
def 				A__    (  lowerCamelCase = 20  )     ->		int:

				try:
								UpperCamelCase_:							int		=  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_:							Any		=  0
				while 1:
								i += n * (n - 1)
								UpperCamelCase_:							List[Any]		=  0
								for j in range(2   ,			lowerCamelCase  ):
												if i % j != 0:
																UpperCamelCase_:							Union[str, Any]		=  1
																break
								if nfound == 0:
												if i == 0:
																UpperCamelCase_:							List[str]		=  1
												return i
				return None


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








from math import cos, sin







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_:							int		=  float(lowerCamelCase  )
				return [[scaling_factor * int(x == y  ) for x in range(2  )] for y in range(2  )]







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_,      UpperCamelCase_:							Union[str, Any]		=  cos(lowerCamelCase  ), sin(lowerCamelCase  )
				return [[c, -s], [s, c]]







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_,      UpperCamelCase_:							Any		=  cos(lowerCamelCase  ), sin(lowerCamelCase  )
				UpperCamelCase_:							List[Any]		=  c * s
				return [[c * c, cs], [cs, s * s]]







def 				A__    (  lowerCamelCase  )     ->		list[list[float]]:
				UpperCamelCase_,      UpperCamelCase_:							List[str]		=  cos(lowerCamelCase  ), sin(lowerCamelCase  )
				UpperCamelCase_:							int		=  c * s
				return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F"""    {scaling(5) = }""")
print(F"""  {rotation(45) = }""")
print(F"""{projection(45) = }""")





print(F"""{reflection(45) = }""")






