






'''simple docstring'''

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






def 						_UpperCAmelCase     (	a		:						float				)      ->      float:





						"""simple docstring"""
						return (
						    (1 - 2 * point) * sqrt(point - point**2				) + 2 * point + asin(sqrt(1 - point				)				)
						) / 4






def 						_UpperCAmelCase     (	a		:						int				)      ->      float:





						"""simple docstring"""
						lowercase_   : Optional[Any]   	=      (circles_number + 1 - sqrt(2 * circles_number				)) / (
						    2 * (circles_number**2 + 1)
						)
						lowercase_   : Union[str, Any]   	=      circles_number * intersection_y

						lowercase_   : List[str]   	=      intersection_x * intersection_y / 2
						lowercase_   : str   	=      circle_bottom_arc_integral(
						    1 / 2				) - circle_bottom_arc_integral(UpperCAmelCase_				)

						return triangle_area + concave_region_area






def 						_UpperCAmelCase     (	a		:						float = 1 / 1_0_0_0				)      ->      int:





						"""simple docstring"""
						lowercase_   : Optional[int]   	=      (1 - pi / 4) / 4

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

						return -1


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






from typing import TYPE_CHECKING

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


_lowerCamelCase							=      {'''configuration_cvt''': ['''CVT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''CvtConfig''']}


try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    _lowerCamelCase							=      [
        '''CVT_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''CvtForImageClassification''',
        '''CvtModel''',
        '''CvtPreTrainedModel''',
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    _lowerCamelCase							=      [
        '''TF_CVT_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''TFCvtForImageClassification''',
        '''TFCvtModel''',
        '''TFCvtPreTrainedModel''',
    ]

if TYPE_CHECKING:
    from .configuration_cvt import CVT_PRETRAINED_CONFIG_ARCHIVE_MAP, CvtConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_cvt import (
            CVT_PRETRAINED_MODEL_ARCHIVE_LIST,
            CvtForImageClassification,
            CvtModel,
            CvtPreTrainedModel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_cvt import (
            TF_CVT_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFCvtForImageClassification,
            TFCvtModel,
            TFCvtPreTrainedModel,
        )


else:
    import sys

    _lowerCamelCase							=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
