'''simple docstring'''





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






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float  )   ->				float:







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






def SCREAMING_SNAKE_CASE__  (				snake_case       :				int  )   ->				float:







     """simple docstring"""
     a					:							List[str]							= (circles_number + 1 - sqrt(2 * circles_number  )) / (
         2 * (circles_number**2 + 1)
     )
     a					:							int							= circles_number * intersection_y

     a					:							List[Any]							= intersection_x * intersection_y / 2
     a					:							List[str]							= circle_bottom_arc_integral(
         1 / 2  ) - circle_bottom_arc_integral(snake_case  )

     return triangle_area + concave_region_area






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float = 1 / 1_000  )   ->				int:







     """simple docstring"""
     a					:							str							= (1 - pi / 4) / 4

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

     return -1


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


'''simple docstring'''





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


UpperCamelCase       :     Any			=    logging.get_logger(__name__)

UpperCamelCase       :     Optional[int]			=    {
    """openbmb/cpm-ant-10b""": """https://huggingface.co/openbmb/cpm-ant-10b/blob/main/config.json"""
    # See all CPMAnt models at https://huggingface.co/models?filter=cpmant
}



class   UpperCamelCase					(       a_       ):







    """simple docstring"""





    A     :    List[str]				=			"cpmant"





    def __init__(					self     :						Tuple							,							UpperCAmelCase_     :						int = 3_0_7_2_0							,							UpperCAmelCase_     :						int = 4_0_9_6							,							UpperCAmelCase_     :						int = 3_2							,							UpperCAmelCase_     :						int = 1_2_8							,							UpperCAmelCase_     :						int = 1_0_2_4_0							,							UpperCAmelCase_     :						int = 4_8							,							UpperCAmelCase_     :						int = 0.0							,							UpperCAmelCase_     :						int = 5_1_2							,							UpperCAmelCase_     :						int = 2_0_4_8							,							UpperCAmelCase_     :						int = 1e-6							,							UpperCAmelCase_     :						float = 1.0							,							UpperCAmelCase_     :						int = 3_2							,							UpperCAmelCase_     :						int = 3_2							,							UpperCAmelCase_     :						int = 3_2							,							UpperCAmelCase_     :						bool = True							,							**UpperCAmelCase_     :						Tuple							,							):


         """simple docstring"""







         super().__init__(**UpperCAmelCase_)
         a					:							Union[str, Any]							= prompt_types
         a					:							List[str]							= prompt_length
         a					:							List[Any]							= segment_types
         a					:							Any							= hidden_size
         a					:							Optional[int]							= num_attention_heads
         a					:							Union[str, Any]							= dim_head
         a					:							int							= dim_ff
         a					:							Union[str, Any]							= num_hidden_layers
         a					:							List[Any]							= position_bias_num_buckets
         a					:							Optional[int]							= position_bias_max_distance
         a					:							str							= dropout_p
         a					:							List[str]							= eps
         a					:							Dict							= use_cache
         a					:							Tuple							= vocab_size
         a					:							Optional[Any]							= init_std

