






def    __lowerCAmelCase   (    __snake_case = 1000							):
     __lowerCAmelCase             =       -1
     __lowerCAmelCase             =       0
     for a in range(1       ,			n // 3							):
          # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
          __lowerCAmelCase             =       (n * n - 2 * a * n) // (2 * n - 2 * a)
          __lowerCAmelCase             =       n - a - b
          if c * c == (a * a + b * b):
               __lowerCAmelCase             =       a * b * c
               if candidate >= product:
                    __lowerCAmelCase             =       candidate
     return product


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














from math import pow, sqrt





def    __lowerCAmelCase   (    *__snake_case							):
     __lowerCAmelCase             =       len(__snake_case							) > 0 and all(value > 0.0 for value in values							)
     return result





def    __lowerCAmelCase   (    __snake_case       ,			__snake_case							):
     return (
         round(sqrt(molar_mass_a / molar_mass_a							)       ,			6							)
         if validate(__snake_case       ,			__snake_case							)
         else ValueError("Input Error: Molar mass values must greater than 0."							)
     )





def    __lowerCAmelCase   (    __snake_case       ,			__snake_case       ,			__snake_case							):
     return (
         round(effusion_rate * sqrt(molar_mass_a / molar_mass_a							)       ,			6							)
         if validate(__snake_case       ,			__snake_case       ,			__snake_case							)
         else ValueError(
             "Input Error: Molar mass and effusion rate values must greater than 0."							)
     )





def    __lowerCAmelCase   (    __snake_case       ,			__snake_case       ,			__snake_case							):
     return (
         round(effusion_rate / sqrt(molar_mass_a / molar_mass_a							)       ,			6							)
         if validate(__snake_case       ,			__snake_case       ,			__snake_case							)
         else ValueError(
             "Input Error: Molar mass and effusion rate values must greater than 0."							)
     )





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





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






