code: 
  
  """simple docstring"""
  from math import cos, sin
  
  
  
  
  def 				a__	(	lowerCAmelCase						)  ->   list[list[float]]:
        UpperCAmelCase__ :       str						=						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__ :       str						=						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__ :       Optional[int]						=						cos(lowerCAmelCase						), sin(lowerCAmelCase						)
        UpperCAmelCase__ :       Dict						=						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) = }''')
  
  
style_context: 
  
  """simple docstring"""
  from __future__ import annotations
  
  
  
  
  def 				a__	(	lowerCAmelCase						)  ->   set[int]:
        UpperCAmelCase__ :       List[Any]						=						{1}
        UpperCAmelCase__ :       Optional[int]						=						[1]
        for _ in range(2 ,  depth + 1						):
              UpperCAmelCase__ :       Tuple						=						[*previous_coefficients, 0]
              UpperCAmelCase__ :       List[str]						=						[0, *previous_coefficients]
              UpperCAmelCase__ :       Dict						=						[]
              for x, y in zip(lowerCAmelCase ,  lowerCAmelCase						):
                    coefficients.add(x + y						)
                    previous_coefficients.append(x + y						)
        return coefficients
  
  
  
  
  def 				a__	(	lowerCAmelCase						)  ->   set[int]:
        UpperCAmelCase__ :       List[str]						=						set()
        for number in unique_coefficients:
              UpperCAmelCase__ :       int						=						2
              UpperCAmelCase__ :       List[Any]						=						number
              while divisor**2 <= copy_number:
                    UpperCAmelCase__ :       Tuple						=						0
                    while copy_number % divisor == 0:
                          copy_number //= divisor
                          multiplicity += 1
                    if multiplicity >= 2:
                          non_squarefrees.add(lowerCAmelCase						)
                          break
                    divisor += 1
  
        return unique_coefficients.difference(lowerCAmelCase						)
  
  
  
  
  def 				a__	(	lowerCAmelCase = 51						)  ->   int:
        UpperCAmelCase__ :       Any						=						get_pascal_triangle_unique_coefficients(lowerCAmelCase						)
        UpperCAmelCase__ :       Dict						=						get_squarefrees(lowerCAmelCase						)
        return sum(lowerCAmelCase						)
  
  
  if __name__ == "__main__":
      print(f'''{solution() = }''')
  
  