The main machinery (arms 1 through 12)
First output takes air, fire and earth from the dispersed quint 1, air from the dispersed quint 2 and uses quint 3.
Consecutive outputs only grab 2 quint and take the leftover water from the previous output as the extra air instead.
The odd one out pipeline (arms 13 through 21) uses the now available extra quint.

arm 8 moves back across the track to avoid a swing by arm 1, is the bottleneck for the rate of the main pipeline and is only a hexarm so it doesn't have to rotate back.