You are given a $0$ indexed $2 {D}$ integer array grid of size m $\times$ n. Each cell in grid contains either:

• $0$, representing an empty cell, or

• $1$, representing an obstacle that can be removed.

You can travel between cells by moving up, down, left, or right to an adjacent cell.

Return the minimum number of obstacles you need to remove to travel from the top left cell (0, 0) to the bottom right cell (m - 1, n - 1).

Constraints:

• m $==$ grid.length

• n $==$ grid[i].length

• $1 \leq$ m, n $\leq 10^5$

• $2 \leq$ m $\times$ n $\leq 10^5$

• 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.