'''simple docstring'''
from __future__ import annotations







def 				__UpperCamelCase (					__UpperCAmelCase  :					str			)							->	bool:
  lowercase				:							int
  lowercase				:							list[str]									=   list(__UpperCAmelCase			)
  lowercase				,      lowercase				:							Optional[int]									=   _vector[:-1], int(_vector[-1]			)
  lowercase				:							list[int]									=   [int(__UpperCAmelCase			) for digit in __vector]

  vector.reverse()
  for i, digit in enumerate(__UpperCAmelCase			):
    if i & 1 == 0:
      lowercase				:							int									=   digit * 2
      if doubled > 9:
        doubled -= 9
      check_digit += doubled
    else:
      check_digit += digit

  return check_digit % 10 == 0


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 assert is_luhn('''79927398713''')
 assert not is_luhn('''79927398714''')
'''simple docstring'''
import math







def 				__UpperCamelCase (					__UpperCAmelCase  :					str			)							->	Optional[int]:
  lowercase				:							Tuple									=   0
  if n % 2 == 0:
    count += 1
    while n % 2 == 0:
      lowercase				:							Optional[int]									=   int(n / 2			)
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

  lowercase				:							Dict									=   3

  while i <= int(math.sqrt(__UpperCAmelCase			)			):
    if n % i == 0:
      count += 1
      while n % i == 0:
        lowercase				:							Dict									=   int(n / i			)
    lowercase				:							List[Any]									=   i + 2

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

  if n > 2:
    count += 1
  return count


if __name__ == "__main__":
 _A		:      List[Any]						   =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}""")