When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown in the above figure. 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 $N$?
$N \to \text{\_\_\_\_\_} \to \text{\_\_\_\_\_} \to \text{\_\_\_\_\_} \to \text{\_\_\_\_\_} \to \text{\_\_\_\_\_} \to 1$

A. 73

B. 74

C. 75

D. 82

E. 83