#include<bits/stdc++.h>
#define ll long long
#define rep(i,m) for(long long i=0; i<m; i++)
#define FOR(i,n,m) for(long long i=n; i<m; i++)
#define all(x) (x).begin(),(x).end()
using namespace std;
int main()
{
  int n,l,m,ans;
  char s[500][500];
  ans=0;
  cin >> n;
  rep(i,n){
    rep(j,n){
      cin >> s[i][j];
    }
  }
  rep(k,n){
    rep(i,n){
      FOR(j,i,n){
        l=(i+k)%n;
        m=(j+k)%n;
        if(s[l][j]!=s[m][i])goto P;
      }
    }
    ans++;
    P:;
  }
  printf("%d",ans*n);
}
### Prompt

Your challenge is to write a Cpp solution to the following problem:

Snuke has two boards, each divided into a grid with N rows and N columns. For both of these boards, the square at the i-th row from the top and the j-th column from the left is called Square (i,j).

There is a lowercase English letter written in each square on the first board. The letter written in Square (i,j) is S_{i,j}. On the second board, nothing is written yet.

Snuke will write letters on the second board, as follows:

* First, choose two integers A and B ( 0 \leq A, B < N ).
* Write one letter in each square on the second board. Specifically, write the letter written in Square ( i+A, j+B ) on the first board into Square (i,j) on the second board. Here, the k-th row is also represented as the (N+k)-th row, and the k-th column is also represented as the (N+k)-th column.



After this operation, the second board is called a good board when, for every i and j ( 1 \leq i, j \leq N ), the letter in Square (i,j) and the letter in Square (j,i) are equal.

Find the number of the ways to choose integers A and B ( 0 \leq A, B < N ) such that the second board is a good board.

Constraints

* 1 \leq N \leq 300
* S_{i,j} ( 1 \leq i, j \leq N ) is a lowercase English letter.

Input

Input is given from Standard Input in the following format:


N
S_{1,1}S_{1,2}..S_{1,N}
S_{2,1}S_{2,2}..S_{2,N}
:
S_{N,1}S_{N,2}..S_{N,N}


Output

Print the number of the ways to choose integers A and B ( 0 \leq A, B < N ) such that the second board is a good board.

Examples

Input

2
ab
ca


Output

2


Input

4
aaaa
aaaa
aaaa
aaaa


Output

16


Input

5
abcde
fghij
klmno
pqrst
uvwxy


Output

0

### Response

```cpp
#include<bits/stdc++.h>
#define ll long long
#define rep(i,m) for(long long i=0; i<m; i++)
#define FOR(i,n,m) for(long long i=n; i<m; i++)
#define all(x) (x).begin(),(x).end()
using namespace std;
int main()
{
  int n,l,m,ans;
  char s[500][500];
  ans=0;
  cin >> n;
  rep(i,n){
    rep(j,n){
      cin >> s[i][j];
    }
  }
  rep(k,n){
    rep(i,n){
      FOR(j,i,n){
        l=(i+k)%n;
        m=(j+k)%n;
        if(s[l][j]!=s[m][i])goto P;
      }
    }
    ans++;
    P:;
  }
  printf("%d",ans*n);
}
```