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You are an analyst at the Central Intelligence Agency (CIA). You are assigned the job of developing a program that will analyze PIN numbers that are used to encrypt sensitive data. The CIA uses a very specific set of rules for PINs to identify non-CIA operatives who attempt to access the sensitive data (these non-CIA operatives will try PINs that do not conform to CIA rules). The rules are complicated enough that the CIA has assigned you the job of developing a program to test whether a PIN meets their rules. CIA personnel will then use the program to make sure the PINs they select to protect data conform to the rules.

The rules that your program must use to determine if the password is valid are as follows:

1. The password must be an integer greater than or equal to 100,000 and less than 1,000,000
2. All the digits in the number have to be unique.
3. The sum of the digits must be a prime number.
4. The permutation of the left - most digit (n) and the smallest digit (k) must be odd - for example: in 645923, the left - most is 6 and the smallest digit is 2.

n! / (n - k)!
Where the ! denotes a factorial. For example, for the number 645923, the permutation with n = 6 and k = 2 is: 6 * 5 * 4 * 3 * 2 * 1 / (4 * 3 * 2 * 1) = 30. You will list all valid passwords. In addition, you will need to list the total number of valid passwords at the end.

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