<image>When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below.
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For example, starting with an input of $N = 7$, the machine will output $3 \cdot 7 + 1 = 22$. Then if the output is repeatedly inserted into the machine five more times, the final output is $26$. $$ 7 \to 22 \to 11 \to 34  \to 17 \to 52 \to 26$$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 $N$? $$ N \to \_\_ \to \_\_ \to \_\_  \to \_\_ \to \_\_  \to 1$$
A. 73
B. 74
C. 75
D. 82
E. 83