Curious Number

145 is a curious number, as \(1!\) \(+\) \(4!\) \(+\) \(5!\) \(=\) \(1 + 24 + 120 = 145\).

Find the sum of all numbers which are equal to the sum of the factorial of their digits that are less than 1 million.

Note: \(1! = 1\) and \(2! = 2\) are not considered sums and they are not included.


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