"""
== Liouville Lambda Function ==
The Liouville Lambda function, denoted by λ(n)
and λ(n) is 1 if n is the product of an even number of prime numbers,
and -1 if it is the product of an odd number of primes.

https://en.wikipedia.org/wiki/Liouville_function
"""

# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
from maths.prime_factors import prime_factors


def liouville_lambda(number: int) -> int:
 """
 This functions takes an integer number as input.
 returns 1 if n has even number of prime factors and -1 otherwise.
 >>> liouville_lambda(10)
 1
 >>> liouville_lambda(11)
 -1
 >>> liouville_lambda(0)
 Traceback (most recent call last):
 ...
 ValueError: Input must be a positive integer
 >>> liouville_lambda(-1)
 Traceback (most recent call last):
 ...
 ValueError: Input must be a positive integer
 >>> liouville_lambda(11.0)
 Traceback (most recent call last):
 ...
 TypeError: Input value of [number=11.0] must be an integer
 """
 if not isinstance(number, int):
 msg = f"Input value of [number={number}] must be an integer"
 raise TypeError(msg)
 if number < 1:
 raise ValueError("Input must be a positive integer")
 return -1 if len(prime_factors(number)) % 2 else 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()