"""simple docstring"""


import math





def       lowerCamelCase_			( __lowerCAmelCase    )							-> List[str]:




						'''simple docstring'''



						lowerCamelCase__ =0
						if n % 2 == 0:
												count += 1
												while n % 2 == 0:
																		lowerCamelCase__ =int(n / 2    )
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

						lowerCamelCase__ =3

						while i <= int(math.sqrt(__lowerCAmelCase    )    ):
												if n % i == 0:
																		count += 1
																		while n % i == 0:
																								lowerCamelCase__ =int(n / i    )
												lowerCamelCase__ =i + 2

						# this condition checks the prime
						# number n is greater than 2

						if n > 2:
												count += 1
						return count


if __name__ == "__main__":
	a							=5124_2183
	print(F'''The number of distinct prime factors is/are {exact_prime_factor_count(n)}''')
	print(F'''The value of log(log(n)) is {math.log(math.log(n)):.4f}''')



"""simple docstring"""


def       lowerCamelCase_			( __lowerCAmelCase    )							-> bool:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ):
												raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
						if len(__lowerCAmelCase    ) == 0:
												raise ValueError("Input list must be a non empty list"    )
						if len(__lowerCAmelCase    ) == 1:
												return True
						try:
												lowerCamelCase__ =series[1] / series[0]
												for index in range(len(__lowerCAmelCase    ) - 1    ):
																		if series[index + 1] / series[index] != common_ratio:
																								return False
						except ZeroDivisionError:
												return False
						return True





def       lowerCamelCase_			( __lowerCAmelCase    )							-> float:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase       ,   __lowerCAmelCase    ):
												raise ValueError("Input series is not valid, valid series - [2, 4, 8]"    )
						if len(__lowerCAmelCase    ) == 0:
												raise ValueError("Input list must be a non empty list"    )
						lowerCamelCase__ =1
						for value in series:
												answer *= value
						return pow(__lowerCAmelCase       ,   1 / len(__lowerCAmelCase    )    )


if __name__ == "__main__":
	import doctest

	doctest.testmod()


