You are given an array of integers start and an integer d.

There are start.length intervals, where the ith interval is defined as $[$start[i], start[i] $+$ d$]$.

You must choose a single integer from each interval. The score of the chosen integers is defined as the minimum absolute difference between any two chosen integers.

Return the maximum possible score that can be achieved.

Constraints:

• $2 \leq$ start.length $\leq 10^5$

• $0 \leq$ start[i] $\leq 10^9$

• $0 \leq$ d $\leq 10^9$

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.