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.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());
        int[][] matrix = Enumerable.Repeat(0, n).Select(_ => Console.ReadLine().Select(x => x == '1' ? 1 : int.MaxValue / 2).ToArray()).ToArray();
        PotentializedUnionFind<bool> puf = new PotentializedUnionFind<bool>(n, (x, y) => x ^ y, x => !x, false);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                if (matrix[i][j] == 1 && !puf.TryUnite(i, j, true))
                {
                    Console.WriteLine(-1);
                    return;
                }
         
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                for (int k = 0; k < n; k++)
                    matrix[j][k] = Min(matrix[j][k], matrix[j][i] + matrix[i][k]);
        Console.WriteLine(matrix.Max(x => x.Max()));
    }
}

class PotentializedUnionFind<T> where T : IEquatable<T>
{
    public int Size { get; private set; }
    public int GroupCount { get; private set; }
    public IEnumerable<int> AllRepresents => Parent.Where((x, y) => x == y);
    int[] Sizes;
    int[] Parent;
    T[] Value;
    Func<T, T, T> Operate;
    Func<T, T> Inverse;
    T Identity;

    public PotentializedUnionFind(int count, Func<T, T, T> operate, Func<T, T> inverse, T identity)
    {
        Size = count;
        GroupCount = count;
        Parent = new int[count];
        Sizes = new int[count];
        Value = new T[count];
        for (int i = 0; i < count; i++) { Sizes[Parent[i] = i] = 1; Value[i] = identity; }
        Operate = operate;
        Inverse = inverse;
        Identity = identity;
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public bool TryUnite(int x, int y, T distance)
    {
        T xd, yd;
        int xp = Find(x, out xd);
        int yp = Find(y, out yd);

        if (yp == xp) return Operate(distance, yd).Equals(xd);

        GroupCount--;
        if (Sizes[xp] < Sizes[yp])
        {
            Value[xp] = Operate(Operate(Inverse(xd), distance), yd);
            Parent[xp] = yp;
            Sizes[yp] += Sizes[xp];
        }
        else
        {
            Value[yp] = Operate(Operate(Inverse(yd), Inverse(distance)), xd);
            Parent[yp] = xp;
            Sizes[xp] += Sizes[yp];
        }
        return true;
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int GetSize(int x) => Sizes[Find(x)];

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T GetPotential(int x, int y)
    {
        T xd, yd;
        int xp = Find(x, out xd);
        int yp = Find(y, out yd);
        if (yp == xp) return Operate(Inverse(xd), yd);
        else return Identity;
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int Find(int x)
    {
        while (x != Parent[x]) { Value[x] = Operate(Value[x], Value[Parent[x]]); Parent[x] = Parent[Parent[x]]; x = Parent[x]; }
        return x;
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private int Find(int x, out T distance)
    {
        distance = Identity;
        while (x != Parent[x])
        {
            Value[x] = Operate(Value[x], Value[Parent[x]]);
            Parent[x] = Parent[Parent[x]];
            distance = Operate(distance, Value[x]);
            x = Parent[x];
        }
        return x;
    }
}