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.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        struct EC : IComparable<EC>
        {
            public int vertex;
            public int edgeCount;

            public int CompareTo(EC e)
            {
                return edgeCount.CompareTo(e.edgeCount);
            }
        }

        struct Element
        {
            public int destVertex;
            public int distance;
        }


        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            int[] v = new int[N];
            EC[] c = new EC[N];
            
            List<int>[] e = new List<int>[N];
            for (int i = 0; i < N; i++)
            {
                v[i] = int.MaxValue;
                e[i] = new List<int>();
                c[i].vertex = i;
            }

            for (int i = 0; i < N; i++)
            {
                string s = Console.ReadLine();
                for (int j = 0; j < N; j++)
                {
                    if(s[j] == '1')
                    {
                        e[i].Add(j);
                        c[i].edgeCount++;
                    }
                }
            }
            Array.Sort(c);

            // 辺の少ないものから処理
            int start = c[0].vertex;

            Queue<Element> q = new Queue<Element>();

            Element ele = new Element();
            ele.destVertex = c[0].vertex;
            ele.distance = 1;
            q.Enqueue(ele);

            while(q.Count > 0)
            {
                ele = q.Dequeue();

                if(v[ele.destVertex] > ele.distance)
                {
                    v[ele.destVertex] = ele.distance;
                    
                    foreach(int dest in e[ele.destVertex])
                    {
                        Element to = new Element();
                        to.destVertex = dest;
                        to.distance = ele.distance + 1;

                        q.Enqueue(to);
                    }
                }
            }

            int ans = 0;
            for (int i = 0; i < N; i++)
            {
                ans = Math.Max(ans, v[i]);

                foreach(int dest in e[i])
                {
                    if(Math.Abs(v[i]-v[dest]) != 1)
                    {
                        Console.WriteLine(-1);
                        return;
                    }
                }
            }

            Console.WriteLine(ans);
        }
    }
}