Need help with a script

Hello all,
I'm learning python with the help of a book called think python 2. In chapter 6 there is an exercyse where you have to make a program that counts down from 10 to 0. When it reaches 0 it should print blast off.
Now as an extra exercyse, I thought I'm going to let the user put the number in themselves instead of having the number written in the script already, but there is something wrong in my code.
I have tried everything I could think of and I wanted to ask if somebody could have a look into it and tell me what is wrong.
Code
def countdown(n):
    n = input('Put a number in.')
    if n <= 0:
        print('blastoff')
    else:
        print(n)
        countdown(n-1)
countdown(n)
Thanks a lot and have a good day.

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