Do not forget to submit your work to gradescope before the deadline. A Makefile is provided.Exercise $1.(50$ points$)$ DiffusionIn this exercise, we use a $3$D random walk to simulate a diffusion process.Imagine a particle starting atthe 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 $($z$,$ y$,$ z$),$ with equal probability $1/6,$ its next location isat $1,9\mathrm{.}2+1,9\mathrm{.}2\mathrm{.}9-1,2.$U$+1\mathrm{.}22\mathrm{.}9,2-1$ or$1-$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 thedistance 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 arg, char arg$])$if $($arge $|=3)$printi $("$Usage: $(1)/(2)$a n a$\backslash$a$",$ argv $(0])$: return $0$;int n $"$ atoi$($argv $(1))$;int n$-$ atoi$($argv $[2])$;srand $(12345)$ :diffusion$($n$,$ m$)$;return $0$;We need to implement the function void diffusion $($int n$,$ int m$)$In this function, we need to dynamically allocate memory to represent a $3$D grid where z$,$ y$.=$ coordinates range from $-$n to n$.$ For all the possible z$,$ y$,$ z coordinates within the range, we save the number of particles that end up at the location $($r$.$y$,).$ During the simulation, if the final location of a particle is $($r$,$ y$,=),$ the corresponding value will be incremented by $1.$Generate a random number using rand$()\%6.$ If this number is $0$ or $1,$ you should move left or right on the x$-$axis, respectively. If it is $2$ or $3,$ you should move up or down on the y$-$axis, respectively. If it is $4$ or $5,$ move up or down on the z$-$axis, respectively.In the implementation of main, we use the below function to print out results.