code: 
  
  
  '''simple docstring'''
  
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->List[str]:
  
  
  
  
  
  
  
        """simple docstring"""
  
        if not root or root not in binary_tree_mirror_dictionary:
              return
        lowercase			:   Union[str, Any]					   =		binary_tree_mirror_dictionary[root][:2]
        lowercase			:   Union[str, Any]					   =		[right_child, left_child]
        binary_tree_mirror_dict(_UpperCamelCase,    _UpperCamelCase     )
        binary_tree_mirror_dict(_UpperCamelCase,    _UpperCamelCase     )
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase = 1     )    ->dict:
  
  
  
  
  
  
  
        """simple docstring"""
  
        if not binary_tree:
              raise ValueError('''binary tree cannot be empty'''     )
        if root not in binary_tree:
              lowercase			:   List[str]					   =		f"""root {root} is not present in the binary_tree"""
              raise ValueError(_UpperCamelCase     )
        lowercase			:   Any					   =		dict(_UpperCamelCase     )
        binary_tree_mirror_dict(_UpperCamelCase,    _UpperCamelCase     )
        return binary_tree_mirror_dictionary
  
  
  if __name__ == "__main__":
    __a   				=      {1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
    print(F'''Binary tree: {binary_tree}''')
    __a   				=      binary_tree_mirror(binary_tree, 5)
    print(F'''Binary tree mirror: {binary_tree_mirror_dictionary}''')
  
  
style_context: 
  
  
  import math
  
  
  
  
  def 			__lowercase	(						_UpperCamelCase     )    ->Union[str, Any]:
  
  
  
  
  
  
  
        """simple docstring"""
  
        lowercase			:   List[Any]					   =		0
        if n % 2 == 0:
              count += 1
              while n % 2 == 0:
                    lowercase			:   Any					   =		int(n / 2     )
      # the n input value must be odd so that
      # we can skip one element (ie i += 2)
  
        lowercase			:   Optional[int]					   =		3
  
        while i <= int(math.sqrt(_UpperCamelCase     )     ):
              if n % i == 0:
                    count += 1
                    while n % i == 0:
                          lowercase			:   Optional[Any]					   =		int(n / i     )
              lowercase			:   str					   =		i + 2
  
        # this condition checks the prime
        # number n is greater than 2
  
        if n > 2:
              count += 1
        return count
  
  
  if __name__ == "__main__":
    __a   				=      51_24_21_83
    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}''')
  
  