


"""simple docstring"""






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


_lowerCAmelCase							:    Dict					   =	{'''configuration_yolos''': ['''YOLOS_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''YolosConfig''', '''YolosOnnxConfig''']}

try:
  if not is_vision_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _lowerCAmelCase							:    List[Any]					   =	['''YolosFeatureExtractor''']
  _lowerCAmelCase							:    Optional[Any]					   =	['''YolosImageProcessor''']

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _lowerCAmelCase							:    Any					   =	[
      '''YOLOS_PRETRAINED_MODEL_ARCHIVE_LIST''',
      '''YolosForObjectDetection''',
      '''YolosModel''',
      '''YolosPreTrainedModel''',
  ]


if TYPE_CHECKING:
  from .configuration_yolos import YOLOS_PRETRAINED_CONFIG_ARCHIVE_MAP, YolosConfig, YolosOnnxConfig

  try:
    if not is_vision_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .feature_extraction_yolos import YolosFeatureExtractor
    from .image_processing_yolos import YolosImageProcessor

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_yolos import (
        YOLOS_PRETRAINED_MODEL_ARCHIVE_LIST,
        YolosForObjectDetection,
        YolosModel,
        YolosPreTrainedModel,
    )


else:
  import sys

  _lowerCAmelCase							:    Dict					   =	_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)

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

from math import ceil, floor, sqrt




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ = 200_0000			)  ->							int:


		'''simple docstring'''


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

		for idx_a, triangle_a in enumerate(triangle_numbers[1:] ,       1			):
				snake_case  :       int     			=						(-1 + sqrt(1 + 8 * target / triangle_a			)) / 2
				snake_case  :       Optional[int]     			=						floor(SCREAMING_SNAKE_CASE__			)
				snake_case  :       int     			=						ceil(SCREAMING_SNAKE_CASE__			)
				snake_case  :       Optional[Any]     			=						triangle_numbers[b_floor]
				snake_case  :       Union[str, Any]     			=						triangle_numbers[b_ceil]

				if abs(target - triangle_b_first_guess * triangle_a			) < abs(
				    target - best_product			):
						snake_case  :       str     			=						triangle_b_first_guess * triangle_a
						snake_case  :       int     			=						idx_a * b_floor

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

		return area


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


