Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

2
ab
ca

Sample Output 1

2

For each pair of A and B, the second board will look as shown below:

The second board is a good board when (A,B) = (0,1) or (A,B) = (1,0), thus the answer is 2.

Sample Input 2

4
aaaa
aaaa
aaaa
aaaa

Sample Output 2

16

Every possible choice of A and B makes the second board good.

Sample Input 3

5
abcde
fghij
klmno
pqrst
uvwxy

Sample Output 3

0

No possible choice of A and B makes the second board good.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#pragma GCC optimize("Ofast")
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>

using namespace std;

const int N=1e3+1e2+7;

int n;

char a[N][N],b[N][N],c[N][N];

inline void pre()
{
	for(int i=0;i<n;i++)
		memcpy(b[i],a[i],n);
	for(int i=0;i<n;i++)
		memcpy(b[i]+n,b[i],n);
	for(int i=0;i<n;i++)
		memcpy(b[n+i],b[i],n*2);
	for(int i=0;i<n;i++)
		for(int j=0;j<n;j++)
			c[j][i]=a[i][j];
	for(int i=0;i<n;i++)
		memcpy(c[n+i],c[i],n*2);
	for(int i=0;i<n;i++)
		memcpy(c[i]+n,c[i],n);
}

inline bool check(int x,int y)
{
	for(int i=0;i<n;i++)
		if(memcmp(c[i+y]+x,b[i+x]+y,n))
			return false;
	return true;
}

inline int solve()
{
	pre();
	int ret=0;
	for(int i=0;i<n;i++)
		for(int j=0;j<n;j++)
			ret+=check(i,j);
	printf("%d",ret);
}

int main(){
	scanf("%d",&n);
	for(int i=0;i<n;i++)
		scanf("%s",a[i]);
	solve();
}