Maximum Beauty of an Array After Applying Operation

You are given a **0-indexed** array `nums` and a **non-negative** integer `k`. In one operation, you can do the following: - Choose an index `i` that **hasn't been chosen before** from the range `[0, nums.length - 1]`. - Replace `nums[i]` with any integer from the range `[nums[i] - k, nums[i] + k]`. The **beauty** of the array is the length of the longest subsequence consisting of equal elements. Return _the **maximum** possible beauty of the array _`nums`_ after applying the operation any number of times._ **Note** that you can apply the operation to each index **only once**. A **subsequence** of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the order of the remaining elements.   **Example 1:** **Input:** nums = [4,6,1,2], k = 2 **Output:** 3 **Explanation:** In this example, we apply the following operations: - Choose index 1, replace it with 4 (from range [4,8]), nums = [4,4,1,2]. - Choose index 3, replace it with 4 (from range [0,4]), nums = [4,4,1,4]. After the applied operations, the beauty of the array nums is 3 (subsequence consisting of indices 0, 1, and 3). It can be proven that 3 is the maximum possible length we can achieve. ``` **Example 2:** **Input:** nums = [1,1,1,1], k = 10 **Output:** 4 **Explanation:** In this example we don't have to apply any operations. The beauty of the array nums is 4 (whole array). ```   **Constraints:** - `1 <= nums.length <= 105` - `0 <= nums[i], k <= 105`