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: Accepted)

#include <numeric>
#include<iostream>
#include<set>
#include<queue>
#include<vector>
#include<map>
#include<stack>
#include <cstdio>
#include<algorithm>
#include <sstream>
#include<string>
#include<string.h>
#include <cmath>
#include <iomanip>
#include <string>
#include<list>
using namespace std;
#define int long long
#define inf 1000000007
#define rep(i,j,n) for(int i=j;i<n;i++)
typedef pair<int,int>  P;
double pi = 3.141592653589793;
//使うやつはここから下に置こうな
signed main(){
    int n;cin>>n;
    int ans=0;
    char gri[605][605];
    rep(i,0,n)rep(j,0,n){
        cin>>gri[i][j];
        gri[i][j+n]=gri[i][j];
        gri[i+n][j]=gri[i][j];
        gri[i+n][j+n]=gri[i][j];
    }
    rep(k,0,n){
        bool ch=true;
        rep(i,0,n){
            rep(j,0,n){
                if(gri[i][j+k]!=gri[j][i+k])ch=false;
            }
        }
        if(ch)ans+=n;
    }
    cout<<ans<<endl;
    return 0;
}