Complete the following proof that there cannot be a perfect data compression program, i.e. a program that will reduce the length of any file it encounters. [Hint: a data compression program must be a 1-1 function. If two input files had the same compressed output, then the compressed output would not contain the information which one of the two input file:s it came from, and the decompressor then could not restore the input file. ] 5. Suppose we had such a program. It follows that when we apply this program to an input file of bit length n, it produces an output file of bit length at most n 1. There are 2" possible input files of length n, and at most 2- 1 output files of length at most n 1 6. A site requires you to pick a password that has exactly 9 letters (upper or lower case English alphabet) and 4 digits. The numbers and letters can be mixed and do not need to grouped with each other. How many possible passwords are there? Give the exact answer, but do not evaluate