The Collatz sequence is generated by applying these $2$ operations on the previous number. The rules are:

When the current number is even, the next term is half of the current term.

When the current number is odd, the next term is $3$n$+1($three times the current number plus $1).$

For example: $5$ generates the sequence $->5,16,8,4,2,1$

For this assignment, you will be writing a program that generates the Collatz sequence for a given positive integer.

First, prompt the user for a positive number greater than $1.$ You can assume the user will always enter integers, but not necessarily greater than $1.$ You will need to validate their input before you continue $($i$.$e$.$ entering $-10$ or $0$ should cause your program to tell the user that their input is invalid$).$ You should re$-$prompt the user to enter a value if they supply bad data. Hint: use a "while" loop to keep the user "trapped" until they supply you with "good" data.

Next, your user should continually generate the next term in Collatz sequence until you reach the number $1.$ The program should display whether the given number is even or odd, whether it increased from the previous number, and is it a factor of the starting number.

At the end, your program should report:

The number of steps it took to reach the number $1.$

The number of even numbers in the overall sequence $($including the starting number and $1).$

The number of odd numbers in the overall sequence $($including the starting number and $1).$

The number of increases in the overall sequence $($including the starting number and $1).$

The number of factors of the starting number found in the overall sequence $($EXCLUDING the starting number and $1).$

The average of the overall sequence $($including the starting number and $1).$

PLEASE DO NOT USE FOR LOOP AND def return. ONLY USE WHILE loops