Find the Spruce

1000ms

262144K

Description:

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 ".".

$\text{[math]}$

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:

$\text{[math]}$

Now Rick wants to know how many spruces his $$$n \times m$$$ matrix contains. Help Rick solve this problem.

Input:

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:

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

Sample Input:

4
2 3
.*.
***
2 3
.*.
**.
4 5
.***.
*****
*****
*.*.*
5 7
..*.*..
.*****.
*******
.*****.
..*.*..

Sample Output:

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 $$$(2, 2)$$$.

Informação

Provedor Codeforces

Código CF1461B