You are given an array nums consisting of positive integers.

The greatest common divisor (GCD) of a sequence of integers is the largest positive integer that divides every integer in the sequence.

Return the total number of distinct greatest common divisors among all nonempty subsequences of nums.

Note: A subsequence of an array is a sequence that can be derived from the array by deleting zero or more elements without changing the relative order of the remaining elements.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 2 imes 10^5$

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.