Advent of Code

   sub y{2016}

--- Day 16: Dragon Checksum ---

You're done scanning this part of the network, but you've left traces of your presence. You need to overwrite some disks with random-looking data to cover your tracks and update the local security system with a new checksum for those disks.

For the data to not be suspicious, it needs to have certain properties; purely random data will be detected as tampering. To generate appropriate random data, you'll need to use a modified dragon curve.

Start with an appropriate initial state (your puzzle input). Then, so long as you don't have enough data yet to fill the disk, repeat the following steps:

For example, after a single step of this process,

Repeat these steps until you have enough data to fill the desired disk.

Once the data has been generated, you also need to create a checksum of that data. Calculate the checksum only for the data that fits on the disk, even if you generated more data than that in the previous step.

The checksum for some given data is created by considering each non-overlapping pair of characters in the input data. If the two characters match (00 or 11), the next checksum character is a 1. If the characters do not match (01 or 10), the next checksum character is a 0. This should produce a new string which is exactly half as long as the original. If the length of the checksum is even, repeat the process until you end up with a checksum with an odd length.

For example, suppose we want to fill a disk of length 12, and when we finally generate a string of at least length 12, the first 12 characters are 110010110100. To generate its checksum:

Therefore, the checksum for 110010110100 is 100.

Combining all of these steps together, suppose you want to fill a disk of length 20 using an initial state of 10000:

In this example, the correct checksum would therefore be 01100.

The first disk you have to fill has length 272. Using the initial state in your puzzle input, what is the correct checksum?

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