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 static System.Console;
using System.Runtime.CompilerServices;
using static MyUtil;

class MyUtil
{
    public static int[] ReadIntArray()
    {
	return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }

    public static void WarshallFloyd(int[,] d, int v)
    {
	for (int k = 0; k < v; k++)
	    for (int i = 0; i < v; i++)
		for (int j = 0; j < v; j++)
		    d[i, j] = Math.Min(d[i, j], d[i, k] + d[k, j]);
    }
}

class Program
{
    
    
    public static void Main()
    {
	int INF = 3000000;
	
	int n = int.Parse(ReadLine());

	int[,] d = new int[n,n];
	int[,] v = new int[n,n];
	for (int i = 0; i < n; i++)
	    for (int j = 0; j < n; j++)
		d[i,j] = (i == j) ? 0 : INF;

	for (int i = 0; i < n; i++)
	{
	    string s = ReadLine();
	    for (int j = 0; j < s.Length; j++)
	    {
		if (s[j] == '1'){
		    d[i,j] = 1;
		    v[i,j] = 1;
		}
	    }
	}

	WarshallFloyd(d, n);

	int farNode = -1;
	int farLength = 0;
	for (int i = 1; i < n; i++)
	{
	    if (d[0, i] > farLength)
	    {
		farLength = d[0, i];
		farNode = i;
	    }
	}

	int farNode2 = -1;
	farLength = 0;
	for (int i = 0; i < n; i++)
	{
	    if (d[farNode, i] > farLength)
	    {
		farLength = d[farNode, i];
		farNode2 = i;
	    }
	}

	int maxLen = 0;
	int maxLen2 = 0;
	int[] l = new int[n];
	int[] l2 = new int[n];
	for (int i = 0; i < n; i++)
	{
	    l[i] = d[farNode2, i];
	    l2[i] = d[farNode, i];
	    maxLen = Math.Max(maxLen, l[i]);
	    maxLen2 = Math.Max(maxLen2, l2[i]);
	}

	for (int i = 0; i < n; i ++)
	    for (int j = 0; j < n; j++)
	    {
		if (v[i,j] == 1 && Math.Abs(l[i] - l[j]) != 1)
		{
		    WriteLine(-1);
		    return;
		}
		if (v[i,j] == 1 && Math.Abs(l2[i] - l2[j]) != 1)
		{
		    WriteLine(-1);
		    return;
		}
	    }

	WriteLine(Math.Max(maxLen, maxLen2) + 1);
    }
}