Describe a polynomial time algorithm to solve the following problem: Input: A boolean function in CNF such that each clause has exactly three literals. Output: An assignment of the variables such that each clause has all TRUE literals or all FALSE literals, if such assignment exists, and report NO otherwise. Briefly explain the correctness of your design and state and analyse its runtime. Hint: there are multiple ways to solve this problem. You can use a similar construction to the one used in problem 1 and the 2-SAT algorithm from lecture as a black-box!