code: 
  
  
  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}''')
  
  
style_context: 
  
  
  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     )     )
  
  