

from collections import defaultdict
from math import gcd
def   a   (    A__			:     int = 1500000  )					->   int:





      """simple docstring"""



      _lowercase			 =defaultdict(A__  )
      _lowercase			 =2
      while 2 * euclid_m * (euclid_m + 1) <= limit:
            for euclid_n in range((euclid_m % 2) + 1   ,     A__   ,     2  ):
                  if gcd(A__   ,     A__  ) > 1:
                        continue
                  _lowercase			 =2 * euclid_m * (euclid_m + euclid_n)
                  for perimeter in range(A__   ,     limit + 1   ,     A__  ):
                        frequencies[perimeter] += 1
            euclid_m += 1
      return sum(1 for frequency in frequencies.values() if frequency == 1  )


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





from math import pow, sqrt
def   a   (    *A__			:     float  )					->   bool:





      """simple docstring"""



      _lowercase			 =len(A__  ) > 0 and all(value > 0.0 for value in values  )
      return result
def   a   (    A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(sqrt(molar_mass_a / molar_mass_a  )   ,     6  )
          if validate(A__   ,     A__  )
          else ValueError('Input Error: Molar mass values must greater than 0.'  )
      )
def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(effusion_rate * sqrt(molar_mass_a / molar_mass_a  )   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )
def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(effusion_rate / sqrt(molar_mass_a / molar_mass_a  )   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )
def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(molar_mass / pow(effusion_rate_a / effusion_rate_a   ,     2  )   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )







def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(pow(effusion_rate_a / effusion_rate_a   ,     2  ) / molar_mass   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )


