#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <math.h>
using namespace std;

const int MAXN = 300 + 10;
int N;
char S[MAXN][MAXN];
int ans;

int main() {
	register int i, j, k;
	scanf( "%d", &N );
	for( i = 0; i < N; ++i )
		scanf( "%s", S[i] );
	for( i = 0; i < N; ++i ) {
		bool flag = 1;
		for( j = 0; j < N; ++j )
			for( k = j + 1; k < N; ++k )
				if( S[( i + j ) % N][k] != S[( i + k ) % N][j] )
					flag = 0;
		ans += flag;
	}
	printf( "%d\n", ans * N );
	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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <math.h>
using namespace std;

const int MAXN = 300 + 10;
int N;
char S[MAXN][MAXN];
int ans;

int main() {
	register int i, j, k;
	scanf( "%d", &N );
	for( i = 0; i < N; ++i )
		scanf( "%s", S[i] );
	for( i = 0; i < N; ++i ) {
		bool flag = 1;
		for( j = 0; j < N; ++j )
			for( k = j + 1; k < N; ++k )
				if( S[( i + j ) % N][k] != S[( i + k ) % N][j] )
					flag = 0;
		ans += flag;
	}
	printf( "%d\n", ans * N );
	return 0;
}
```