Product Digit Not Zero

Define p(n) p(n) to be the product of all (decimal) digits of the number nn.

What is the value of

p(1)+p(2)+p(3)+p(4)++p(999)? p(1) + p(2) + p(3) + p(4) + \ldots + p(999)?

Do not include leading zeros in the product.

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