Exercise $1.(50$ points$)$ DiffusionIn this exercise, we use a $3$D random walk to simulate a diffusion process. Imagine a particle starting at the origin $(0,0,0)$ that has equal probabilities to go in $6$ possible directions $-$ left, right, backward, forward, down, and up$.$ For example, when the particle is at $($r$,$ y$,$ z$),$ with equal probability $1/6,$ its next location isat $(2-1,$y$,2),(2+1,3,2),(2,3-1,2),(2,2+1,2),(2,$ V$,2-1)$ or $(2,3,2+1).$The particle will conduct the random walk for n steps. We are interested in the distribution of the final locations of particles after each takes n steps. Specifically, we would like to know the distribution of the distance between the final location and the origin. In order to obtain this distribution, we simulate m such particles, and check the proportion of the particles that lies within rn distance from the origin, where r is a real number between $0$ and $1.$ Note all the particles will be within a sphere with radius n since particles only move n steps and the furthest they can go is a distance n from the origin. In our simulation, we will calculatethe proportion of particles that are within rn from the origin for r $=0\mathrm{.}05,0\mathrm{.}10,0\mathrm{.}15,...,0\mathrm{.}90,0\mathrm{.}95,1\mathrm{.}00.$Below is the main function for this program. Note how we use command line arguments. int main $($int argc, char $*$argv$])$