#include <iostream>
using namespace std;
typedef long long ll;
ll n, res;
string str[310];
int main(void){
    // Your code here!
    cin >> n;
    for (ll i = 0; i < n; i++) {
        cin >> str[i];
    }
    for (ll k = 0; k < n; k++) {
        ll ans = 0;
        for (ll i = 0; i < n; i++) {
            for (ll j = i + 1; j < n; j++) {
                if (str[(i + k) % n][j] != str[(j + k) % n][i]) ans++;
            }
        }
        if (ans == 0) res += n;
    }
    cout << res << endl;
}

### Prompt

Create a solution in Cpp for 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 <iostream>
using namespace std;
typedef long long ll;
ll n, res;
string str[310];
int main(void){
    // Your code here!
    cin >> n;
    for (ll i = 0; i < n; i++) {
        cin >> str[i];
    }
    for (ll k = 0; k < n; k++) {
        ll ans = 0;
        for (ll i = 0; i < n; i++) {
            for (ll j = i + 1; j < n; j++) {
                if (str[(i + k) % n][j] != str[(j + k) % n][i]) ans++;
            }
        }
        if (ans == 0) res += n;
    }
    cout << res << endl;
}

```