Having trouble understanding mixture density network

Hi guys, I'm trying to follow this paper, http://arxiv.org/pdf/1308.0850v3.pdf. I'm currently stuck on the handwriting prediction part. I guess first of all, my understanding of what the section is actually trying to accomplish is pretty weak. My understanding is that given a sequence of pen strokes, the network should be able to predict the future pen stroke locations.

My major problem though is understanding how to create the input vectors for the predicted part. Is the probability density (eq 23) only useful for the training part? How can I convert the 121 variable output to 3 variables?

I'm sorry if I've horribly misunderstood the paper or if my question is poorly worded/lacking information. If you want me to clarify anything, please just let me know.