




import numpy as np

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				List[str]:
       lowerCamelCase     :   Optional[int]    				=      np.array(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Optional[int]    				=      np.array(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   str    				=      abs(predict - actual					)
       lowerCamelCase     :   Optional[Any]    				=      difference.mean()

       return score

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				Dict:
       lowerCamelCase     :   Union[str, Any]    				=      np.array(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   List[Any]    				=      np.array(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   Union[str, Any]    				=      predict - actual
       lowerCamelCase     :   List[Any]    				=      np.square(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   Any    				=      square_diff.mean()
       return score

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				Tuple:
       lowerCamelCase     :   List[str]    				=      np.array(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Tuple    				=      np.array(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   Tuple    				=      predict - actual
       lowerCamelCase     :   str    				=      np.square(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Any    				=      square_diff.mean()
       lowerCamelCase     :   Tuple    				=      np.sqrt(_SCREAMING_SNAKE_CASE					)
       return score

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				List[str]:
       lowerCamelCase     :   Optional[Any]    				=      np.array(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Union[str, Any]    				=      np.array(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   Dict    				=      np.log(predict + 1					)
       lowerCamelCase     :   str    				=      np.log(actual + 1					)

       lowerCamelCase     :   Union[str, Any]    				=      log_predict - log_actual
       lowerCamelCase     :   List[Any]    				=      np.square(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Any    				=      square_diff.mean()

       lowerCamelCase     :   Any    				=      np.sqrt(_SCREAMING_SNAKE_CASE					)

       return score

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				Optional[Any]:
       lowerCamelCase     :   str    				=      np.array(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Dict    				=      np.array(_SCREAMING_SNAKE_CASE					)

       lowerCamelCase     :   Optional[Any]    				=      predict - actual
       lowerCamelCase     :   str    				=      np.sum(_SCREAMING_SNAKE_CASE					) / len(_SCREAMING_SNAKE_CASE					)
       lowerCamelCase     :   Any    				=      np.sum(_SCREAMING_SNAKE_CASE					) / len(_SCREAMING_SNAKE_CASE					)
       # print(numerator, denumerator)
       lowerCamelCase     :   Any    				=      float(_SCREAMING_SNAKE_CASE					) / denumerator * 100

       return score


def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				str:
       return np.mean(np.array(_SCREAMING_SNAKE_CASE					) == np.array(_SCREAMING_SNAKE_CASE					)					)












from __future__ import annotations

def   A   (   _SCREAMING_SNAKE_CASE				,_SCREAMING_SNAKE_CASE					)			->				list:
       lowerCamelCase     :   int    				=      [None] * (len(_SCREAMING_SNAKE_CASE					) + len(_SCREAMING_SNAKE_CASE					))

       lowerCamelCase     :   Any    				=      0  # pointer to current index for left Half
       lowerCamelCase     :   int    				=      0  # pointer to current index for the right Half
       lowerCamelCase     :   Optional[int]    				=      0  # pointer to current index for the sorted array Half

       while pointera < len(_SCREAMING_SNAKE_CASE					) and pointera < len(_SCREAMING_SNAKE_CASE					):
              if left_half[pointera] < right_half[pointera]:
                     lowerCamelCase     :   Any    				=      left_half[pointera]
                     pointera += 1
                     index += 1
              else:
                     lowerCamelCase     :   Any    				=      right_half[pointera]
                     pointera += 1
                     index += 1
       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   Optional[Any]    				=      left_half[pointera]
              pointera += 1
              index += 1

       while pointera < len(_SCREAMING_SNAKE_CASE					):
              lowerCamelCase     :   str    				=      right_half[pointera]
              pointera += 1
              index += 1

       return sorted_array

def   A   (   _SCREAMING_SNAKE_CASE					)			->				list:
       if len(_SCREAMING_SNAKE_CASE					) <= 1:
              return array
       # the actual formula to calculate the middle element = left + (right - left) // 2
       # this avoids integer overflow in case of large N
       lowerCamelCase     :   int    				=      0 + (len(_SCREAMING_SNAKE_CASE					) - 0) // 2

       # Split the array into halves till the array length becomes equal to One
       # merge the arrays of single length returned by mergeSort function and
       # pass them into the merge arrays function which merges the array
       lowerCamelCase     :   Optional[Any]    				=      array[:middle]
       lowerCamelCase     :   Optional[Any]    				=      array[middle:]

       return merge(merge_sort(_SCREAMING_SNAKE_CASE					)				,merge_sort(_SCREAMING_SNAKE_CASE					)					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






