#include<bits/stdc++.h>
using namespace std;
const int N=205;
int n,i,j,k,s[N][N],f[N][N],col[N],ans;
char c[N];
bool dfs(int u){
	for(int i=1;i<=n;++i)if(s[u][i]){if(col[i]==-1 && s[u][i]){
		col[i]=col[u]^1;
		if(!dfs(i))return 0;
	}else if(col[i]==col[u])return 0;}
	return 1;
}
int main(){
	scanf("%d",&n);
	memset(col+1,-1,n<<2);
	for(i=1;i<=n;++i){
		for(j=1;j<=n;++j)f[i][j]=i==j?0:1<<25;
		scanf("%s",c+1);
		for(j=1;j<=n;++j)if(c[j]=='1')f[i][j]=s[i][j]=1;
	}
	col[1]=0;
	if(!dfs(1)){puts("-1");return 0;}
	for(i=1;i<=n;++i)for(j=1;j<=n;++j)for(k=1;k<=n;++k)
		f[j][k]=std::min(f[j][k],f[j][i]+f[i][k]);
	for(i=1;i<=n;++i)for(j=1;j<=n;++j)ans=max(ans,f[i][j]);
	printf("%d\n",ans+1);
	return 0;
}
### Prompt

Your task is to create 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=205;
int n,i,j,k,s[N][N],f[N][N],col[N],ans;
char c[N];
bool dfs(int u){
	for(int i=1;i<=n;++i)if(s[u][i]){if(col[i]==-1 && s[u][i]){
		col[i]=col[u]^1;
		if(!dfs(i))return 0;
	}else if(col[i]==col[u])return 0;}
	return 1;
}
int main(){
	scanf("%d",&n);
	memset(col+1,-1,n<<2);
	for(i=1;i<=n;++i){
		for(j=1;j<=n;++j)f[i][j]=i==j?0:1<<25;
		scanf("%s",c+1);
		for(j=1;j<=n;++j)if(c[j]=='1')f[i][j]=s[i][j]=1;
	}
	col[1]=0;
	if(!dfs(1)){puts("-1");return 0;}
	for(i=1;i<=n;++i)for(j=1;j<=n;++j)for(k=1;k<=n;++k)
		f[j][k]=std::min(f[j][k],f[j][i]+f[i][k]);
	for(i=1;i<=n;++i)for(j=1;j<=n;++j)ans=max(ans,f[i][j]);
	printf("%d\n",ans+1);
	return 0;
}
```