Happy Number

For a natural number $n$, define the function $f$ as follows.

$f(n)$ is the sum of the squares of the digits of $n$ written in base ten.

For example, if $n = 19$, then $f(19) = 82$ because $1^2 + 9^2 = 82$.

Applying $f$ over and over, some natural numbers eventually reach 1. Such a number is called a happy number. 19 is one of them.

• $f(19) = 1^2 + 9^2 = 82$
• $f(82) = 8^2 + 2^2 = 68$
• $f(68) = 6^2 + 8^2 = 100$
• $f(100) = 1^2 + 0^2 + 0^2 = 1$

Not every natural number is happy. Work 5 out by hand and you will see that 5 is not a happy number. Mathematicians proved that when $n$ is not a happy number, repeated application of $f$ always falls into this cycle.

$4 \to 16 \to 37 \to 58 \to 89 \to 145 \to 42 \to 20 \to 4$

Write a program that decides whether a given natural number $n$ is a happy number.

Your program reads from standard input. The input is a single line holding one integer $n$ ($1 \le n \le 1{,}000{,}000{,}000$).

Your program writes to standard output. Print exactly one line. If $n$ is a happy number, print HAPPY. Otherwise print UNHAPPY.