You are given the following:

An array $$$a$$$ consisting of $$$n$$$ elements and an integer $$$k$$$. For each $$$(1 ≤ i ≤ n)$$$ , perform the following operation exactly one time:

Replace $$$a_i$$$, by $$$a_i + x$$$ where $$$x € [-k, k]$$$ which denotes, $$$x$$$ should lie in the range of $$$-k$$$ and $$$k$$$, both inclusive.

Determine the maximum length of the subsequence of array $$$a$$$, such that all numbers in that subsequence are equal after applying the given operation.

Task

A subsequence of array a is an array that can be derived from array a by removing some elements from it. (maybe none or all of them) Assume 1-based indexing

Example

$$$n = 4$$$

$$$k = 1$$$

Array $$$a = [2, 5, 1, 2]$$$

Approach Applying one operation on indices 1, 2, and 4, with $$$x = 0$$$ to get array $$$a$$$ as $$$[2, 5, 1, 2]$$$.

Applying one operation on index 3, with $$$x = 1$$$ to get array a as $$$[2, 5, 2, 2]$$$

Therefore, the maximum length of the subsequence with equal numbers is 3.