When Multiples And Digit Sums Collide

Number Theory Level 1

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 $1 + 1 + 2 + 3 = 7$ .