


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}''')





import numpy as np




def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->Dict:







      """simple docstring"""

      lowercase			:   Optional[Any]					   =		np.array(_UpperCamelCase     )
      lowercase			:   Dict					   =		np.array(_UpperCamelCase     )

      lowercase			:   List[Any]					   =		abs(predict - actual     )
      lowercase			:   int					   =		difference.mean()

      return score




def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->List[Any]:







      """simple docstring"""

      lowercase			:   Tuple					   =		np.array(_UpperCamelCase     )
      lowercase			:   str					   =		np.array(_UpperCamelCase     )

      lowercase			:   List[str]					   =		predict - actual
      lowercase			:   Tuple					   =		np.square(_UpperCamelCase     )

      lowercase			:   Union[str, Any]					   =		square_diff.mean()
      return score




def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->str:







      """simple docstring"""

      lowercase			:   Union[str, Any]					   =		np.array(_UpperCamelCase     )
      lowercase			:   Optional[Any]					   =		np.array(_UpperCamelCase     )

      lowercase			:   Tuple					   =		predict - actual
      lowercase			:   Dict					   =		np.square(_UpperCamelCase     )
      lowercase			:   Union[str, Any]					   =		square_diff.mean()
      lowercase			:   Union[str, Any]					   =		np.sqrt(_UpperCamelCase     )
      return score




def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->List[Any]:







      """simple docstring"""

      lowercase			:   List[str]					   =		np.array(_UpperCamelCase     )
      lowercase			:   List[Any]					   =		np.array(_UpperCamelCase     )

      lowercase			:   Dict					   =		np.log(predict + 1     )
      lowercase			:   List[str]					   =		np.log(actual + 1     )

      lowercase			:   int					   =		log_predict - log_actual
      lowercase			:   Tuple					   =		np.square(_UpperCamelCase     )
      lowercase			:   List[Any]					   =		square_diff.mean()

      lowercase			:   int					   =		np.sqrt(_UpperCamelCase     )

      return score




def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->List[str]:







      """simple docstring"""

      lowercase			:   List[Any]					   =		np.array(_UpperCamelCase     )
      lowercase			:   Optional[int]					   =		np.array(_UpperCamelCase     )

      lowercase			:   Optional[int]					   =		predict - actual
      lowercase			:   Optional[int]					   =		np.sum(_UpperCamelCase     ) / len(_UpperCamelCase     )
      lowercase			:   Dict					   =		np.sum(_UpperCamelCase     ) / len(_UpperCamelCase     )
      # print(numerator, denumerator)
      lowercase			:   int					   =		float(_UpperCamelCase     ) / denumerator * 100

      return score




def 			__lowercase	(						_UpperCamelCase,    _UpperCamelCase     )    ->List[Any]:







      """simple docstring"""

      return np.mean(np.array(_UpperCamelCase     ) == np.array(_UpperCamelCase     )     )

