#include <stdio.h>

int main(void) {
  int i, j, k, n, ans = 0;
  scanf("%d", &n);
  char s[n][n + 10];
  for(i = 0; i < n; ++i) scanf("%s", s[i]);
  for(i = 0; i < n; ++i) {
    bool b = true;
    for(j = 0; j < n; ++j) for(k = 0; k < n; ++k) if(s[k][(i + j) % n] != s[j][(i + k) % n]) b = false;
    if(b) ans += n;
  }
  printf("%d", ans);
  return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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 <stdio.h>

int main(void) {
  int i, j, k, n, ans = 0;
  scanf("%d", &n);
  char s[n][n + 10];
  for(i = 0; i < n; ++i) scanf("%s", s[i]);
  for(i = 0; i < n; ++i) {
    bool b = true;
    for(j = 0; j < n; ++j) for(k = 0; k < n; ++k) if(s[k][(i + j) % n] != s[j][(i + k) % n]) b = false;
    if(b) ans += n;
  }
  printf("%d", ans);
  return 0;
}
```