First of all, delete those two out of there. You cant call "the_flying_circus", if you haven't even defined it...
As for the input, you should be able to input every time, you call the function, so it's not good as where it is right now
The error tells you, that the function shouldn't take any arguments, so delete the "input" from there.
About the number input I talked about before, should be placed around here:
input = raw_input("Pick a number:")
As for the variable, you shouldn't use input, because there is a built-in function called input(). Better use another name, so you don't mix things up. Because you want a number (an integer), you should turn the input in an integer too, like int(raw_input("Pick a number: ") or input("Pick a number: "), both work fine.
If you used raw_input() and call the function, you type 3 for example, the "3" will be a string, so it will never be True if you ask 3 == "3".