## --- Day 23: Experimental Emergency Teleportation ---

Using your torch to search the darkness of the rocky cavern, you finally locate the man's friend: a small *reindeer*.

You're not sure how it got so far in this cave. It looks sick - too sick to walk - and too heavy for you to carry all the way back. Sleighs won't be invented for another 1500 years, of course.

The only option is *experimental emergency teleportation*.

You hit the "experimental emergency teleportation" button on the device and push *I accept the risk* on no fewer than 18 different warning messages. Immediately, the device deploys hundreds of tiny *nanobots* which fly around the cavern, apparently assembling themselves into a very specific *formation*. The device lists the `X,Y,Z`

position (`pos`

) for each nanobot as well as its *signal radius* (`r`

) on its tiny screen (your puzzle input).

Each nanobot can transmit signals to any integer coordinate which is a distance away from it *less than or equal to* its signal radius (as measured by Manhattan distance). Coordinates a distance away of less than or equal to a nanobot's signal radius are said to be *in range* of that nanobot.

Before you start the teleportation process, you should determine which nanobot is the *strongest* (that is, which has the largest signal radius) and then, for that nanobot, the *total number of nanobots that are in range* of it, *including itself*.

For example, given the following nanobots:

```
pos=<0,0,0>, r=4
pos=<1,0,0>, r=1
pos=<4,0,0>, r=3
pos=<0,2,0>, r=1
pos=<0,5,0>, r=3
pos=<0,0,3>, r=1
pos=<1,1,1>, r=1
pos=<1,1,2>, r=1
pos=<1,3,1>, r=1
```

The strongest nanobot is the first one (position `0,0,0`

) because its signal radius, `4`

is the largest. Using that nanobot's location and signal radius, the following nanobots are in or out of range:

- The nanobot at
`0,0,0`

is distance`0`

away, and so it is*in range*. - The nanobot at
`1,0,0`

is distance`1`

away, and so it is*in range*. - The nanobot at
`4,0,0`

is distance`4`

away, and so it is*in range*. - The nanobot at
`0,2,0`

is distance`2`

away, and so it is*in range*. - The nanobot at
`0,5,0`

is distance`5`

away, and so it is*not*in range. - The nanobot at
`0,0,3`

is distance`3`

away, and so it is*in range*. - The nanobot at
`1,1,1`

is distance`3`

away, and so it is*in range*. - The nanobot at
`1,1,2`

is distance`4`

away, and so it is*in range*. - The nanobot at
`1,3,1`

is distance`5`

away, and so it is*not*in range.

In this example, in total,

nanobots are in range of the nanobot with the largest signal radius.*7*

Find the nanobot with the largest signal radius. *How many nanobots are in range* of its signals?