Problem 3: Design a minimal perfect hash function for the following set of numbers U= {8,15,21,24,25,28,35}. You can only use simple arithmetic operations: addition, multiplication, and taking remainders modulo a number. (In particular, no conditional statements.) The fewer operations the better. The submission should include the definition of your hash function and justification of correctness. For the justification, you can include a piece of code that computes all values of your function on the numbers in U, and an output of its execution