





from __future__ import annotations

class 	__snake_case					:






    '''simple docstring'''





    def __init__( self    :		List[Any]      ,    snake_case    :		str				):

      """simple docstring"""





      __lowerCAmelCase								=					value
      __lowerCAmelCase								=					None
      __lowerCAmelCase								=					None


class 	__snake_case					:






    '''simple docstring'''
    _lowerCAmelCase  =						42





    def __init__( self    :		Any				):

      """simple docstring"""





      __lowerCAmelCase								=					0





    def 						A		( self    :		Tuple      ,    snake_case    :		Optional[int]      ,    snake_case    :		Tuple				):

      """simple docstring"""





      if node is None:
        return

      if path_sum == self.target:
        self.paths += 1

      if node.left:
        self.depth_first_search(node.left      ,    path_sum + node.left.value				)
      if node.right:
        self.depth_first_search(node.right      ,    path_sum + node.right.value				)





    def 						A		( self    :		int      ,    snake_case    :		int      ,    snake_case    :		int = None				):

      """simple docstring"""





      if node is None:
        return 0
      if target is not None:
        __lowerCAmelCase								=					target

      self.depth_first_search(lowerCAmelCase__      ,    node.value				)
      self.path_sum(node.left				)
      self.path_sum(node.right				)

      return self.paths


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}')



