You are given an integer array nums of length n.

Construct an array prefixGcd of size n, where prefixGcd[i] is the greatest common divisor ($\gcd$) of nums[i] and the maximum value in nums from index $0$ to index $i$.

Sort prefixGcd in non decreasing order. Then, form pairs by pairing the $j^{ ext{th}}$ element from the start with the $j^{ ext{th}}$ element from the end, for all $0 \le j < \lfloor n / 2 \rfloor$. If $n$ is odd, the middle element is left unpaired.

Return the sum of the greatest common divisor of each formed pair.

Constraints:

• $1 \le n ==$ nums.length $\le 10^5$

• $1 \le$ nums[i] $\le 10^9$

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.