#D2963. Find Symmetries
Find Symmetries
Find Symmetries
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
inputFormat
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}
outputFormat
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
样例
2
ab
ca2