You are given an array of integers nums of length n, indexed from $1$ to n.

A subset of indices is defined as complete if the product of any two chosen indices from the subset is a perfect square. That is, for every pair of indices i and j in the subset, the product $i imes j$ must be a perfect square. A subset containing a single index is always complete.

Return the maximum sum of elements in nums corresponding to a complete subset of indices.

Constraints:

• $1 \leq n ==$ nums.length $\leq 10^4$

• $1 \leq$ 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.