1461B · Find the Spruce

Problem: 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.

Input Format: 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 $500^2$ ($\sum n \cdot m \le 500^2$).

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

Note: 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 $(2, 2)$.