CF1461B Find the Spruce

Holidays are coming up really soon. Rick realized that it's time to think about buying a traditional spruce tree. But Rick doesn't want real trees to get hurt so he decided to find some in an $ n \times m $ matrix consisting of "\*" and ".". To find every spruce first let's define what a spruce in the matrix is. A set of matrix cells is called a spruce of height $ k $ with origin at point $ (x, y) $ if: - All cells in the set contain an "\*". - For each $ 1 \le i \le k $ all cells with the row number $ x+i-1 $ and columns in range $ [y - i + 1, y + i - 1] $ must be a part of the set. All other cells cannot belong to the set. Examples of correct and incorrect spruce trees: Now Rick wants to know how many spruces his $ n \times m $ matrix contains. Help Rick solve this problem.

Each test contains one or more test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10 $ ). The first line of each test case contains two integers $ n $ and $ m $ ( $ 1 \le n, m \le 500 $ ) — matrix size. Next $ n $ lines of each test case contain $ m $ characters $ c_{i, j} $ — matrix contents. It is guaranteed that $ c_{i, j} $ is either a "." or an "\*". It is guaranteed that the sum of $ n \cdot m $ over all test cases does not exceed $ 500^2 $ ( $ \sum n \cdot m \le 500^2 $ ).

For each test case, print single integer — the total number of spruces in the matrix.

In the first test case the first spruce of height $ 2 $ has its origin at point $ (1, 2) $ , the second spruce of height $ 1 $ has its origin at point $ (1, 2) $ , the third spruce of height $ 1 $ has its origin at point $ (2, 1) $ , the fourth spruce of height $ 1 $ has its origin at point $ (2, 2) $ , the fifth spruce of height $ 1 $ has its origin at point $ (2, 3) $ . In the second test case the first spruce of height $ 1 $ has its origin at point $ (1, 2) $ , the second spruce of height $ 1 $ has its origin at point $ (2, 1) $ , the third spruce of height $ 1 $ has its origin at point $ (2, 2) $ .