Given an m $ imes$ n integer matrix mat, you can choose any cell in the matrix as your starting point.

From a cell (r, c), you can move to any other cell located in the same row or column, provided that the value in the destination cell is strictly greater than mat[r][c].

Return the maximum number of cells that can be visited along a valid path.

Constraints:

• m == mat.length

• n == mat[i].length

• $1 \leq$ m, n $\leq 10^5$

• $1 \leq$ m $ imes$ n $\leq 10^5$

• $-10^5 \leq$ mat[i][j] $\leq 10^5$

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.