You are given a $2$D integer array grid of size m $ imes$ n.

You can begin at any cell in the first column (column $0$) and perform moves according to the following rules. From a cell (row, col), you can move to any of the following cells provided that the target cell lies within the grid and contains a value strictly greater than the value of grid[row][col]:

• (row - $1$, col + $1$)

• (row, col + $1$)

• (row + $1$, col + $1$)

Return the maximum number of moves that can be performed.

Constraints:

• m == grid.length

• n == grid[i].length

• $2 \leq$ m, n $\leq 1000$

• $4 \leq$ m * n $\leq 10^5$

• $1 \leq$ grid[i][j] $\leq 10^6$

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.