# 2021 Day 14: Extended Polymerization
Copyright (c) Eric Wastl
#### [Direct Link](https://adventofcode.com/2021/day/14)

## Part 1

The incredible pressures at this depth are starting to put a strain on your submarine. The submarine has [polymerization](https://en.wikipedia.org/wiki/Polymerization) equipment that would produce suitable materials to reinforce the submarine, and the nearby volcanically-active caves should even have the necessary input elements in sufficient quantities.

The submarine manual contains instructions for finding the optimal polymer formula; specifically, it offers a **polymer template** and a list of **pair insertion** rules (your puzzle input). You just need to work out what polymer would result after repeating the pair insertion process a few times.

For example:

```
NNCB

CH -> B
HH -> N
CB -> H
NH -> C
HB -> C
HC -> B
HN -> C
NN -> C
BH -> H
NC -> B
NB -> B
BN -> B
BB -> N
BC -> B
CC -> N
CN -> C
```

The first line is the **polymer template** - this is the starting point of the process.

The following section defines the **pair insertion** rules. A rule like `AB -> C` means that when elements `A` and `B` are immediately adjacent, element `C` should be inserted between them. These insertions all happen simultaneously.

So, starting with the polymer template `NNCB`, the first step simultaneously considers all three pairs:

- The first pair (`NN`) matches the rule `NN` -> `C`, so element `C` is inserted between the first `N` and the second `N`.
- The second pair (`NC`) matches the rule `NC` -> `B`, so element `B` is inserted between the `N` and the `C`.
- The third pair (`CB`) matches the rule `CB -> H`, so element `H is inserted between the `C` and the `B`.

Note that these pairs overlap: the second element of one pair is the first element of the next pair. Also, because all pairs are considered simultaneously, inserted elements are not considered to be part of a pair until the next step.

After the first step of this process, the polymer becomes `NCNBCHB`.

Here are the results of a few steps using the above rules:

```
Template:     NNCB
After step 1: NCNBCHB
After step 2: NBCCNBBBCBHCB
After step 3: NBBBCNCCNBBNBNBBCHBHHBCHB
After step 4: NBBNBNBBCCNBCNCCNBBNBBNBBBNBBNBBCBHCBHHNHCBBCBHCB
```

This polymer grows quickly. After step 5, it has length 97; After step 10, it has length 3073. After step 10, `B` occurs 1749 times, `C` occurs 298 times, `H` occurs 161 times, and `N` occurs 865 times; taking the quantity of the most common element (B, 1749) and subtracting the quantity of the least common element (`H`, 161) produces `1749 - 161 = 1588`.

Apply 10 steps of pair insertion to the polymer template and find the most and least common elements in the result. **What do you get if you take the quantity of the most common element and subtract the quantity of the least common element?**

## Part 2

The resulting polymer isn't nearly strong enough to reinforce the submarine. You'll need to run more steps of the pair insertion process; a total of **40 steps** should do it.

In the above example, the most common element is `B` (occurring `2192039569602` times) and the least common element is `H` (occurring `3849876073` times); subtracting these produces **`2188189693529`**.

Apply **40** steps of pair insertion to the polymer template and find the most and least common elements in the result. **What do you get if you take the quantity of the most common element and subtract the quantity of the least common element?**