Enqueue(0);
        while (q.Count > 0)
        {
            int i = q.Dequeue();
            foreach (int j in edges[i])
            {
                if (colors[j] == 0)
                {
                    colors[j] = -colors[i];
                    q.Enqueue(j);
                }
                else if (colors[i] == colors[j])
                {
                    return -1;
                }
            }
        }
        int a = Farthest(Distances(edges, 0));
        int[] d = Distances(edges, a);
        int b = Farthest(d);
        return d[b] + 1;
    }

    static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());
        var edges = new List<int>[N];
        for (int i = 0; i < N; ++i)
        {
            edges[i] = new List<int>();
            string S = Console.ReadLine();
            for (int j = 0; j < N; ++j)
            {
                if (S[j] == '1') { edges[i].Add(j); }
            }
        }
        Console.WriteLine(Solve(edges));
    }
}