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.InputStream;
import java.io.PrintStream;
import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        solve(System.in, System.out);
    }

    static void solve(InputStream is, PrintStream os) {
        // Your code here!
        Scanner scan = new Scanner(is);
        int N = scan.nextInt();
        HashMap<Integer, Set<Integer>> graph = new HashMap<>();
        for (int i = 0 ; i < N ; i++) {
            graph.put(i, new HashSet<>());
        }

        for(int i = 0; i < Math.ceil(N/2.0); i++) {
            String S = scan.next();
            char sChar[] = S.toCharArray();
            for (int j = 0; j < sChar.length; j++) {
                if(sChar[j] == '1') {
                    graph.get(i).add(j);
                    graph.get(j).add(i);
                }
            }
        }

        long answer = 0;
        for (int i = 0; i < graph.size(); i++) {
            ArrayList<Integer> firstGp = new ArrayList<>();
            ArrayList<Integer> secondGp = new ArrayList<>();
            HashSet<Integer> visited = new HashSet<>();
            firstGp.add(i);
            long count = 0;
//            HashMap<Integer, Set<Integer>> tempGraph = new HashMap<>();
//            for (int j = 0 ; j < N ; j++) {
//                tempGraph.put(j, new HashSet<>(graph.get(j)));
//            }
            while(!firstGp.isEmpty()) {
                count++;
                for (Integer pos : firstGp) {
                    for (Integer childPos : graph.get(pos)) {
                        if (visited.contains(childPos))
                            continue;
                        if (firstGp.contains(childPos)) {
                            os.println(-1);
                            return;
                        }
                        if (!secondGp.contains(childPos))
                            secondGp.add(childPos);
                    }
                    visited.add(pos);
                }
//                for (Integer deletePos : firstGp) {
//                    for (Integer pos : secondGp) {
//                        graph.get(pos).remove(deletePos);
//                    }
//                }
                firstGp.clear();
                firstGp.addAll(secondGp);
                secondGp.clear();
            }
//            graph = tempGraph;
            answer = Math.max(answer, count);
        }
        os.println(answer);

    }

}