A happy number is a number 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 either 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.