

from math import pi, sqrt







def       lowercase					(	__A :					float		)				->			float:





    '''simple docstring'''




    if num <= 0:
        raise ValueError("""math domain error"""		)
    if num > 171.5:
        raise OverflowError("""math range error"""		)
    elif num - int(__A		) not in (0, 0.5):
        raise NotImplementedError("""num must be an integer or a half-integer"""		)
    elif num == 0.5:
        return sqrt(__A		)
    else:
        return 1.0 if num == 1 else (num - 1) * gamma(num - 1		)







def       lowercase					(	)				->			None:





    '''simple docstring'''




    assert gamma(0.5		) == sqrt(__A		)
    assert gamma(1		) == 1.0
    assert gamma(2		) == 1.0


if __name__ == "__main__":
     from doctest import testmod

     testmod()
     __lowercase     : Optional[int]       =						1.0
     while num:
          __lowercase     : Dict       =						float(input('''Gamma of: '''))
          print(f'''gamma({num}) = {gamma(num)}''')
          print('''\nEnter 0 to exit...''')







'''simple docstring'''





from __future__ import annotations

import math

UpperCAmelCase__  			=				'''2020.9.26'''
UpperCAmelCase__  			=				'''xcodz-dot, cclaus, dhruvmanila'''






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float ):






			"""simple docstring"""




			if not all(isinstance(_SCREAMING_SNAKE_CASE,(float, int) ) for val in locals().values() ):
						__A=	f"""Input values must either be float or int: {list(locals().values() )}"""
						raise TypeError(_SCREAMING_SNAKE_CASE )
			__A=	((x * distance) / (z + distance)) * scale
			__A=	((y * distance) / (z + distance)) * scale
			return projected_x, projected_y






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: str,_SCREAMING_SNAKE_CASE					: float ):






			"""simple docstring"""




			if not isinstance(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE ):
						raise TypeError('Axis must be a str' )
			__A=	locals()
			del input_variables["axis"]
			if not all(isinstance(_SCREAMING_SNAKE_CASE,(float, int) ) for val in input_variables.values() ):
						__A=	(
						    'Input values except axis must either be float or int: '
						    f"""{list(input_variables.values() )}"""
						)
						raise TypeError(_SCREAMING_SNAKE_CASE )
			__A=	(angle % 360) / 450 * 180 / math.pi
			if axis == "z":
						__A=	x * math.cos(_SCREAMING_SNAKE_CASE ) - y * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	y * math.cos(_SCREAMING_SNAKE_CASE ) + x * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z
			elif axis == "x":
						__A=	y * math.cos(_SCREAMING_SNAKE_CASE ) - z * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z * math.cos(_SCREAMING_SNAKE_CASE ) + y * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	x
			elif axis == "y":
						__A=	x * math.cos(_SCREAMING_SNAKE_CASE ) - z * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z * math.cos(_SCREAMING_SNAKE_CASE ) + x * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	y
			else:
						raise ValueError('not a valid axis, choose one of \'x\', \'y\', \'z\'' )

			return new_x, new_y, new_z


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(F"""{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }""")
					print(F"""{rotate(1.0, 2.0, 3.0, 'y', 90.0) = }""")



