You are given an m $ imes$ n integer matrix grid. You can start at any cell and move to any of its $4$ adjacent cells (up, down, left, right).

Return the total number of strictly increasing paths in grid. Since the answer can be very large, return it modulo $10^9 + 7$.

Two paths are considered distinct if they visit a different sequence of cells.

Constraints:

• m == grid.length

• n == grid[i].length

• $1 \leq$ m, n $\leq 1000$

• $1 \leq$ m * n $\leq 10^5$

• $1 \leq$ grid[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.