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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CompetitiveProgCsLib
{
	static class MainProg
	{
		static string R => Console.ReadLine();
		static int RI => int.Parse(R);
		static double RD => double.Parse(R);
		static int[] RIs => R.Split(' ').Select(int.Parse).ToArray();
		static double[] RDs => R.Split(' ').Select(double.Parse).ToArray();
		static void Out(object obj) => Console.WriteLine(obj);
		static void Outb(bool b) => Out(b ? "Yes" : "No");
		static void OutB(bool b) => Out(b ? "YES": "NO");

		static void Main(string[] args)
		{
			var N = RI;
			string[] str = new string[N];
			for (int i = 0;i < N;i++)
			{
				str[i] = R;
			}
			int count = 0;
			for (int i = 0;i < str.Length;i++)
			{
				if(check(str,0,i))count+= str.Length;
			}
			Out(count);
		}

		static bool check(string[] str,int a,int b)
		{
			var n = str.Length;
			for(int i = 0;i < n;i++)
			{
				for(int j = i+1;j < n;j++)
				{
					if (str[(i + a) % n][(j + b) % n] != str[(j + b) % n][(i + a) % n]) return false;
				}
			}
			return true;
		}
		
	}
}