You are given an integer array nums.

A subsequence of nums is called beautiful if it is strictly increasing. The beauty of a non empty strictly increasing subsequence is defined as the greatest common divisor (GCD) of all its elements.

Return the total sum of the beauty across all non empty strictly increasing subsequences of nums.

Constraints:

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

• $1 \leq$ nums[i] $\leq 7 imes 10^4$

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.