#include<bits/stdc++.h>
using namespace std;
const int N = 210;
char s[N][N];
int stg[N];
int n;
int main()
{
	cin >> n;
	for(int i=1;i<=n;i++){
		scanf("%s",s[i]+1);
	}
	int ret=-1;
	for(int S=1;S<=n;S++){
		queue<int> q;
		q.push(S);
		for(int i=1;i<=n;i++)stg[i]=0;
		stg[S]=1;
		int ans = 1;
		while(q.size()){
			int x=q.front();q.pop();
			ans=max(ans, stg[x]);
			for(int j=1;j<=n;j++)if(s[x][j]=='1'){
				if(!stg[j])stg[j]=stg[x]+1,q.push(j);
			}
		}
		for(int i=1;i<=n;i++){
			for(int j=1;j<=n;j++)if(s[i][j]=='1'){
				if(abs(stg[i]-stg[j])!=1)ans=-1;
			}
		}
		ret=max(ret,ans);
	}
	cout << ret << endl;
}
### Prompt

Your challenge is to write a cpp solution to 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;
const int N = 210;
char s[N][N];
int stg[N];
int n;
int main()
{
	cin >> n;
	for(int i=1;i<=n;i++){
		scanf("%s",s[i]+1);
	}
	int ret=-1;
	for(int S=1;S<=n;S++){
		queue<int> q;
		q.push(S);
		for(int i=1;i<=n;i++)stg[i]=0;
		stg[S]=1;
		int ans = 1;
		while(q.size()){
			int x=q.front();q.pop();
			ans=max(ans, stg[x]);
			for(int j=1;j<=n;j++)if(s[x][j]=='1'){
				if(!stg[j])stg[j]=stg[x]+1,q.push(j);
			}
		}
		for(int i=1;i<=n;i++){
			for(int j=1;j<=n;j++)if(s[i][j]=='1'){
				if(abs(stg[i]-stg[j])!=1)ans=-1;
			}
		}
		ret=max(ret,ans);
	}
	cout << ret << endl;
}
```