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When a positive integer N is fed into a machine, the output is a number calculated according to the rule shown below. For example, starting with an input of N=7, the machine will output 3*7+1 = 22. Then if the output is repeatedly inserted into the machine five more times, the final output is 26. When the same 6-step process is applied to a different starting value of N, the final output is 1. What is the sum of all such integers N?