




from __future__ import annotations

from collections.abc import Generator



def 					UpperCAmelCase__     (   ):
  lowercase			:Dict							=  {}
  lowercase			:int							=  2
  while True:
    lowercase			:int							=  factor_map.pop(__UpperCamelCase,	__UpperCamelCase      )
    if factor:
      lowercase			:List[Any]							=  factor + prime
      while x in factor_map:
        x += factor
      lowercase			:List[Any]							=  factor
    else:
      lowercase			:Union[str, Any]							=  prime
      yield prime
    prime += 1



def 					UpperCAmelCase__     (   lowerCamelCase = 1e10      ):
  lowercase			:List[Any]							=  sieve()

  lowercase			:Optional[Any]							=  1
  while True:
    lowercase			:Dict							=  next(__UpperCamelCase      )
    if (2 * prime * n) > limit:
      return n
    # Ignore the next prime as the reminder will be 2.
    next(__UpperCamelCase      )
    n += 2


if __name__ == "__main__":
     print(solution())




def    a__       (						__UpperCamelCase = 1_0_0_0 ):
      SCREAMING_SNAKE_CASE_      =     -1
      SCREAMING_SNAKE_CASE_      =     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
            SCREAMING_SNAKE_CASE_      =     (n * n - 2 * a * n) // (2 * n - 2 * a)
            SCREAMING_SNAKE_CASE_      =     n - a - b
            if c * c == (a * a + b * b):
                  SCREAMING_SNAKE_CASE_      =     a * b * c
                  if candidate >= product:
                        SCREAMING_SNAKE_CASE_      =     candidate
      return product


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


