Plotting Graph on matplotlib under while loop- graph not plotting

Python Help
1

Hello guys, I have been into python for just couple of months and I wanted to plot the graph from the output of arithmetic (These arithmetic program works fine for me). When I try to incorporate matplotlib to while loop for plotting data, I am not getting any graph.

Working Arithmetic code:

n=int(input("Enter the Number "))
            count=0
            a=0
            a=n
            while(n!=1):
                if(n%2==0):
                    n=n//2
                    print(str(n)+ '\n')
                    count=count+1
                else:
                    n=3*n+1
                    print(str(n)+'\n')
                    count=count+1
            print("Collatz for "+ str(a) + " count is " + str(count))

Graph Plotting code (I am not getting desired output)

import matplotlib.pyplot as plt
def collatz():
    n=int(input("Enter the Number "))
    count=0
    a=0
    a=n
    while(n!=1):
        if(n%2==0):
            n=n//2
            print(str(n)+ '\n')
            count=count+1
            plt.show()
        else:
            n=3*n+1
            print(str(n)+'\n')
            count=count+1
        x=[count]
        y=[n]
        plt.plot(x,y)
        plt.xlabel('x - axis')
        plt.ylabel('y - axis')
        plt.title('My first graph!')
collatz()

Basically if I enter number (say 8) then output will be 8,4,2,1 and these data must be plotted to 1,2,3,4

Something like below:
Figure_1