Find that Factorial!

Note that 40585 = 4! + 0! + 5! + 8! + 5! (i.e. the number can be expressed as the sum of the factorial of each of its digits).

There is only one three digit number that can be expressed this way. Find the sum of the digits of that number.

(P.S: I would really appreciate it if somebody could share their complete solutions to this problem.)

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