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 Python (3.4.3) (judge verdict: Accepted)

N = int(input())
S = []
for i in range(N):
    S.append(input())
T = []
for i in range(N):
    tmp = ''
    for j in range(N):
        tmp += S[j][i]
    T.append(tmp[:])
#print(S)
#print(T)

ans = 0
for i in range(N):
    #print(i)
    flag = True
    for y in range(N):
        #print(S[y][i:]+S[y][:i])
        #for x in range(N):
            #if x==y:
            #    continue
            #print(x,y,(x+i)%N, S[y][(x+i)%N],S[(x+i)%N][y])
            #if S[y][(x+i)%N]!=S[(y+i)%N][x]:
        #print(y, T[(y+i)%N], S[y][i:]+S[y][:i])
        if T[(y+i)%N]!=S[y][i:]+S[y][:i]:
            flag = False
            break
    if flag:
        ans += 1

print(ans*N)