You are given a 0-indexed $m \times n$ binary matrix grid. Compute a 0-indexed $m \times n$ difference matrix $\text{diff}$.

For every cell $(i, j)$, the element $\text{diff}[i][j]$ is calculated as:

• Let the number of ones in the $i^{th}$ row be $\text{onesRow}[i]$.

• Let the number of ones in the $j^{th}$ column be $\text{onesCol}[j]$.

• Let the number of zeros in the $i^{th}$ row be $\text{zerosRow}[i]$.

• Let the number of zeros in the $j^{th}$ column be $\text{zerosCol}[j]$.

• $\text{diff}[i][j] = \text{onesRow}[i] + \text{onesCol}[j] - \text{zerosRow}[i] - \text{zerosCol}[j]$

Constraints:

• $m = \text{grid.length}$

• $n = \text{grid}[i].\text{length}$

• $1 \leq m, n \leq 10^5$

• $1 \leq m \times n \leq 10^5$

• $\text{grid}[i][j]$ is either $0$ or $1$.

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.