Happy Numbers

Given any number, we can create a new number by adding the sums of squares of digits of that number. For example, given 203, our new number is 4 + 0 + 9 = 13. If we repeat this process, we get a sequence of numbers:

203 -> 13 -> 10 -> 1 -> 1

Sometimes, like with 203, the sequence reaches (and stays at) 1. Numbers like this are called happy.

Not all numbers are happy. If we started with 11, the sequence would be:

11 -> 2 -> 4 -> 16 -> ...

This sequence will never reach 1, and so the number 11 is called unhappy.

Given a positive whole number, you have to determine whether that number is happy or unhappy.

Examples

happy(203) ➞ True

happy(11) ➞ False

happy(107) ➞ False

Notes

• You can assume (and it is actually true!) that all positive whole numbers are either happy or unhappy. Any happy number will have a 1 in its sequence, and every unhappy number will have a 4 in its sequence.
• The only numbers passed to your function will be positive whole numbers.