There is an $n \times n$ grid containing several buried artifacts. You are given the integer n and an array artifacts where artifacts[i] $= [r1_i, c1_i, r2_i, c2_i]$ describes the $i^{ th}$ artifact covering the rectangular region from the top left cell $(r1_i, c1_i)$ to the bottom right cell $(r2_i, c2_i)$ inclusive.

You are also given an array dig where each dig[i] $= [r_i, c_i]$ represents a cell $(r_i, c_i)$ that has been excavated.

An artifact is successfully extracted if all of the cells it occupies have been excavated.

Return the total number of artifacts that can be extracted.

Constraints:

• $1 \le$ n $\le 1000$

• $1 \le$ artifacts.length, dig.length $\le \min(n^2, 10^5)$

• artifacts[i].length $= 4$

• dig[i].length $= 2$

• $0 \le r1_i, c1_i, r2_i, c2_i, r_i, c_i \le n - 1$

• $r1_i \le r2_i$

• $c1_i \le c2_i$

• No two artifacts will overlap.

• The number of cells covered by an artifact is at most $4$.

• The entries of dig are unique.

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.