Given an array of positive integers nums, return the number of distinct prime factors present in the product of all elements of nums.

Note: A prime number is a positive integer greater than $1$ that has no positive divisors other than $1$ and itself. An integer is a prime factor of a number if it is a prime number that divides that number completely.

Constraints:

• $1 \leq$ nums.length $\leq 10^4$

• $2 \leq$ nums[i] $\leq 1000$

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