Suppose Professor chao asks students in his TIC 400 class to implement a pseudorandom random number (bit) generator (PRNG). A good random bit generator is supposed to generate bits in-dependently, i.e., the probability of bit 0 (p0) is the same as the probability of bit 1 (p1), where p0 = p1 = 0.5 and p0 + p1 = 1. However, one student (Alice) implemented it in a bad way, i.e., p0 6= p1. For example, p0 = 0.3 and p1 = 0.7, or p0 = 0.2 and p1 = 0.8. Of course, the actual probabilities and her implementation details are unknown to you. You job is to use Alices defective generator to produce an unbiased random bit string without using additional cryptographic tools. First, clearly explain your step-by-step algorithms (or pseudocode). Second, provide a formal proof of correctness.