






'''simple docstring'''



from __future__ import annotations

import math

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


def 							lowercase_				(    __A :       float					,      __A :       float					,      __A :       float					,      __A :       float					,      __A :       float			)       ->      tuple[float, float]:



 """simple docstring"""




 if not all(isinstance(__A					,      (float, int)			) for val in locals().values()			):
  lowercase					:   Dict				  =F'Input values must either be float or int: {list(locals().values()			)}'
  raise TypeError(__A			)
 lowercase					:   int				  =((x * distance) / (z + distance)) * scale
 lowercase					:   List[Any]				  =((y * distance) / (z + distance)) * scale
 return projected_x, projected_y


def 							lowercase_				(    __A :       float					,      __A :       float					,      __A :       float					,      __A :       str					,      __A :       float			)       ->      tuple[float, float, float]:



 """simple docstring"""




 if not isinstance(__A					,      __A			):
  raise TypeError('''Axis must be a str'''			)
 lowercase					:   Dict				  =locals()
 del input_variables["axis"]
 if not all(isinstance(__A					,      (float, int)			) for val in input_variables.values()			):
  lowercase					:   Tuple				  =(
      '''Input values except axis must either be float or int: '''
      F'{list(input_variables.values()			)}'
  )
  raise TypeError(__A			)
 lowercase					:   Optional[Any]				  =(angle % 3_6_0) / 4_5_0 * 1_8_0 / math.pi
 if axis == "z":
  lowercase					:   List[Any]				  =x * math.cos(__A			) - y * math.sin(__A			)
  lowercase					:   List[str]				  =y * math.cos(__A			) + x * math.sin(__A			)
  lowercase					:   Union[str, Any]				  =z
 elif axis == "x":
  lowercase					:   int				  =y * math.cos(__A			) - z * math.sin(__A			)
  lowercase					:   Optional[Any]				  =z * math.cos(__A			) + y * math.sin(__A			)
  lowercase					:   Any				  =x
 elif axis == "y":
  lowercase					:   Any				  =x * math.cos(__A			) - z * math.sin(__A			)
  lowercase					:   Any				  =z * math.cos(__A			) + x * math.sin(__A			)
  lowercase					:   Optional[int]				  =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) = }""")











'''simple docstring'''



def 							lowercase_				(    __A :       int = 6_0_0_8_5_1_4_7_5_1_4_3			)       ->      int:



 """simple docstring"""




 try:
  lowercase					:   Any				  =int(__A			)
 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.'''			)
 lowercase					:   Optional[Any]				  =1
 lowercase					:   Dict				  =2
 while i * i <= n:
  while n % i == 0:
   lowercase					:   Optional[int]				  =i
   n //= i
  i += 1
 if n > 1:
  lowercase					:   Dict				  =n
 return int(__A			)


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



