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.Collections.Generic;

namespace AGC039_B___Graph_Partition
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine(solve());
        }
        static int solve()
        {
            var N = int.Parse(Console.ReadLine());
            var connection = new int[N + 1, N + 1];
            for (int i = 0; i < N; i++)
            {
                var read = Console.ReadLine();
                for (int j = 0; j < N; j++)
                {
                    connection[i + 1, j + 1] = read[j] == '0' ? int.MaxValue : 1;
                    if (i == j) connection[i + 1, j + 1] = 0;
                }
            }

            var partition = new int[N + 1];
            partition[1] = 1;
            var queue = new Queue<int>();
            queue.Enqueue(1);
            while (queue.Count > 0)
            {
                var current = queue.Dequeue();
                for (int next = 1; next < N + 1; next++)
                {
                    if (connection[current, next] != 1) continue;
                    if (partition[current] == partition[next]) return -1;
                    if (partition[next] == 0)
                    {
                        partition[next] = -partition[current];
                        queue.Enqueue(next);
                    }
                }
            }

            for (int via = 1; via < N + 1; via++)
            {
                for (int from = 1; from < N + 1; from++)
                {
                    for (int to = 1; to < N + 1; to++)
                    {
                        if (connection[from, via] == int.MaxValue || connection[via, to] == int.MaxValue) continue;
                        connection[from, to] = Math.Min(connection[from, to], connection[from, via] + connection[via, to]);
                    }
                }
            }

            var max = 0;
            for (int i = 1; i < N + 1; i++) for (int j = 1; j < N + 1; j++) max = Math.Max(max, connection[i, j]);
            return max + 1;
        }
    }
}