The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

~~~
1! + 4! + 5! = 1 + 24 + 120 = 145
~~~

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169;
it turns out that there are only three such loops that exist:

~~~
169 -> 363601 -> 1454 -> 169
871 -> 45361 -> 871
872 -> 45362 -> 872
~~~

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

~~~
69 -> 363600 -> 1454 -> 169 -> 363601 (-> 1454)
78 -> 45360 -> 871 -> 45361 (-> 871)
540 -> 145 (-> 145)
~~~

Starting with 69 produces a chain of five non-repeating terms,
but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?