code: 
  
  
  from math import gcd
  
  
  
  
  
  
  def 		_A		(		_lowercase = 1_20_00   )				->   int:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = 0
       for d in range(max_d + 1   ):
            for n in range(d // 3 + 1				,     (d + 1) // 2   ):
                 if gcd(_lowercase				,     _lowercase   ) == 1:
                      fractions_number += 1
       return fractions_number
  
  
  if __name__ == "__main__":
      print(f"""{solution() = }""")
  
  
  
style_context: 
  
  
  from math import cos, sin
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = float(_lowercase   )
       return [[scaling_factor * int(x == y   ) for x in range(2   )] for y in range(2   )]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       return [[c, -s], [s, c]]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       __UpperCamelCase   = c * s
       return [[c * c, cs], [cs, s * s]]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       __UpperCamelCase   = c * s
       return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]
  
  
  print(f"""    {scaling(5) = }""")
  print(f"""  {rotation(4_5) = }""")
  print(f"""{projection(4_5) = }""")
  
  
  print(f"""{reflection(4_5) = }""")
  
  
  