You are given a $0$ indexed integer array nums and a non negative integer k.

In one operation, you can:

1. Choose any index i that has not been chosen previously.

2. Replace nums[i] with any integer from the range $[$nums[i] $-$ k, nums[i] $+$ k$]$.

The beauty of the array is defined as the length of the longest subsequence consisting of equal elements.

Return the maximum possible beauty of nums after applying the operation any number of times.

Note: You can apply the operation to each index at most $1$ time.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $0 \leq$ nums[i], k $\leq 10^5$

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.