#include<bits/stdc++.h>
using namespace std;
int main(){
  int N;
  cin >> N;
  vector<string> S(N);
  for (int i=0;i<N;i++){
    cin >> S.at(i);
  }
  int p = 1, F = 0;
  for (int i=0;i<N;i++){
    p = 1;
    for (int j=0;j<N;j++){
      for (int k=0;k<N;k++){
        if (S.at((j+i)%N).at(k) != S.at((k+i)%N).at(j)){
          p = 0;
          break;
        }
      }
      if (p == 0){
        break;
      }
    }
    F += N * p;
  }
  cout << F << endl;
  return 0;
}
### Prompt

Generate 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>
using namespace std;
int main(){
  int N;
  cin >> N;
  vector<string> S(N);
  for (int i=0;i<N;i++){
    cin >> S.at(i);
  }
  int p = 1, F = 0;
  for (int i=0;i<N;i++){
    p = 1;
    for (int j=0;j<N;j++){
      for (int k=0;k<N;k++){
        if (S.at((j+i)%N).at(k) != S.at((k+i)%N).at(j)){
          p = 0;
          break;
        }
      }
      if (p == 0){
        break;
      }
    }
    F += N * p;
  }
  cout << F << endl;
  return 0;
}
```