A factorion is a number that equals the sum of the factorials of its decimal digits, e.g. 145 is a factorion because 1! + 4! + 5! = 1 + 24 + 120 = 145.

There are exactly four (in base 10) such numbers;
1, 2, 145, and the last one is for you to find.

Bonus task: Determine all numbers such that the sum of factorials of their digits - expressed in any imaginable base- is exactly the same regardless of the base chosen.