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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
// iostream is too mainstream
#include <cstdio>
// bitch please
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <list>
#include <cmath>
#include <iomanip>
#include <time.h>
#define dibs reserve
#define OVER9000 1234567890
#define ALL_THE(CAKE,LIE) for(auto LIE =CAKE.begin(); LIE != CAKE.end(); LIE++)
#define tisic 47
#define soclose 1e-8
#define chocolate win
// so much chocolate
#define patkan 9
#define ff first
#define ss second
#define abs(x) (((x) < 0)?-(x):(x))
#define uint unsigned int
#define dbl long double
#define pi 3.14159265358979323846
using namespace std;
// mylittledoge

using cat = long long;

#ifdef DONLINE_JUDGE
	// palindromic tree is better than splay tree!
	#define lld I64d
#endif

int main() {
	cin.sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(10);
	int N;
	cin >> N;
	vector<string> S(N);
	for(int i = 0; i < N; i++) cin >> S[i];
	queue<int> q;
	vector<int> part(N, -1);
	part[0] = 0;
	q.push(0);
	while(!q.empty()) {
		for(int i = 0; i < N; i++) if(part[i] == -1 && S[q.front()][i] == '1') {
			part[i] = 1-part[q.front()];
			q.push(i);
		}
		q.pop();
	}
	for(int i = 0; i < N; i++) for(int j = 0; j < N; j++) if(S[i][j] == '1' && part[i] == part[j]) {
		cout << "-1\n";
		return 0;
	}
	int ans = 0;
	for(int i = 0; i < N; i++) {
		vector<int> dist(N, -1);
		dist[i] = 0;
		q.push(i);
		while(!q.empty()) {
			for(int j = 0; j < N; j++) if(dist[j] == -1 && S[q.front()][j] == '1') {
				dist[j] = 1 + dist[q.front()];
				q.push(j);
			}
			q.pop();
		}
		for(int j = 0; j < N; j++) ans = max(ans, dist[j]+1);
	}
	cout << ans << "\n";
	return 0;
}

// look at my code
// my code is amazing