Suppose a computer's login mechanism first asks for a user name, and rejects the login if the name is not one of those in its password file. If the login name is in the password file, then the system prompts for the password, and admits the user to the system if (and only if) the password is correct. Henrietta the Hacker has a list of 10,000 commonly used login names, and a list of 100,000 commonly used passwords. On this computer, there are 100 accounts that have both a login name on the first list and a password on the second list. For simplicity, assume that no other accounts have either a login name or password on these lists. Henrietta has written code that can attempt 1000 logins per second on this computer. This program repeatedly chooses a random login name from the first list, until it finds one that is not rejected. It then repeatedly and randomly picks a password from the second list and uses it in conjunction with the found login name.

Required:
Compute the expected number of seconds it will take Henrietta to break into some account on the machine.