





from __future__ import annotations

from math import ceil, floor, sqrt



def A_     (		A__ = 200_0000    )  ->		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__						:     Optional[int]			=    floor(A__    )
              a__						:     Tuple			=    ceil(A__    )
              a__						:     Union[str, Any]			=    triangle_numbers[b_floor]
              a__						:     Any			=    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__						:     Optional[Any]			=    idx_a * b_floor

              if abs(target - triangle_b_second_guess * triangle_a    ) < abs(
                  target - best_product    ):
                     a__						:     List[str]			=    triangle_b_second_guess * triangle_a
                     a__						:     Dict			=    idx_a * b_ceil

       return area


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









import re

from filelock import FileLock


try:
    import nltk

    lowercase				:	List[str]      						=  True
except (ImportError, ModuleNotFoundError):
    lowercase				:	Tuple      						=  False

if NLTK_AVAILABLE:
    with FileLock(""".lock""") as lock:
        nltk.download("""punkt""", quiet=True)



def A_     (		A__    )  ->		str:
       re.sub('<n>'		,				''		,				A__    )  # remove pegasus newline char
       assert NLTK_AVAILABLE, "nltk must be installed to separate newlines between sentences. (pip install nltk)"
       return "\n".join(nltk.sent_tokenize(A__    )    )


