You are given an integer n representing a street with positions numbered from $0$ to n $- 1$.

You are also given a 2D integer array lights, where lights[i] $= [\text{position}_i, \text{range}_i]$ indicates that there is a street lamp at position $\text{position}_i$ that illuminates the range $[\max(0, \text{position}_i - \text{range}_i), \min(n - 1, \text{position}_i + \text{range}_i)]$ (inclusive).

Additionally, you are given a 0-indexed integer array requirement of length n, where requirement[i] represents the minimum brightness required at position i. The brightness of position i is defined as the total number of street lamps that illuminate it.

Return the total number of positions i for which the brightness at position i is at least requirement[i].

Constraints:

• $1 \leq$ n $\leq 10^5$

• $1 \leq$ lights.length $\leq 10^5$

• $0 \leq \text{position}_i <$ n

• $0 \leq \text{range}_i \leq 10^5$

• requirement.length $==$ n

• $0 \leq$ requirement[i] $\leq 10^5$

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.