Happy Numbers

Have the function HappyNumbers(num) determine if a number is Happy, which is a number whose sum of the square of the digits eventually converges to 1. Return true if it's a Happy number, otherwise return false.

For example: the number 10 is Happy because 1^2 + 0^2 converges to 1.

Examples

Input: 1
Output: true

Input: 101
Output: false