--- Day 16: Permutation Promenade ---

You come upon a very unusual sight; a group of programs here appear to be dancing.

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?

--- Part Two ---

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?