Problem 3: (30 points) We have a function F: {0,..,n-1 } {0, ,m-1). We know that, for 0 mod n)- (F(x)+F) mod m. The only way we have for evaluating F is to use a lookup table that stores the values of F. Unfortunately, an Evil Adversary has changed the value of 1/5 of the table entries when we were not looking. x, y n-1, FOx + y) Describe a simple randomized algorithm that, given an input z, outputs a value that equals Fe) with probability at least 1/2. Your algorithm should work for every value of z, regardless of what values the Adversary changed. Your algorithm should use as few lookups and as little computation as possible Suppose I allow you to repeat your initial algorithm three times. What should you do in this case, and what is the probability that your enhanced algorithm returns the correct