#include <bits/stdc++.h>
using namespace std;

int main(){
int N, M=200; cin >> N; string S[N]; int d[N][N];
for(int i=0; i<N; i++){ cin >> S[i];
for(int j=0; j<N; j++){ if(i==j){d[i][j]=0;}else{d[i][j]=(S[i][j]=='1')?1:M;} }
}

for(int k=0; k<N; k++){ for(int i=0; i<N; i++){ for(int j=0; j<N; j++){ 
  d[i][j]=min(d[i][j], d[i][k]+d[k][j]);
}}}
  
for(int k=0; k<N; k++){ for(int i=0; i<N; i++){ for(int j=0; j<N; j++){ 
  if((d[i][j]+d[i][k]+d[k][j])%2){cout << -1 << "\n"; return 0;}
}}}
  
int ans=0;  
for(int i=0; i<N-1; i++){ for(int j=i+1; j<N; j++){ ans=max(ans, d[i][j]); }}
cout << ans+1 << "\n";
}
### Prompt

Generate 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;

int main(){
int N, M=200; cin >> N; string S[N]; int d[N][N];
for(int i=0; i<N; i++){ cin >> S[i];
for(int j=0; j<N; j++){ if(i==j){d[i][j]=0;}else{d[i][j]=(S[i][j]=='1')?1:M;} }
}

for(int k=0; k<N; k++){ for(int i=0; i<N; i++){ for(int j=0; j<N; j++){ 
  d[i][j]=min(d[i][j], d[i][k]+d[k][j]);
}}}
  
for(int k=0; k<N; k++){ for(int i=0; i<N; i++){ for(int j=0; j<N; j++){ 
  if((d[i][j]+d[i][k]+d[k][j])%2){cout << -1 << "\n"; return 0;}
}}}
  
int ans=0;  
for(int i=0; i<N-1; i++){ for(int j=i+1; j<N; j++){ ans=max(ans, d[i][j]); }}
cout << ans+1 << "\n";
}
```