"A [**factorion**](http://mathworld.wolfram.com/Factorion.html) is an integer which is equal to the sum of factorials of its digits."

I read from [mathworld](http://mathworld.wolfram.com/Factorion.html) that the factorion of a $n$-digit number cannot exceed $n\cdot 9!$.

Why is this? I mean what is the proof?