https://adventofcode.com/2021/day/14

## \--- Day 14: Extended Polymerization ---

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:

[code]

    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
    
[/code]

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 `N _C_ N _B_ C _H_
B`.

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

[code]

    Template:     NNCB
    After step 1: NCNBCHB
    After step 2: NBCCNBBBCBHCB
    After step 3: NBBBCNCCNBBNBNBBCHBHHBCHB
    After step 4: NBBNBNBBCCNBCNCCNBBNBBNBBBNBBNBBCBHCBHHNHCBBCBHCB
    
[/code]

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?_