You are given an integer array nums.

In one operation, you can choose two indices a and b such that nums[a] % nums[b] == $0$, and replace nums[a] with the value of nums[b].

You may apply this operation any number of times.

Return the minimum possible sum of the elements in nums after any number of operations.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ 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.