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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.stream.IntStream;
import java.util.Arrays;
import java.util.Collection;
import java.util.Scanner;
import java.util.HashMap;
import java.util.OptionalInt;
import java.util.ArrayList;
import java.util.List;
import java.util.stream.Stream;
import java.util.Map;
import java.util.Map.Entry;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        B solver = new B();
        solver.solve(1, in, out);
        out.close();
    }

    static class B {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int N = in.nextInt();
            Map<Integer, List<Integer>> map = new HashMap<>();
            for (int i = 0; i < N; i++) {
                map.put(i, new ArrayList<>());
            }

            for (int i = 0; i < N; i++) {
                String S = in.next();
                for (int j = 0; j < N; j++) {
                    if (S.charAt(j) == '1') {
                        map.get(i).add(j);
                        map.get(j).add(i);
                    }
                }
            }

            int min = map.values().stream().mapToInt(List::size).min().getAsInt();
            int start = map.entrySet().stream().filter(e -> e.getValue().size() == min).mapToInt(Map.Entry::getKey).min().getAsInt();

            int[] gs = new int[N + 1];
            Arrays.fill(gs, -1);
            gs[start] = N;
            List<List<Integer>> next = new ArrayList<>();
            for (int right : map.get(start)) {
                next.add(Arrays.asList(start, right));
            }
            while (!next.isEmpty()) {
                List<Integer> pair = next.remove(0);
                int li = pair.get(0);
                int ri = pair.get(1);
                if (gs[ri] == -1) {
                    gs[ri] = gs[li] + 1;
                    for (int n : map.get(ri)) {
                        next.add(Arrays.asList(ri, n));
                    }
                } else if (Math.abs(gs[li] - gs[ri]) != 1) {
                    out.println(-1);
                    return;
                }
            }
            long sum = Arrays.stream(gs).filter(n -> n >= 0).distinct().count();
            out.println(sum);
        }

    }
}