## \-\-- Day 16: Permutation Promenade \-\--

You come upon a very unusual sight; a group of programs here appear to
be [dancing](https://www.youtube.com/watch?v=lyZQPjUT5B4&t=53).

There are sixteen programs in total, named `a` through `p`. They start
by standing in a line: `a` stands
in position `0`, `b` stands in position `1`, and so on until `p`, which
stands in position `15`.

The programs\' *dance* consists of a sequence of *dance moves*:

-   *Spin*, written `sX`, makes `X` programs move from the end to the
    front, but maintain their order otherwise. (For example, `s3` on
    `abcde` produces `cdeab`).
-   *Exchange*, written `xA/B`, makes the programs at positions `A` and
    `B` swap places.
-   *Partner*, written `pA/B`, makes the programs named `A` and `B` swap
    places.

For example, with only five programs standing in a line (`abcde`), they
could do the following dance:

-   `s1`, a spin of size `1`: `eabcd`.
-   `x3/4`, swapping the last two programs: `eabdc`.
-   `pe/b`, swapping programs `e` and `b`: `baedc`.

After finishing their dance, the programs end up in order `baedc`.

You watch the dance for a while and record their dance moves (your
puzzle input). *In what order are the programs standing* after their
dance?

Your puzzle answer was `ehdpincaogkblmfj`.

The first half of this puzzle is complete! It provides one gold star: \*

## \-\-- Part Two \-\-- {#part2}

Now that you\'re starting to get a feel for the dance moves, you turn
your attention to *the dance as a whole*.

Keeping the positions they ended up in from their previous dance, the
programs perform it again and again: including the first dance, a total
of *one billion* (`1000000000`) times.

In the example above, their second dance would *begin* with the order
`baedc`, and use the same dance moves:

-   `s1`, a spin of size `1`: `cbaed`.
-   `x3/4`, swapping the last two programs: `cbade`.
-   `pe/b`, swapping programs `e` and `b`: `ceadb`.

*In what order are the programs standing* after their billion dances?

Answer:

Although it hasn\'t changed, you can still [get your puzzle
input](16/input).