You are given an m $\times$ n binary matrix grid where each cell has a value of either $0$ (empty) or $1$ (occupied). You are also given two integers stampHeight and stampWidth representing the dimensions of a rectangular stamp.

You want to determine if it is possible to cover every empty cell using any number of stamps according to these rules:

• A stamp must fit entirely within the boundaries of grid.

• A stamp cannot cover any cell with a value of $1$.

• Stamps are allowed to overlap each other.

• Every cell with a value of $0$ must be covered by at least one stamp.

Return true if all empty cells can be covered, or false otherwise.

Constraints:

• m $==$ grid.length

• n $==$ grid[r].length

• $1 \leq$ m, n $\leq 10^5$

• $1 \leq$ m $\times$ n $\leq 2 \times 10^5$

• grid[r][c] is either $0$ or $1$.

• $1 \leq$ stampHeight, stampWidth $\leq 10^5$

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.