--- Day 20: Particle Swarm ---

Suddenly, the GPU contacts you, asking for help. Someone has asked it
to simulate too many particles, and it won't be able to finish them
all in time to render the next frame at this rate.

It transmits to you a buffer (your puzzle input) listing each particle
in order (starting with particle 0, then particle 1, particle 2, and
so on). For each particle, it provides the X, Y, and Z coordinates for
the particle's position (p), velocity (v), and acceleration (a), each
in the format <X,Y,Z>.

Each tick, all particles are updated simultaneously. A particle's
properties are updated in the following order:

    Increase the X velocity by the X acceleration.

    Increase the Y velocity by the Y acceleration.

    Increase the Z velocity by the Z acceleration.

    Increase the X position by the X velocity.

    Increase the Y position by the Y velocity.

    Increase the Z position by the Z velocity.

Because of seemingly tenuous rationale involving z-buffering, the GPU
would like to know which particle will stay closest to position
<0,0,0> in the long term. Measure this using the Manhattan distance,
which in this situation is simply the sum of the absolute values of a
particle's X, Y, and Z position.

For example, suppose you are only given two particles, both of which
stay entirely on the X-axis (for simplicity). Drawing the current
states of particles 0 and 1 (in that order) with an adjacent a number
line and diagram of current X positions (marked in parenthesis), the
following would take place:

p=< 3,0,0>, v=< 2,0,0>, a=<-1,0,0>    -4 -3 -2 -1  0  1  2  3  4
p=< 4,0,0>, v=< 0,0,0>, a=<-2,0,0>                         (0)(1)

p=< 4,0,0>, v=< 1,0,0>, a=<-1,0,0>    -4 -3 -2 -1  0  1  2  3  4
p=< 2,0,0>, v=<-2,0,0>, a=<-2,0,0>                      (1)   (0)

p=< 4,0,0>, v=< 0,0,0>, a=<-1,0,0>    -4 -3 -2 -1  0  1  2  3  4
p=<-2,0,0>, v=<-4,0,0>, a=<-2,0,0>          (1)               (0)

p=< 3,0,0>, v=<-1,0,0>, a=<-1,0,0>    -4 -3 -2 -1  0  1  2  3  4
p=<-8,0,0>, v=<-6,0,0>, a=<-2,0,0>                         (0)   

At this point, particle 1 will never be closer to <0,0,0> than
particle 0, and so, in the long run, particle 0 will stay closest.

Which particle will stay closest to position <0,0,0> in the long term?

Your puzzle answer was 150.

--- Part Two ---

To simplify the problem further, the GPU would like to remove any
particles that collide. Particles collide if their positions ever
exactly match. Because particles are updated simultaneously, more than
two particles can collide at the same time and place. Once particles
collide, they are removed and cannot collide with anything else after
that tick.

For example:

p=<-6,0,0>, v=< 3,0,0>, a=< 0,0,0>    
p=<-4,0,0>, v=< 2,0,0>, a=< 0,0,0>    -6 -5 -4 -3 -2 -1  0  1  2  3
p=<-2,0,0>, v=< 1,0,0>, a=< 0,0,0>    (0)   (1)   (2)            (3)
p=< 3,0,0>, v=<-1,0,0>, a=< 0,0,0>

p=<-3,0,0>, v=< 3,0,0>, a=< 0,0,0>    
p=<-2,0,0>, v=< 2,0,0>, a=< 0,0,0>    -6 -5 -4 -3 -2 -1  0  1  2  3
p=<-1,0,0>, v=< 1,0,0>, a=< 0,0,0>             (0)(1)(2)      (3)   
p=< 2,0,0>, v=<-1,0,0>, a=< 0,0,0>

p=< 0,0,0>, v=< 3,0,0>, a=< 0,0,0>    
p=< 0,0,0>, v=< 2,0,0>, a=< 0,0,0>    -6 -5 -4 -3 -2 -1  0  1  2  3
p=< 0,0,0>, v=< 1,0,0>, a=< 0,0,0>                       X (3)      
p=< 1,0,0>, v=<-1,0,0>, a=< 0,0,0>

------destroyed by collision------    
------destroyed by collision------    -6 -5 -4 -3 -2 -1  0  1  2  3
------destroyed by collision------                      (3)         
p=< 0,0,0>, v=<-1,0,0>, a=< 0,0,0>

In this example, particles 0, 1, and 2 are simultaneously destroyed at
the time and place marked X. On the next tick, particle 3 passes
through unharmed.

How many particles are left after all collisions are resolved?

Your puzzle answer was 657.

Both parts of this puzzle are complete! They provide two gold stars: **