{"raw_statement":[{"iden":"problem statement","content":"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 $(i,j)$.\nThere 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.\nSnuke will write letters on the second board, as follows:\n\n*   First, choose two integers $A$ and $B$ ( $0 \\leq A, B < N$ ).\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.\n\nAfter 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.\nFind 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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 300$\n*   $S_{i,j}$ ( $1 \\leq i, j \\leq N$ ) is a lowercase English letter."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$S_{1,1}S_{1,2}..S_{1,N}$\n$S_{2,1}S_{2,2}..S_{2,N}$\n$:$\n$S_{N,1}S_{N,2}..S_{N,N}$"},{"iden":"sample input 1","content":"2\nab\nca"},{"iden":"sample output 1","content":"2\n\nFor each pair of $A$ and $B$, the second board will look as shown below:\n![image](https://img.atcoder.jp/agc023/2414e26dc3abb6dd7bfa0c800bb4af0c.png)\nThe second board is a good board when $(A,B) = (0,1)$ or $(A,B) = (1,0)$, thus the answer is $2$."},{"iden":"sample input 2","content":"4\naaaa\naaaa\naaaa\naaaa"},{"iden":"sample output 2","content":"16\n\nEvery possible choice of $A$ and $B$ makes the second board good."},{"iden":"sample input 3","content":"5\nabcde\nfghij\nklmno\npqrst\nuvwxy"},{"iden":"sample output 3","content":"0\n\nNo possible choice of $A$ and $B$ makes the second board good."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}