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 amazing is that EVERY starting number will eventually arrive at 1 or 89.

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