You are given an m by n grid of cells, where some cells are colored black. The black cells are specified by coordinates, where each coordinates[i] = [r, c] marks the cell at row r and column c as black.

Consider every $2 \times 2$ subgrid (block) fully contained in the grid. For each $k$ from $0$ to $4$, compute how many such blocks contain exactly $k$ black cells.

Return an array ans of length $5$ where ans[k] is the number of $2 \times 2$ blocks with exactly $k$ black cells.

Constraints:

• $2 \leq$ m $\leq 10^5$

• $2 \leq$ n $\leq 10^5$

• $0 \leq$ coordinates.length $\leq 10^4$

• coordinates[i].length $==$ $2$

• $0 \leq$ coordinates[i][0] $<$ m

• $0 \leq$ coordinates[i][1] $<$ n

• It is guaranteed that all entries in coordinates are pairwise distinct.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.