You are given an integer array prizePositions sorted in non decreasing order, representing the coordinates of prizes placed along a number line. Multiple prizes may share the same position. You are also given an integer k.

You may choose $2$ segments on the number line, each of length at most k. A segment covering the interval $[a, b]$ has length at most k if $b - a \leq$ k. A prize is collected if its position lies within either of the chosen segments.

Return the maximum number of prizes you can collect.

Note: The $2$ segments may overlap, but each prize can only be counted at most once.

Constraints:

• $1 \leq$ prizePositions.length $\leq 10^5$

• $1 \leq$ prizePositions[i] $\leq 10^9$

• $0 \leq$ k $\leq 10^9$

• prizePositions is sorted in non decreasing order.

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.