Maximum number of 1wire temp sensors

There are 5 strands, one of them is a T shape. There is a 1wire every 16 inches. There's 60 sensors all together. I'm powering it with +5 volts and ground from the Arduino Mega 2560. I'm not using parasite power. I have a 4.7k resistor between data and +5v. Every strand works fine if it's the only one connected to the Arduino. Iif I connect the 9 device strand and 10 device strand together, it works, as does the 9 + 9 device strands. But when I try to connect the 15 or 17 device strands to any other strand, it reads zero devices found. That's why I suspect I'm exceeding some maximum.

Here's the topology: