You are given an integer matrix grid of size m by n and an integer array queries of size k.

For each query queries[i], you start at the top left cell $(0, 0)$ and earn points based on the following rules:
If the value at grid$[0][0]$ is greater than or equal to queries[i], you cannot visit any cells and earn $0$ points.
Otherwise, you start at cell $(0, 0)$ and can repeatedly move to any adjacent cell (up, down, left, or right) that has not been visited yet, as long as the value in that adjacent cell is strictly less than queries[i].
Each uniquely visited cell adds $1$ point to your total score.

Return an array answer of size k where answer[i] is the maximum number of points you can earn for the query queries[i].

Constraints:

• m == grid.length

• n == grid[i].length

• $2 \leq$ m, n $\leq 1000$

• $4 \leq$ m * n $\leq 10^5$

• k == queries.length

• $1 \leq$ k $\leq 10^4$

• $1 \leq$ grid[i][j], queries[i] $\leq 10^6$

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.