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>
#define int long long
#define db long double
#define x first
#define y second
#define mp make_pair
#define pb push_back
#define all(a) a.begin(), a.end()

using namespace std;

bool matrix[200][200];
int n;

int colour[200];
vector<int> cmp;

void dfs(int vertex, int c){
	colour[vertex] = c;
	cmp.push_back(vertex);
	for (int to=0;to<n;++to){
		if (!matrix[vertex][to]) continue;
		if (colour[to] == -1){
			dfs(to, 1-c);
		}
		if (colour[to] == c){
			cout << -1;
			exit(0);
		}
		continue;
	}
}

/*

void bfs(int vertex){
	vector<int> d(n, 1e9);
	d[vertex] = 0;
	queue<int> q;
	q.push(vertex);
	while (q.size()){
		int V = q.pop();
		q.front();
		if (d[V] != 1 && matrix[V][vertex]) return (d[V]+1)/2;
		for (int i=0; i < n; ++i){
			if (!matrix[vertex][i]) continue;
			if (d[i] <= d[vertex]+1) continue;
			d[i] = d[vertex]+1;
			q.push(i);
		}
	}

	return -1;




}

*/

int f[200][200];

main(){
#ifdef LOCAL
	freopen("A_input.txt", "r", stdin);
	//freopen("A_output.txt", "w", stdout);
#endif
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	cin >> n;
	for (int i=0;i<n;++i) for (int j=0;j<n;++j){
		char ch;
		cin >> ch;
		if (ch=='1'){
			matrix[i][j] = true;
			f[i][j] = 1;
		}
		else if (i != j){
			f[i][j] = 1e9;
		}
	}

	int ans=0;

	for (int i=0;i<n;++i) colour[i] = -1;

	for (int k=0; k<n; ++k)
	for (int i=0; i<n; ++i)
		for (int j=0; j<n; ++j)
			f[i][j] = min (f[i][j], f[i][k] + f[k][j]);



	for (int i=0;i<n;++i){
		if (colour[i] != -1) continue;
		cmp.clear();
		dfs(i, 0);
		int tut = 0;
		for (int j=0; j < cmp.size(); ++j) for (int e=0; e < cmp.size(); ++e){
			tut = max(tut, f[cmp[j]][cmp[e]]);
		}
		ans += tut+1;
	}

	cout << ans;
	

}