Given an m $ imes$ n 2D binary matrix grid, a robot begins at the top left cell (0, 0) and wants to reach the bottom right cell (m - 1, n - 1).

From any cell with a value of $0$, the robot can choose to move in one of two directions:

• Move right

• Move down

Cells with a value of $1$ act as mirrors and cannot be stopped on:

• Entering a mirror while moving right deflects the robot downward.

• Entering a mirror while moving down deflects the robot rightward.

• If the deflected destination is another mirror, the robot continues to deflect according to its current direction of movement until it lands on an empty cell containing $0$ or moves outside the grid boundaries.

Any path that moves outside the boundaries of the grid is invalid.

Return the total number of unique paths from (0, 0) to (m - 1, n - 1).

Constraints:

• m == grid.length

• n == grid[i].length

• $2 \leq$ m, n $\leq 500$

• grid[i][j] is either $0$ or $1$.

• grid[0][0] == grid[m - 1][n - 1] == 0

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.