from __future__ import annotations

from math import ceil, floor, sqrt



def A__  (			lowercase:     int = 2_000_000					)				->		int:
       A						:     list[int]         =[0]
       A						:     int

       for idx in range(1,		ceil(sqrt(target * 2					) * 1.1					)					):
              triangle_numbers.append(triangle_numbers[-1] + idx					)

       # we want this to be as close as possible to target
       A						:     int         =0
       # the area corresponding to the grid that gives the product closest to target
       A						:     int         =0
       # an estimate of b, using the quadratic formula
       A						:     float
       # the largest integer less than b_estimate
       A						:     int
       # the largest integer less than b_estimate
       A						:     int
       # the triangle number corresponding to b_floor
       A						:     int
       # the triangle number corresponding to b_ceil
       A						:     int

       for idx_a, triangle_a in enumerate(triangle_numbers[1:],		1					):
              A						:     Any         =(-1 + sqrt(1 + 8 * target / triangle_a					)) / 2
              A						:     Dict         =floor(lowercase					)
              A						:     List[Any]         =ceil(lowercase					)
              A						:     Optional[Any]         =triangle_numbers[b_floor]
              A						:     int         =triangle_numbers[b_ceil]

              if abs(target - triangle_b_first_guess * triangle_a					) < abs(
                  target - best_product					):
                     A						:     Optional[Any]         =triangle_b_first_guess * triangle_a
                     A						:     Union[str, Any]         =idx_a * b_floor

              if abs(target - triangle_b_second_guess * triangle_a					) < abs(
                  target - best_product					):
                     A						:     Tuple         =triangle_b_second_guess * triangle_a
                     A						:     Dict         =idx_a * b_ceil

       return area


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







def A__  (			lowercase:     int					)				->		int:
       if not isinstance(lowercase,		lowercase					) or number < 0:
              raise ValueError('Input must be a non-negative integer'					)

       A						:     Any         =0
       while number:
              # This way we arrive at next set bit (next 1) instead of looping
              # through each bit and checking for 1s hence the
              # loop won't run 32 times it will only run the number of `1` times
              number &= number - 1
              count += 1
       return count


if __name__ == "__main__":
    import doctest

    doctest.testmod()






