OMCC 2009 Problem 1

Let $P$ be the product of all non-zero digits of the positive integer $n$ . For example, $P(4) = 4$ , $P(50) = 5$ , $P(123) = 6$ , $P(2009) = 18$ . Find the value of the sum: P(1) + P(2) + ... + P(2008) + P(2009).