A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.

For example,

44>>>32>>>13>>>10>>>1>>>1
85>>>89>>>145>>>42>>>20>>>4>>>16>>>37>>>58>>>89

Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most significant is that every starting number will eventually arrive at 1 or 89.

How many starting numbers below one million will arrive at 89?

(This problem and its text come from Project Euler).