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.

Examples

Input

2
ab
ca

Output

2

Input

4
aaaa
aaaa
aaaa
aaaa

Output

16

Input

5
abcde
fghij
klmno
pqrst
uvwxy

Output

0

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