You are given an m $ imes$ n integer matrix grid consisting of non-negative integers.

In one operation, you can increment the value of any element grid[i][j] by $1$.

Return the minimum number of operations required to make all columns of grid strictly increasing from top to bottom. That is, for every column j, the condition grid[i][j] < grid[i + 1][j] must hold for all $0 \le i < m - 1$.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \le$ m, n $\le 50$

• $0 \le$ grid[i][j] $< 2500$

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.