Happy Number Checker

This problem asks you to determine whether a given integer is a Happy Number. A number is considered happy if, after a sequence of steps computing the sum of the squares of its digits, the result becomes 1. Otherwise, the process falls into an endless loop.

Formally, define the function:

[ S(n) = \sum_{d \in \text{digits of } n} d^2 ]

Starting from the initial number \(n\), repeatedly replace \(n\) with \(S(n)\). If the process terminates in 1, then the number is happy, otherwise it is not.

For example, for \(n = 19\):

19 \(\to\) 1^2 + 9^2 = 1 + 81 = 82
82 \(\to\) 8^2 + 2^2 = 64 + 4 = 68
68 \(\to\) 6^2 + 8^2 = 36 + 64 = 100
100 \(\to\) 1^2 + 0^2 + 0^2 = 1 + 0 + 0 = 1

Thus, 19 is a Happy Number.

inputFormat

The input consists of a single integer n provided via STDIN.

outputFormat

Output a single line to STDOUT containing True if n is a Happy Number, otherwise output False.

## sample

19

True