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 Training20200528.Questions;
using Training20200528.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Training20200528.Questions
{
    /// <summary>
    /// https://atcoder.jp/contests/agc039/tasks/agc039_b
    /// </summary>
    public class QuestionH : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var n = inputStream.ReadInt();
            var graph = Enumerable.Range(0, n).Select(_ => new List<int>()).ToArray();
            var graphMatrix = new int[n][];

            for (int i = 0; i < n; i++)
            {
                var edges = inputStream.ReadLine();
                graphMatrix[i] = edges.Select(c => c - '0').ToArray();
                for (int j = 0; j < n; j++)
                {
                    if (edges[j] == '1')
                    {
                        graph[i].Add(j);
                    }
                }
            }

            if (IsBipartite(graph))
            {
                yield return GetDiameterOf(graphMatrix) + 1;
            }
            else
            {
                yield return -1;
            }
        }

        bool IsBipartite(List<int>[] graph)
        {
            var color = new bool?[graph.Length];
            var todo = new Queue<int>();
            todo.Enqueue(0);
            color[0] = true;

            while (todo.Count > 0)
            {
                var current = todo.Dequeue();
                foreach (var next in graph[current])
                {
                    if (color[next] == null)
                    {
                        color[next] = !color[current];
                        todo.Enqueue(next);
                    }
                    else if (!(color[current].Value ^ color[next].Value))
                    {
                        return false;
                    }
                }
            }
            return true;
        }

        int GetDiameterOf(int[][] graph)
        {
            for (int i = 0; i < graph.Length; i++)
            {
                for (int j = 0; j < graph.Length; j++)
                {
                    if (i != j && graph[i][j] == 0)
                    {
                        graph[i][j] = 1 << 28;
                    }
                }
            }

            for (int k = 0; k < graph.Length; k++)
            {
                for (int i = 0; i < graph.Length; i++)
                {
                    for (int j = 0; j < graph.Length; j++)
                    {
                        graph[i][j] = Math.Min(graph[i][j], graph[i][k] + graph[k][j]);
                    }
                }
            }

            return graph.Max(row => row.Max());
        }
    }
}


namespace Training20200528
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionH();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Training20200528.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Training20200528.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion