
'''simple docstring'''
from itertools import count
from math import asin, pi, sqrt







def 						A_(			A		:						float):
							return (
							    (1 - 2 * point) * sqrt(point - point**2) + 2 * point + asin(sqrt(1 - point))
							) / 4







def 						A_(			A		:						int):
							UpperCamelCase					       =			(circles_number + 1 - sqrt(2 * circles_number)) / (
							    2 * (circles_number**2 + 1)
							)
							UpperCamelCase					       =			circles_number * intersection_y

							UpperCamelCase					       =			intersection_x * intersection_y / 2
							UpperCamelCase					       =			circle_bottom_arc_integral(
							    1 / 2) - circle_bottom_arc_integral(A)

							return triangle_area + concave_region_area







def 						A_(			A		:						float = 1 / 1000):
							UpperCamelCase					       =			(1 - pi / 4) / 4

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

							return -1


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





from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCAmelCase__							= logging.get_logger(__name__)

lowerCAmelCase__							= {
    'dandelin/vilt-b32-mlm': 'https://huggingface.co/dandelin/vilt-b32-mlm/blob/main/config.json'
}
class 				a_ (						SCREAMING_SNAKE_CASE						):






 '''simple docstring'''






 UpperCAmelCase_	 =					'vilt'




 def __init__(			self					:  Optional[Any]			,    lowercase__					:  Dict=30_522			,    lowercase__					:  Tuple=2			,    lowercase__					:  int=2			,    lowercase__					:  Optional[int]=40			,    lowercase__					:  Optional[int]=768			,    lowercase__					:  Tuple=12			,    lowercase__					:  Tuple=12			,    lowercase__					:  Union[str, Any]=3_072			,    lowercase__					:  int="gelu"			,    lowercase__					:  Tuple=0.0			,    lowercase__					:  Dict=0.0			,    lowercase__					:  Optional[int]=0.02			,    lowercase__					:  Tuple=1e-12			,    lowercase__					:  Dict=384			,    lowercase__					:  int=32			,    lowercase__					:  List[str]=3			,    lowercase__					:  int=True			,    lowercase__					:  List[str]=-1			,    lowercase__					:  Union[str, Any]=False			,    lowercase__					:  List[str]=-1			,    **lowercase__					:  int			,    ):







        '''simple docstring'''



        super().__init__(tie_word_embeddings=lowercase__			,    **lowercase__)

        lowerCAmelCase__     	=					vocab_size
        lowerCAmelCase__     	=					type_vocab_size
        lowerCAmelCase__     	=					modality_type_vocab_size
        lowerCAmelCase__     	=					max_position_embeddings

        lowerCAmelCase__     	=					hidden_size
        lowerCAmelCase__     	=					num_hidden_layers
        lowerCAmelCase__     	=					num_attention_heads
        lowerCAmelCase__     	=					intermediate_size
        lowerCAmelCase__     	=					hidden_act
        lowerCAmelCase__     	=					hidden_dropout_prob
        lowerCAmelCase__     	=					attention_probs_dropout_prob
        lowerCAmelCase__     	=					initializer_range
        lowerCAmelCase__     	=					layer_norm_eps

        lowerCAmelCase__     	=					image_size
        lowerCAmelCase__     	=					patch_size
        lowerCAmelCase__     	=					num_channels
        lowerCAmelCase__     	=					qkv_bias
        lowerCAmelCase__     	=					max_image_length
        lowerCAmelCase__     	=					num_images
