#include<bits/stdc++.h>
using namespace std;const int N=2e2+7;
struct data{int to,next;}e[N*N*2];int head[N],col[N],cnt,h[N],flag,ans,t,w,n,m,i,j,k,q[N];char ch;
void ins(int u,int v){e[++cnt].to=v;e[cnt].next=head[u];head[u]=cnt;}
void dfs(int x){
	if(flag)return;
	for(int i=head[x];i;i=e[i].next)if(!col[e[i].to]){
		col[e[i].to]=-col[x];dfs(e[i].to);
	}else if(col[e[i].to]==col[x])flag=1;
} 
void bfs(int S){
	memset(h,-1,sizeof(h));t=0;w=1;q[0]=S;h[S]=0;
	while(t!=w){
		int x=q[t++];ans=max(ans,h[x]);
		for(i=head[x];i;i=e[i].next)if(h[e[i].to]==-1)h[e[i].to]=h[x]+1,q[w++]=e[i].to;
	}
}
int main(){
	for(scanf("%d",&n),i=1;i<=n;++i)for(j=1;j<=n;++j){
		scanf(" %c",&ch);k=ch-'0';if(k)ins(i,j);
	}col[1]=1;dfs(1);if(flag)puts("-1");
	else{for(int i=1;i<=n;++i)bfs(i);printf("%d\n",ans+1);}
}
### Prompt

Please create a solution in Cpp 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=2e2+7;
struct data{int to,next;}e[N*N*2];int head[N],col[N],cnt,h[N],flag,ans,t,w,n,m,i,j,k,q[N];char ch;
void ins(int u,int v){e[++cnt].to=v;e[cnt].next=head[u];head[u]=cnt;}
void dfs(int x){
	if(flag)return;
	for(int i=head[x];i;i=e[i].next)if(!col[e[i].to]){
		col[e[i].to]=-col[x];dfs(e[i].to);
	}else if(col[e[i].to]==col[x])flag=1;
} 
void bfs(int S){
	memset(h,-1,sizeof(h));t=0;w=1;q[0]=S;h[S]=0;
	while(t!=w){
		int x=q[t++];ans=max(ans,h[x]);
		for(i=head[x];i;i=e[i].next)if(h[e[i].to]==-1)h[e[i].to]=h[x]+1,q[w++]=e[i].to;
	}
}
int main(){
	for(scanf("%d",&n),i=1;i<=n;++i)for(j=1;j<=n;++j){
		scanf(" %c",&ch);k=ch-'0';if(k)ins(i,j);
	}col[1]=1;dfs(1);if(flag)puts("-1");
	else{for(int i=1;i<=n;++i)bfs(i);printf("%d\n",ans+1);}
}
```