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.IO;
using System.Net;
using System.Net.Sockets;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Threading.Tasks;
using System.Text.RegularExpressions;
using static System.Math;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

public static class P
{
    static int n;
    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        var matrix = Enumerable.Repeat(0, n).Select(_ => Console.ReadLine()).ToArray();
        int res = 0;
        for (int target = 0; target < n; target++)
        {
            var arrivedStep = new int[n];
            Queue<State> queue = new Queue<State>();
            queue.Enqueue(new State() { Pos = target, Step = 1 });
            arrivedStep[target] = 1;
            while (queue.Count > 0)
            {
                var state = queue.Dequeue();
                for (int i = 0; i < n; i++)
                {
                    if (matrix[state.Pos][i] == '0') continue;
                    if (arrivedStep[i] != 0 && (arrivedStep[i] < state.Step - 1 || arrivedStep[i] == state.Step)) goto end;
                    if (arrivedStep[i] != 0) continue;
                    arrivedStep[i] = state.Step + 1;
                    queue.Enqueue(new State() { Pos = i, Step = state.Step + 1 });
                }
            }
            res = Max(res, arrivedStep.Max());
        end:;
        }
        Console.WriteLine(res == 0 ? -1 : res);
    }
}

struct State
{
    public int Pos;
    public int Step;
}