




def    UpperCAmelCase_				( )   ->					Tuple:
      for n in range(1     ,     1_00_00_00				):
            yield n * (n + 1) // 2

def    UpperCAmelCase_				( __UpperCAmelCase		:      Union[str, Any]				)   ->					Union[str, Any]:
      SCREAMING_SNAKE_CASE_      		=     1
      SCREAMING_SNAKE_CASE_      		=     2
      while i * i <= n:
            SCREAMING_SNAKE_CASE_      		=     0
            while n % i == 0:
                  n //= i
                  multiplicity += 1
            divisors_count *= multiplicity + 1
            i += 1
      if n > 1:
            divisors_count *= 2
      return divisors_count

def    UpperCAmelCase_				( )   ->					Union[str, Any]:
      return next(i for i in triangle_number_generator() if count_divisors(__UpperCAmelCase				) > 5_00				)


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





def    UpperCAmelCase_				( __UpperCAmelCase		:      int				)   ->					int:
      assert isinstance(__UpperCAmelCase     ,     __UpperCAmelCase				), f"The input value of [n={number}] is not an integer"

      if number == 1:
            return 2
      elif number < 1:
            SCREAMING_SNAKE_CASE_      		=     f"The input value of [n={number}] has to be > 0"
            raise ValueError(__UpperCAmelCase				)
      else:
            SCREAMING_SNAKE_CASE_      		=     sylvester(number - 1				)
            SCREAMING_SNAKE_CASE_      		=     num - 1
            SCREAMING_SNAKE_CASE_      		=     num
            return lower * upper + 1


if __name__ == "__main__":
   print(f'''The 8th number in Sylvester\'s sequence: {sylvester(8)}''')