Imagine that you are a system administrator developing a password-based authentication system that can allow users to choose passwords of exactly length len from 20 unique characters. Suppose there is an attacker who wants to guess the password of a user by launching a brute-force attack using a machine that can verify 1000 possible guesses per second. As a system administrator, you want to make sure that an attacker cannot successfully guess a password for a period of 6 months (assuming that users change pass- words for every six months). Based on the above input values, please write a program to nd out the length of the password (i.e., the value of len) in order to achieve your goal?

Any programming language is fine.