You are given an array of positive integers nums.

You need to select a subset of nums that can be arranged into a sequence of length $2k + 1$ for some integer $k \ge 0$, such that the sequence follows the pattern:

$[x, x^2, x^4, \dots, x^{2^k}, \dots, x^4, x^2, x]$

for some positive integer $x$.

Return the maximum number of elements in such a subset.

Note: A subset is a collection of elements obtained by deleting zero or more elements from an array without changing the relative order of the remaining elements.

Constraints:

• $2 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

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.