You are given an $m \times n$ integer matrix isWater representing a map composed of land and water cells:

• If isWater[i][j] == 0, cell $(i, j)$ represents a land cell.

• If isWater[i][j] == 1, cell $(i, j)$ represents a water cell.

You need to assign each cell a non-negative integer height such that:

• The height of every water cell is $0$.

• Any two adjacent cells sharing an edge (north, south, east, or west) have an absolute height difference of at most $1$.

Find a valid height assignment such that the maximum height across all cells in the matrix is maximized.

Return an $m \times n$ integer matrix height where height[i][j] is the assigned height of cell $(i, j)$. If there are multiple valid solutions, return any of them.

Constraints:

• m == isWater.length

• n == isWater[i].length

• $1 \leq m, n \leq 1000$

• isWater[i][j] is either $0$ or $1$.

• There is at least one water cell.

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.