




"""simple docstring"""
def 				__lowerCAmelCase					(					__lowerCAmelCase			:		list						)    ->       list:
 _UpperCamelCase      :	Tuple					      =  len(__lowerCAmelCase						)

 # Set the gap value to be decreased by a factor of 1.3
 # after each iteration
 _UpperCamelCase      :	int					      =  1.3

 # Continue sorting until the gap is 1
 while gap > 1:
  # Decrease the gap value
  _UpperCamelCase      :	Dict					      =  int(gap / shrink						)

  # Sort the elements using insertion sort
  for i in range(__lowerCAmelCase  ,	len(__lowerCAmelCase						)						):
   _UpperCamelCase      :	int					      =  collection[i]
   _UpperCamelCase      :	Any					      =  i
   while j >= gap and collection[j - gap] > temp:
    _UpperCamelCase      :	Optional[Any]					      =  collection[j - gap]
    j -= gap
   _UpperCamelCase      :	str					      =  temp

 return collection


if __name__ == "__main__":
    import doctest

    doctest.testmod()









"""simple docstring"""
import math






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

 _UpperCamelCase      :	Tuple					      =  3

 while i <= int(math.sqrt(__lowerCAmelCase						)						):
  if n % i == 0:
   count += 1
   while n % i == 0:
    _UpperCamelCase      :	Any					      =  int(n / i						)
  _UpperCamelCase      :	Optional[Any]					      =  i + 2

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

 if n > 2:
  count += 1
 return count


if __name__ == "__main__":
    _SCREAMING_SNAKE_CASE						 =     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}')



