Some password systems set a minimum length for passwords. We want to compare two systems in which the maximum password length is 16 characters, and passwords may contain any printable ASCII characters. One system allows passwords to be any length, while the other requires passwords to be at least eight characters long.

1. Calculate the search space for these two systems. (Hint: One system reduced the search space because they subtracted a collection of passwords from the range of possibilities. 2. **What is the search space of the subtracted passwords?)**