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 <iostream>
#include <cstdio>
#include <algorithm>
#include <string>
#include <cstring>
#include <cctype>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <set>
#include <map>
#include <list>
#include <stdio.h>
#include <string.h>
#include <cstdlib>
#include <math.h>
#define INF 2000000000
using namespace std;
int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
#define ll long long
#define PL pair<long long, long long>
#define P pair<int,int>
#define mk make_pair
#define en endl;
#define WHITE 0
#define BLACK 2
#define GRAY 1
#define repi(start,end) for(int i=start; i<end; i++)
#define repj(start,end) for(int j=start; j<end; j++)
#define repk(start,end) for(int k=start; k<end; k++)
#define repl(start,end) for(int l=start; l<end; l++)
#define repv(start,end) for(int v=start; v<end; v++)
#define repw(start,end) for(int w=start; w<end; w++)
#define RE return 0;

#define MAX 305
char board[MAX][MAX];
char board_n[MAX][MAX];


int main(){
  int n;
  cin>>n;
  
  repi(1, n+1){
    repj(1, n+1){
      cin>>board[i][j];
    }
  }
  
  int y=1;
  int ans=0;
  repi(0, n){
    repj(0, n){
      
      repk(1, n+1){
        repl(1, n+1){
          board_n[k][l]=board[k][l];
        }
      }
      
      
      
      char b[n+5][n+5];
      repk(1, n+1){
        repv(1, n+1){
          if(!(v<=j)) continue;
          b[k][v]=board[k][n+(v-j)];
        }
        repl(1, n+1){
          if(n-l+1-j<=0) {
            board_n[k][n-l+1]=b[k][n-l+1];
            continue;
          }
          board_n[k][n-l+1]=board_n[k][n-l+1-j];
        }
      }
      
      
      
      repl(1, n+1){
        repv(1, n+1){
          if(!(v<=i)) continue;
          b[v][l]=board[n+(v-i)][l];
        }
        repk(1, n+1){
          if(n-k+1-i<=0){
            board_n[n-k+1][l]=b[n-k+1][l];
            continue;
          }
          board_n[n-k+1][l]=board_n[n-k+1-i][l];
        }
      }
      
      
      bool check=true;
      repk(1, n+1){
        repl(1, n+1){
          if(!(l>k)) continue;
          if(board_n[k][l]!=board_n[l][k]) check=false;
        }
      }
      
      
      
      if(check) {
        ans++;
      }
    }
  }
  
  cout<<ans<<en
}