Probability of having picked every item from the set at least once after n turns, while picking 3 per turn

Question

Let's say I have a set of 100 items. Each turn, I pick three items at random, note which ones I've picked, and put them back. What is the probability I've picked every item at least once after $n$ turns? The only statement I can make right now is that $n \geq \frac{100}{3}$ in order for the probability to be non-zero.