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Question 2 - Collatz Conjecture Quit Consider the following process to generate a sequence m?, m2, m3,.... Start with any positive integer m If m1 is even, divide it by 2, obtaining m2 -mm/2 If m1 is odd, multiply by 3 and add one, obtaining m2 3m1+1. - Repeat (with m2 in place of m? etc.) For example, starting with mi 10 we obtain the sequence 10, 5, 16, 8,4,2,1,4,2,1,.... Notice that starting with mi -1, the process produces the sequence 1, 4, 2, 1,4, 2, etc. It is a famous (and unproven) conjecture, called the Collatz conjecture (or 3n+1 conjecture), that regardless of m, the process will eventually produce the number 1 (and hence enter the cycle i,4,2, ). we will write a function to investigate this phenomenon. 1. Write, using Module, a function Collatz[m] that takes as input a positive integer m and outputs the number of times that the procedure must be repeated until we obtain 1. For example, starting with m = 10 we must repeat 6 times before obtaining 1. Ifm is not a positive integer, the function should print the message "Positive integers only!". 2. Using your function, verify that Collatz[10000]-29, Collatz[27]-111, and that Collatz[-2] and Collatz[Pi] generate the error message. Then compute Collatz[999] and Collatz[2222 3. Find the integer n in the range [1, 750] such that Collatz[n] is maximized. Report both n and Collatz[n