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)

/**********************************************
 *Author*        :XzzF
 *Created Time*  : 2018/4/28 20:29:57
 *Ended  Time*  : 2018/4/28 20:58:36
 *********************************************/

#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long LL;
const int inf = 1 << 30;
const LL INF = 1LL << 60;
const int MaxN = 600;

int n;
char s[MaxN + 5][MaxN + 5];

void Init() {
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= n; j++)
			scanf(" %c", &s[i][j]);
	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= n; j++) {
			s[i + n][j + n] = s[i][j];
			s[i][j + n] = s[i][j];
			s[i + n][j] = s[i][j];
		}
	}
}

bool is_all_same() {
	char ch = s[1][1];
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= n; j++)
			if(s[i][j] != ch)
				return false;
	return true;
}

bool check(int x, int y) {
	for(int i = 0; i < n; i++) 
		for(int j = 0; j <= i; j++) 
			if(s[x + i][y + j] != s[x + j][y + i])
				return false;
	return true;
}

bool is_good() {
	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= n; j++) {
			if(check(i, j)) return true;
		}
	}
	return false;
}

int main()
{
	while(scanf("%d", &n) != EOF)
	{
		Init();
		int ans = 0;
		if(is_all_same()) ans = n * n;
		else {
			if(is_good()) ans = n;
			else ans = 0;
		}
		printf("%d\n", ans);
	}
	return 0;
}