When Multiples And Digit Sums Collide

How many positive integers \(n\) from 1 to 1000 (inclusive) are there, such that \(n\) is a multiple of 3, and the digit sum of \(n\) is also a multiple of 3?

Details and assumptions

The digit sum of a number is the sum of all its digits. For example, the digit sum of 1123 is \(1 + 1 + 2 + 3 = 7\).

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