


'''simple docstring'''
from __future__ import annotations

from math import ceil, floor, sqrt

def 					lowerCamelCase_ ( __UpperCamelCase					:       int = 2_0_0_0_0_0_0		)					->	int:







     """simple docstring"""
     _A				=							[0]
     _A				=							42

     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				=							0
     # the area corresponding to the grid that gives the product closest to target
     _A				=							0
     # an estimate of b, using the quadratic formula
     _A				=							42
     # the largest integer less than b_estimate
     _A				=							42
     # the largest integer less than b_estimate
     _A				=							42
     # the triangle number corresponding to b_floor
     _A				=							42
     # the triangle number corresponding to b_ceil
     _A				=							42

     for idx_a, triangle_a in enumerate(triangle_numbers[1:]							,    1		):
          _A				=							(-1 + sqrt(1 + 8 * target / triangle_a		)) / 2
          _A				=							floor(__UpperCamelCase		)
          _A				=							ceil(__UpperCamelCase		)
          _A				=							triangle_numbers[b_floor]
          _A				=							triangle_numbers[b_ceil]

          if abs(target - triangle_b_first_guess * triangle_a		) < abs(
              target - best_product		):
               _A				=							triangle_b_first_guess * triangle_a
               _A				=							idx_a * b_floor

          if abs(target - triangle_b_second_guess * triangle_a		) < abs(
              target - best_product		):
               _A				=							triangle_b_second_guess * triangle_a
               _A				=							idx_a * b_ceil

     return area


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









'''simple docstring'''
from .testing import (
    are_the_same_tensors,
    execute_subprocess_async,
    require_bnb,
    require_cpu,
    require_cuda,
    require_huggingface_suite,
    require_mps,
    require_multi_gpu,
    require_multi_xpu,
    require_safetensors,
    require_single_gpu,
    require_single_xpu,
    require_torch_min_version,
    require_tpu,
    require_xpu,
    skip,
    slow,
)
from .training import RegressionDataset, RegressionModel, RegressionModelaXPU


from .scripts import test_script, test_sync, test_ops  # isort: skip





