CF1106A Lunar New Year and Cross Counting

Lunar New Year is approaching, and you bought a matrix with lots of "crosses". This matrix $ M $ of size $ n \times n $ contains only 'X' and '.' (without quotes). The element in the $ i $ -th row and the $ j $ -th column $ (i, j) $ is defined as $ M(i, j) $ , where $ 1 \leq i, j \leq n $ . We define a cross appearing in the $ i $ -th row and the $ j $ -th column ( $ 1 < i, j < n $ ) if and only if $ M(i, j) = M(i - 1, j - 1) = M(i - 1, j + 1) = M(i + 1, j - 1) = M(i + 1, j + 1) = $ 'X'. The following figure illustrates a cross appearing at position $ (2, 2) $ in a $ 3 \times 3 $ matrix. ```

X.X

.X.

X.X

``` Your task is to find out the number of crosses in the given matrix $ M $ . Two crosses are different if and only if they appear in different rows or columns.

The first line contains only one positive integer $ n $ ( $ 1 \leq n \leq 500 $ ), denoting the size of the matrix $ M $ . The following $ n $ lines illustrate the matrix $ M $ . Each line contains exactly $ n $ characters, each of them is 'X' or '.'. The $ j $ -th element in the $ i $ -th line represents $ M(i, j) $ , where $ 1 \leq i, j \leq n $ .

Output a single line containing only one integer number $ k $ — the number of crosses in the given matrix $ M $ .

In the first sample, a cross appears at $ (3, 3) $ , so the answer is $ 1 $ . In the second sample, no crosses appear since $ n < 3 $ , so the answer is $ 0 $ . In the third sample, crosses appear at $ (3, 2) $ , $ (3, 4) $ , $ (4, 3) $ , $ (4, 5) $ , so the answer is $ 4 $ .