Problem 22 (2020 AMC 8)

When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below. If $N$ is even: $\frac{N}{2}$ If $N$ is odd: $3N+1$ For example, starting with an input of $N=7$ the machine will output $3\cdot7+1=22.$ Then if the output is repeatedly inserted into the machine five more times, the final output is $26$. $7\rightarrow22\rightarrow11\rightarrow34\rightarrow17\rightarrow52\rightarrow26$ 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 $N$?