Factorial

The factorial of a positive integer n is the product of the first n positive integers.

Write a function named factorial that accepts an integer n as argument.

• It should return the factorial of n if n is a positive integer.
• It should return -1 if n is a negative integer.
• It should return 1 if n is zero.

You do not have to accept input from the user or print anything to the console. You just have to write the function definition.

Example

factorial(5)   ->  120
factorial(0)   ->  1
factorial(-3)  ->  -1

Your task

Implement this function:

def factorial(n):

Write the function only — the arguments are read for you and the return value is printed automatically.

Arguments arrive as one Python literal per line, in this order: n.

Example

Input

5

Output

120