


"""simple docstring"""





from __future__ import annotations

# Define the Gravitational Constant G and the function
__UpperCAmelCase    				=      6.67_43E-11  # unit of G : m^3 * kg^-1 * s^-2





def     lowercase__	(  lowerCamelCase     :  float				,	lowerCamelCase     :  float				,	lowerCamelCase     :  float				,	lowerCamelCase     :  float				)					->     dict[str, float]:
  lowerCAmelCase__    :    List[Any]								=					mass_a * mass_a

  if (force, mass_a, mass_a, distance).count(0				) != 1:
    raise ValueError("One and only one argument must be 0"				)
  if force < 0:
    raise ValueError("Gravitational force can not be negative"				)
  if distance < 0:
    raise ValueError("Distance can not be negative"				)
  if mass_a < 0 or mass_a < 0:
    raise ValueError("Mass can not be negative"				)
  if force == 0:
    lowerCAmelCase__    :    Tuple								=					GRAVITATIONAL_CONSTANT * product_of_mass / (distance**2)
    return {"force": force}
  elif mass_a == 0:
    lowerCAmelCase__    :    str								=					(force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
    return {"mass_1": mass_a}
  elif mass_a == 0:
    lowerCAmelCase__    :    Any								=					(force) * (distance**2) / (GRAVITATIONAL_CONSTANT * mass_a)
    return {"mass_2": mass_a}
  elif distance == 0:
    lowerCAmelCase__    :    Any								=					(GRAVITATIONAL_CONSTANT * product_of_mass / (force)) ** 0.5
    return {"distance": distance}
  raise ValueError("One and only one argument must be 0"				)


# Run doctest
if __name__ == "__main__":
   import doctest

   doctest.testmod()




"""simple docstring"""





from __future__ import annotations





def     lowercase__	(  lowerCamelCase     :  list				,	lowerCamelCase     :  list				)					->     list:
  lowerCAmelCase__    :    Dict								=					[None] * (len(lowerCamelCase				) + len(lowerCamelCase				))

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

  while pointera < len(lowerCamelCase				) and pointera < len(lowerCamelCase				):
    if left_half[pointera] < right_half[pointera]:
      lowerCAmelCase__    :    Tuple								=					left_half[pointera]
      pointera += 1
      index += 1
    else:
      lowerCAmelCase__    :    int								=					right_half[pointera]
      pointera += 1
      index += 1
  while pointera < len(lowerCamelCase				):
    lowerCAmelCase__    :    Tuple								=					left_half[pointera]
    pointera += 1
    index += 1

  while pointera < len(lowerCamelCase				):
    lowerCAmelCase__    :    Optional[int]								=					right_half[pointera]
    pointera += 1
    index += 1

  return sorted_array





def     lowercase__	(  lowerCamelCase     :  list				)					->     list:
  if len(lowerCamelCase				) <= 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__    :    Optional[int]								=					0 + (len(lowerCamelCase				) - 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__    :    Union[str, Any]								=					array[:middle]
  lowerCAmelCase__    :    List[str]								=					array[middle:]

  return merge(merge_sort(lowerCamelCase				)				,	merge_sort(lowerCamelCase				)				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
