





'''simple docstring'''




def 			_lowerCAmelCase     (    __snake_case    :					int = 10_00     )	->	int:
     __A		:					Tuple						=			-1
     __A		:					Tuple						=			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
          __A		:					Optional[int]						=			(n * n - 2 * a * n) // (2 * n - 2 * a)
          __A		:					Optional[int]						=			n - a - b
          if c * c == (a * a + b * b):
               __A		:					Optional[Any]						=			a * b * c
               if candidate >= product:
                    __A		:					List[str]						=			candidate
     return product


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



import math




def  a   (lowerCAmelCase__   ):

   if 1 < number < 4:
      # 2 and 3 are primes
      return True
   elif number < 2 or number % 2 == 0 or number % 3 == 0:
      # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
      return False

   # All primes number are in format of 6k +/- 1
   for i in range(5		,				int(math.sqrt(lowerCAmelCase__   ) + 1   )		,				6   ):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True




def  a   (lowerCAmelCase__ = 10_001   ):

   try:
      __a					=  int(lowerCAmelCase__   )
   except (TypeError, ValueError):
      raise TypeError("""Parameter nth must be int or castable to int."""   ) from None
   if nth <= 0:
      raise ValueError("""Parameter nth must be greater than or equal to one."""   )
   __a					=  []
   __a					=  2
   while len(lowerCAmelCase__   ) < nth:
      if is_prime(lowerCAmelCase__   ):
         primes.append(lowerCAmelCase__   )
         num += 1
      else:
         num += 1
   return primes[len(lowerCAmelCase__   ) - 1]


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



