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

#define int long long

signed main() {
  int N;
  cin >> N;

  string S[N];
  for ( int i = 0; i < N; i++ ) cin >> S[i];

  int ans = 0;
  for ( int i = 0; i < N; i++ ) {
    bool flag = true;
    for ( int j = 0; j < N; j++ ) {
      for ( int k = 0; k < N; k++ ) {
	if ( S[(j+i)%N][k] != S[(k+i)%N][j] ) {
	  flag = false;
	  j = N;
	  break;
	}
      }
    }

    if ( flag ) ans++;
  }

  cout << ans*N << endl;
  
  return 0;
}

### Prompt

Please formulate 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;

#define int long long

signed main() {
  int N;
  cin >> N;

  string S[N];
  for ( int i = 0; i < N; i++ ) cin >> S[i];

  int ans = 0;
  for ( int i = 0; i < N; i++ ) {
    bool flag = true;
    for ( int j = 0; j < N; j++ ) {
      for ( int k = 0; k < N; k++ ) {
	if ( S[(j+i)%N][k] != S[(k+i)%N][j] ) {
	  flag = false;
	  j = N;
	  break;
	}
      }
    }

    if ( flag ) ans++;
  }

  cout << ans*N << endl;
  
  return 0;
}

```