
"""simple docstring"""






from itertools import count
from math import asin, pi, sqrt



def     lowerCAmelCase__ (		__magic_name__			)	->float:
			return (
			    (1 - 2 * point) * sqrt(point - point**2			) + 2 * point + asin(sqrt(1 - point			)			)
			) / 4



def     lowerCAmelCase__ (		__magic_name__			)	->float:
			__lowercase						      =					(circles_number + 1 - sqrt(2 * circles_number			)) / (
			    2 * (circles_number**2 + 1)
			)
			__lowercase						      =					circles_number * intersection_y

			__lowercase						      =					intersection_x * intersection_y / 2
			__lowercase						      =					circle_bottom_arc_integral(
			    1 / 2			) - circle_bottom_arc_integral(__magic_name__			)

			return triangle_area + concave_region_area



def     lowerCAmelCase__ (		__magic_name__ = 1 / 1_0_0_0			)	->int:
			__lowercase						      =					(1 - pi / 4) / 4

			for n in count(1			):
						if concave_triangle_area(__magic_name__			) / l_section_area < fraction:
									return n

			return -1


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







"""simple docstring"""






from collections import OrderedDict
from typing import Mapping

from packaging import version

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging
from ...utils.backbone_utils import BackboneConfigMixin, get_aligned_output_features_output_indices


_lowercase							 =							logging.get_logger(__name__)

_lowercase							 =							{
    '''facebook/convnext-tiny-224''': '''https://huggingface.co/facebook/convnext-tiny-224/resolve/main/config.json''',
    # See all ConvNeXT models at https://huggingface.co/models?filter=convnext
}

class 				__a    (   __a				,      __a					):



							'''simple docstring'''







							_lowerCamelCase				: List[Any]					      =      """convnext"""
							def __init__(    self     ,						_lowerCamelCase=3     ,						_lowerCamelCase=4     ,						_lowerCamelCase=4     ,						_lowerCamelCase=None     ,						_lowerCamelCase=None     ,						_lowerCamelCase="gelu"     ,						_lowerCamelCase=0.02     ,						_lowerCamelCase=1e-12     ,						_lowerCamelCase=1e-6     ,						_lowerCamelCase=0.0     ,						_lowerCamelCase=224     ,						_lowerCamelCase=None     ,						_lowerCamelCase=None     ,						**_lowerCamelCase     ,						) ->       List[str]:




										'''simple docstring'''
										super().__init__(**_lowerCamelCase					)

										__lowercase						      =					num_channels
										__lowercase						      =					patch_size
										__lowercase						      =					num_stages
										__lowercase						      =					[96, 192, 384, 768] if hidden_sizes is None else hidden_sizes
										__lowercase						      =					[3, 3, 9, 3] if depths is None else depths
										__lowercase						      =					hidden_act
										__lowercase						      =					initializer_range
										__lowercase						      =					layer_norm_eps
										__lowercase						      =					layer_scale_init_value
										__lowercase						      =					drop_path_rate
										__lowercase						      =					image_size
										__lowercase						      =					["stem"] + [f'''stage{idx}''' for idx in range(1     ,						len(self.depths					) + 1					)]
										__lowercase      ,				__lowercase						      =					get_aligned_output_features_output_indices(
										    out_features=_lowerCamelCase     ,						out_indices=_lowerCamelCase     ,						stage_names=self.stage_names					)





class 				__a    (   __a					):



							'''simple docstring'''







							_lowerCamelCase				: str					      =      version.parse("""1.11"""					)
							@property
							def      SCREAMING_SNAKE_CASE	(    self					) ->       Mapping[str, Mapping[int, str]]:




										'''simple docstring'''
										return OrderedDict(
										    [
										        ("pixel_values", {0: "batch", 1: "num_channels", 2: "height", 3: "width"}),
										    ]					)





							@property
							def      SCREAMING_SNAKE_CASE	(    self					) ->       float:




										'''simple docstring'''
										return 1e-5





