





from math import cos, sin





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





def    _lowercase    (  _UpperCAmelCase )  ->     list[list[float]]:
				lowerCamelCase       ,     lowerCamelCase		       =cos(_UpperCAmelCase ), sin(_UpperCAmelCase )
				return [[c, -s], [s, c]]





def    _lowercase    (  _UpperCAmelCase )  ->     list[list[float]]:
				lowerCamelCase       ,     lowerCamelCase		       =cos(_UpperCAmelCase ), sin(_UpperCAmelCase )
				lowerCamelCase		       =c * s
				return [[c * c, cs], [cs, s * s]]





def    _lowercase    (  _UpperCAmelCase )  ->     list[list[float]]:
				lowerCamelCase       ,     lowerCamelCase		       =cos(_UpperCAmelCase ), sin(_UpperCAmelCase )
				lowerCamelCase		       =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) = }")









"""simple docstring"""


def    a__       ( __lowercase = 20      )		->		int:

				try:
								_A         =	int(__lowercase      )
				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."      )
				_A         =	0
				while 1:
								i += n * (n - 1)
								_A         =	0
								for j in range(2   ,	__lowercase      ):
												if i % j != 0:
																_A         =	1
																break
								if nfound == 0:
												if i == 0:
																_A         =	1
												return i
				return None


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