Problem 1. Assume that each word of your machine has 32 bits. Assume that you can multiply two n-word numbers in time 2n 2 with a standard algorithm. Assume that you can multiply two n-word numbers in time 10n lg 3 with a ""fancy"" algorithm. For each part briefly justify and show your work. (a) Approximately how large does n have to be for the fancy algorithm to be better? (b) Approximately how many bits is that? (c) Approximately how many decimal digits is that?