






"""simple docstring"""





import math



def      __lowercase       (     a			:					int			)       ->       bool:

      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(a			) + 1			)							,		6			):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True



def      __lowercase       (     a			:					int = 600_851_475_143			)       ->       int:

      try:
            __snake_case   :     Dict	      =int(a			)
      except (TypeError, ValueError):
            raise TypeError('''Parameter n must be int or castable to int.'''			)
      if n <= 0:
            raise ValueError('''Parameter n must be greater than or equal to one.'''			)
      __snake_case   :     Dict	      =0
      if is_prime(a			):
            return n
      while n % 2 == 0:
            n //= 2
      if is_prime(a			):
            return n
      for i in range(3							,		int(math.sqrt(a			)			) + 1							,		2			):
            if n % i == 0:
                  if is_prime(n // i			):
                        __snake_case   :     Union[str, Any]	      =n // i
                        break
                  elif is_prime(a			):
                        __snake_case   :     int	      =i
      return max_number


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










"""simple docstring"""





from itertools import combinations, product



def      __lowercase       (     a			:					int							,		a			:					int							,		a			:					int							,		a			:					int			)       ->       bool:
      if xa == ya == 0 or xa == ya == 0:
            return False
      __snake_case   :     Any	      =xa * xa + ya * ya
      __snake_case   :     Tuple	      =xa * xa + ya * ya
      __snake_case   :     List[Any]	      =(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
      return (
          a_square + b_square == c_square
          or a_square + c_square == b_square
          or b_square + c_square == a_square
      )



def      __lowercase       (     a			:					int = 50			)       ->       int:
      return sum(
          1
          for pta, pta in combinations(product(range(limit + 1			)							,		repeat=2			)							,		2			)
          if is_right(*a							,		*a			)			)


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


