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--- 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?
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