
'''simple docstring'''







from __future__ import annotations

from math import ceil, floor, sqrt
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			int = 2000000							):



						"""simple docstring"""





						lowercase_     :					list[int]													=	[0]
						lowercase_     :					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
						lowercase_     :					int													=	0
						# the area corresponding to the grid that gives the product closest to target
						lowercase_     :					int													=	0
						# an estimate of b, using the quadratic formula
						lowercase_     :					float
						# the largest integer less than b_estimate
						lowercase_     :					int
						# the largest integer less than b_estimate
						lowercase_     :					int
						# the triangle number corresponding to b_floor
						lowercase_     :					int
						# the triangle number corresponding to b_ceil
						lowercase_     :					int

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

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

												if abs(target - triangle_b_second_guess * triangle_a							) < abs(
												    target - best_product							):
																		lowercase_     :					List[Any]													=	triangle_b_second_guess * triangle_a
																		lowercase_     :					List[Any]													=	idx_a * b_ceil

						return area


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





'''simple docstring'''







def  snake_case_		(    __SCREAMING_SNAKE_CASE :			str							):



						"""simple docstring"""





						return [
						    txt[:a] + txt[a].upper() + txt[a + 1 :]
						    for a in range(len(__SCREAMING_SNAKE_CASE							)							)
						    if txt[a].isalpha()
						]


if __name__ == "__main__":
							__import__("doctest").testmod()



