#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD=1e9+7;
const int INF=1e9;

int main(){
	int n;
	cin>>n;
	string s[n];
	for(int i=0;i<n;i++){
		cin>>s[i];
	}
	int ans=-1;
	for(int i=0;i<n;i++){
		int d[n];
		memset(d,-1,sizeof(d));
		d[i]=0;
		queue<int> q;
		q.push(i);
		while(q.size()){
			int v=q.front();
			q.pop();
			for(int j=0;j<n;j++){
				if(s[v][j]=='0')continue;
				if(d[j]!=-1){
					if((d[j]+d[v]+1)%2!=0){
						cout<<-1<<endl;
						return 0;
					}
				}
				else{
					d[j]=d[v]+1;
					ans=max(ans,d[j]);
					q.push(j);
				}
			}
		}
	}
	cout<<ans+1<<endl;
}

### Prompt

Create a solution in CPP for the following problem:

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.

Examples

Input

2
01
10


Output

2


Input

3
011
101
110


Output

-1


Input

6
010110
101001
010100
101000
100000
010000


Output

4

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MOD=1e9+7;
const int INF=1e9;

int main(){
	int n;
	cin>>n;
	string s[n];
	for(int i=0;i<n;i++){
		cin>>s[i];
	}
	int ans=-1;
	for(int i=0;i<n;i++){
		int d[n];
		memset(d,-1,sizeof(d));
		d[i]=0;
		queue<int> q;
		q.push(i);
		while(q.size()){
			int v=q.front();
			q.pop();
			for(int j=0;j<n;j++){
				if(s[v][j]=='0')continue;
				if(d[j]!=-1){
					if((d[j]+d[v]+1)%2!=0){
						cout<<-1<<endl;
						return 0;
					}
				}
				else{
					d[j]=d[v]+1;
					ans=max(ans,d[j]);
					q.push(j);
				}
			}
		}
	}
	cout<<ans+1<<endl;
}

```