It’s Sunday, time for a round of code golf!

Challenge

Write the shortest source code by character count to determine if an input number is a “happy prime”, “sad prime”, “happy non-prime”, or “sad non-prime.”

Input

The input should be a integer that comes from a command line argument or stdin. Don’t worry about handling big numbers, but do so if you can/want.

Output

Output should print the type of number: “happy prime”, “sad prime”, “happy non-prime”, or “sad non-prime.”

Examples

$ happyprime 139
happy prime
$ happyprime 2
sad prime
$ happyprime 440
happy non-prime
$ happyprime 78
sad non-prime

Definitions

Just in case your brain needs a refresher.

Happy Number

From Wikipedia,

A happy number is defined by the
following process. Starting with any
positive integer, replace the number
by the sum of the squares of its
digits, and repeat the process until
the number equals 1 (where it will
stay), or it loops endlessly in a
cycle which does not include 1. Those
numbers for which this process ends in
1 are happy numbers, while those that
do not end in 1 are unhappy numbers
(or sad numbers).

For example,

• 139
• 1^2 + 3^2 + 9^2 = 91
• 9^2 + 1^2 = 82
• 8^2 + 2^2 = 68
• 6^2 + 8^2 = 100
• 1^2 + 0^2 + 0^2 = 1

Prime Number

A prime number is has precisely two divisors: 1 and itself.

Happy Prime

A happy prime, is therefore a number that is both happy and prime.