Man imagine needing math for something so stupid as minecraft

I need help finding out what the best possible layout for a farm is.

Tldr, theres an event that makes chickens drop chocolate eggs instead of normal eggs but there are limitations

It involves a 3d layout in every axis

There is a chicken limit of 30, spaced out a minimum of 20 blocks in every direction

The player can load entities within 25 blocks in the x and z axis (y is vertical, which has no limits)

The chicken "coop" is a 2x2 box which contains the chickens

pic related is my initial design, but it could be improved, I havent started building the vertical coops, which is the easiest part