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)

#include <bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define mt make_tuple
typedef long long int ll;

using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;


typedef long long int ll;

int n;

string s[300];
static int rowhash[300][300], colhash[300][300];

int main(void){
	cin >> n;
	for(int i=0;i<n;i++) cin >> s[i];
	for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			int x = 0, jj = j;
			for(int k=0;k<n;k++){
				x += x + (s[i][jj] - 'a');
				jj++; if (jj==n) jj=0;
			}
			rowhash[i][j] = x;
			//cerr << rowhash[i][j] << "   ";
		}//cerr << endl;
	}
	for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			int x = 0, ii = i;
			for(int k=0;k<n;k++){
				x += x + (s[ii][j] - 'a');
				ii++; if (ii==n) ii=0;
			}
			colhash[i][j] = x;
			//cerr << colhash[i][j] << "    ";
		}//cerr << endl;
	}
	int ans = 0;
	for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			bool ok = true;
			int ii = i, jj = j;
			for(int k=0;k<n;k++){
				if (rowhash[ii][jj] != colhash[ii][jj]) {ok = false; break;}
				ii++; if (ii==n) ii = 0;
				jj++; if (jj==n) jj = 0;
			}
			if (ok) ans++;
		}
	}
	cout << ans << endl;

	return 0;
}