


'''simple docstring'''






from __future__ import annotations

from math import ceil, floor, sqrt





def      UpperCAmelCase      (		lowerCamelCase_  :Optional[int] = 2_00_00_00 ):







		'''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_		:							Optional[Any]			       =						(-1 + sqrt(1 + 8 * target / triangle_a )) / 2
				snake_case_		:							str			       =						floor(_lowercase )
				snake_case_		:							Optional[int]			       =						ceil(_lowercase )
				snake_case_		:							Optional[int]			       =						triangle_numbers[b_floor]
				snake_case_		:							int			       =						triangle_numbers[b_ceil]

				if abs(target - triangle_b_first_guess * triangle_a ) < abs(
				    target - best_product ):
						snake_case_		:							Optional[Any]			       =						triangle_b_first_guess * triangle_a
						snake_case_		:							Union[str, Any]			       =						idx_a * b_floor

				if abs(target - triangle_b_second_guess * triangle_a ) < abs(
				    target - best_product ):
						snake_case_		:							Dict			       =						triangle_b_second_guess * triangle_a
						snake_case_		:							Optional[Any]			       =						idx_a * b_ceil

		return area


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




'''simple docstring'''






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


__A	:	Optional[int]     =     logging.get_logger(__name__)

__A	:	List[Any]     =     {
    'studio-ousia/luke-base': 'https://huggingface.co/studio-ousia/luke-base/resolve/main/config.json',
    'studio-ousia/luke-large': 'https://huggingface.co/studio-ousia/luke-large/resolve/main/config.json',
}
class 						__UpperCamelCase	(						lowercase__							):
							lowercase			:		Union[str, Any]   		=  'luke'





							def __init__(  self		:List[str]  ,_UpperCamelCase		:Tuple=5_0_2_6_7  ,_UpperCamelCase		:Tuple=5_0_0_0_0_0  ,_UpperCamelCase		:str=7_6_8  ,_UpperCamelCase		:List[Any]=2_5_6  ,_UpperCamelCase		:List[str]=1_2  ,_UpperCamelCase		:str=1_2  ,_UpperCamelCase		:Union[str, Any]=3_0_7_2  ,_UpperCamelCase		:int="gelu"  ,_UpperCamelCase		:int=0.1  ,_UpperCamelCase		:Dict=0.1  ,_UpperCamelCase		:Dict=5_1_2  ,_UpperCamelCase		:Optional[Any]=2  ,_UpperCamelCase		:int=0.02  ,_UpperCamelCase		:Any=1E-1_2  ,_UpperCamelCase		:Tuple=True  ,_UpperCamelCase		:Any=None  ,_UpperCamelCase		:Any=1  ,_UpperCamelCase		:int=0  ,_UpperCamelCase		:List[Any]=2  ,**_UpperCamelCase		:str  ,):
									super().__init__(pad_token_id=_UpperCamelCase  ,bos_token_id=_UpperCamelCase  ,eos_token_id=_UpperCamelCase  ,**_UpperCamelCase			)

									snake_case_		:							Any			       =						vocab_size
									snake_case_		:							List[Any]			       =						entity_vocab_size
									snake_case_		:							Optional[Any]			       =						hidden_size
									snake_case_		:							List[Any]			       =						entity_emb_size
									snake_case_		:							Dict			       =						num_hidden_layers
									snake_case_		:							Union[str, Any]			       =						num_attention_heads
									snake_case_		:							Dict			       =						hidden_act
									snake_case_		:							Dict			       =						intermediate_size
									snake_case_		:							Any			       =						hidden_dropout_prob
									snake_case_		:							List[Any]			       =						attention_probs_dropout_prob
									snake_case_		:							Optional[Any]			       =						max_position_embeddings
									snake_case_		:							Any			       =						type_vocab_size
									snake_case_		:							int			       =						initializer_range
									snake_case_		:							Union[str, Any]			       =						layer_norm_eps
									snake_case_		:							Tuple			       =						use_entity_aware_attention
									snake_case_		:							Tuple			       =						classifier_dropout