LDA and the Multinomial Distribution

This might be a really basic question, but I do not seem to find the answer.

In the original LDA algorithm by Blei, it is stated that the topics are drawn:

zn~Multinomial(theta)

theta~Dir(alpha)

In the multinomial distribution, it is usually needed a parameter n, n being the number of trials.

Is the number of trials the same as the number of topics, or pehaps the number of documents we used in the training

Thanks a lot