2020 USOMO Problems/Problem 3

Let p be an odd prime. An integer x is called a quadratic non-residue if p does not divide x − t^2 for any integer t.

Denote by A the set of all integers a such that 1 ≤ a < p, and both a and 4 − a are quadratic non-residues. Calculate the remainder when the product of the elements of A is divided by p.