





import math




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

       UpperCamelCase_ 							=	3

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

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

       if n > 2:
              count += 1
       return count


if __name__ == "__main__":
     _UpperCAmelCase										=					5_1_2_4_2_1_8_3
     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}''')








from __future__ import annotations

def      a    (   _lowercase :  float | int			,    _lowercase :  float | int			,    _lowercase :  float | int			,    )  ->list[float | int]:
		if not all((nth_term, start_term_a, common_ratio_r)							):
				return []
		UpperCamelCase__								=						[]
		UpperCamelCase__								=						1
		UpperCamelCase__								=						common_ratio_r
		for _ in range(int(_lowercase							)							):
				if not series:
						series.append(_lowercase							)
				else:
						power += 1
						series.append(float(start_term_a * multiple							)							)
						UpperCamelCase__								=						pow(float(_lowercase							)			,    _lowercase							)
		return series


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				__lowerCAmelCase 	=      float(input("Enter the last number (n term) of the Geometric Series"))
				__lowerCAmelCase 	=      float(input("Enter the starting term (a) of the Geometric Series"))
				__lowerCAmelCase 	=      float(
				    input("Enter the common ratio between two terms (r) of the Geometric Series")
				)
				print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
				print(geometric_series(nth_term, start_term_a, common_ratio_r))





