#include<cstdio>
#define N 310
#define R register
char dlb[N][N<<1];
int main()
{
	int n,ans=0,pd;
	scanf("%d",&n);
	for (R int i=1;i<=n;++i) scanf("%s",dlb[i]+1);
	for (R int i=1;i<=n;++i)
		for (R int j=1;j<=n;++j)
			dlb[i][n+j]=dlb[i][j];
	for (R int i=0;i<n;++i)
	{
		pd=0;
		for (R int j=1;j<=n;++j)
			for (R int c=j;c<=n;++c)
				if (dlb[j][c+i]==dlb[c][j+i]) pd++;
		if (pd==n*(n+1)/2) ans++;
	}
	printf("%d",ans*n);
	return 0;
}
### Prompt

In CPP, your task is to solve 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<cstdio>
#define N 310
#define R register
char dlb[N][N<<1];
int main()
{
	int n,ans=0,pd;
	scanf("%d",&n);
	for (R int i=1;i<=n;++i) scanf("%s",dlb[i]+1);
	for (R int i=1;i<=n;++i)
		for (R int j=1;j<=n;++j)
			dlb[i][n+j]=dlb[i][j];
	for (R int i=0;i<n;++i)
	{
		pd=0;
		for (R int j=1;j<=n;++j)
			for (R int c=j;c<=n;++c)
				if (dlb[j][c+i]==dlb[c][j+i]) pd++;
		if (pd==n*(n+1)/2) ans++;
	}
	printf("%d",ans*n);
	return 0;
}
```