

"""simple docstring"""






def       UpperCamelCase					(			_lowerCAmelCase     :						int = 20 )				->			int:

	try:
		_UpperCAmelCase    :							List[str]									=					int(_lowerCAmelCase )
	except (TypeError, ValueError):
		raise TypeError("""Parameter n must be int or castable to int.""" )
	if n <= 0:
		raise ValueError("""Parameter n must be greater than or equal to one.""" )
	_UpperCAmelCase    :							Union[str, Any]									=					0
	while 1:
		i += n * (n - 1)
		_UpperCAmelCase    :							Tuple									=					0
		for j in range(2,  _lowerCAmelCase ):
			if i % j != 0:
				_UpperCAmelCase    :							Optional[Any]									=					1
				break
		if nfound == 0:
			if i == 0:
				_UpperCAmelCase    :							Union[str, Any]									=					1
			return i
	return None


if __name__ == "__main__":
						print(F'''{solution() = }''')








"""simple docstring"""






from __future__ import annotations
def       UpperCamelCase					(			_lowerCAmelCase     :						list,  _lowerCAmelCase     :						list )				->			list:
	_UpperCAmelCase    :							List[Any]									=					[None] * (len(_lowerCAmelCase ) + len(_lowerCAmelCase ))

	_UpperCAmelCase    :							Union[str, Any]									=					0  # pointer to current index for left Half
	_UpperCAmelCase    :							str									=					0  # pointer to current index for the right Half
	_UpperCAmelCase    :							Optional[int]									=					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]:
			_UpperCAmelCase    :							Tuple									=					left_half[pointera]
			pointera += 1
			index += 1
		else:
			_UpperCAmelCase    :							int									=					right_half[pointera]
			pointera += 1
			index += 1
	while pointera < len(_lowerCAmelCase ):
		_UpperCAmelCase    :							Tuple									=					left_half[pointera]
		pointera += 1
		index += 1

	while pointera < len(_lowerCAmelCase ):
		_UpperCAmelCase    :							Union[str, Any]									=					right_half[pointera]
		pointera += 1
		index += 1

	return sorted_array
def       UpperCamelCase					(			_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
	_UpperCAmelCase    :							Any									=					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
	_UpperCAmelCase    :							Optional[Any]									=					array[:middle]
	_UpperCAmelCase    :							Optional[int]									=					array[middle:]

	return merge(merge_sort(_lowerCAmelCase ),  merge_sort(_lowerCAmelCase ) )


if __name__ == "__main__":
						import doctest

						doctest.testmod()





