Given an integer array nums, you are permitted to swap the elements at any two distinct indices i and j if and only if the greatest common divisor of nums[i] and nums[j] is strictly greater than $1$. That is, $\gcd(`nums[i]`, `nums[j]`) > 1$.

You may perform this swap operation any number of times.

Return true if it is possible to sort nums in ascending order, or false otherwise.

Constraints:

• $1 \leq$ nums.length $\leq 3 imes 10^4$

• $2 \leq$ nums[i] $\leq 10^5$

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.