Given an integer array nums with all distinct values, count the number of tuples (a, b, c, d) such that a * b == c * d, where a, b, c, and d are values chosen from nums.

A tuple (a, b, c, d) is considered valid when:

1. a, b, c, and d are all taken from nums

2. a * b equals c * d

3. The order of elements in the tuple matters, so different permutations count as different tuples

Return the total number of valid tuples.

Note: Each element of nums can be used at most once within a single tuple because all four values must come from distinct indices.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 10^4$

• All elements in nums are distinct.

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:

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