You are given an array of unique positive integers nums.

Consider an undirected graph where:
• There are nums.length nodes labeled nums[0] through nums[nums.length - 1].
• An edge connects nums[i] and nums[j] if nums[i] and nums[j] share a common factor strictly greater than $1$.

Return the size of the largest connected component in the graph.

Constraints:

• $1 \leq \text{nums.length} \leq 2 \times 10^4$

• $1 \leq \text{nums[i]} \leq 10^5$

• All the values of nums are unique.

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.