Gauss Contest 2022, Problem 23 (Encoded Message)

To encode a message, James first replaces each letter within the message with its corresponding number, where A=1, B=2,…, Y=25 and Z=26. Next, James multiplies each number by 3 and then subtracts 5, and continues this process a total of n times. For example when n=2 the letter D is encoded to the number 16. If James encoded a four letter message to the four numbers 367, 205, 853, 1339, what is the value of the n that he used ?

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