


'''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}''')





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}''')

