Michelle's Number Recycling Machine

Michelle's Number Recycling Machine obeys exactly two rules:

1. If an inserted number has exactly 1 digit, double the number.
2. If an inserted number has exactly 2 digits, compute the sum of the digits.

The first number Michelle inserts is 1. Then every answer she gets is inserted back into the machine until fifty numbers are inserted. What is the fiftieth number to be inserted?

As per the image, after 9 steps input again becomes 1 and the same steps through 1 to 9 repeats.
To get 50th input, steps 1 to 9 has to be repeated 5 times and then steps 1 to 5 once.
i.e; After 45 th step (9 steps * 5 times) input will be again 1.
Then we need 5 more steps to reach 50th input which is the output of step 5 = 7

Fiftieth number to be inserted will be 7.