



from __future__ import annotations

from math import ceil, floor, sqrt



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_ = 200_0000					):
			lowercase__   					=			[0]
			lowercase__   					=			42

			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
			lowercase__   					=			0
			# the area corresponding to the grid that gives the product closest to target
			lowercase__   					=			0
			# an estimate of b, using the quadratic formula
			lowercase__   					=			42
			# the largest integer less than b_estimate
			lowercase__   					=			42
			# the largest integer less than b_estimate
			lowercase__   					=			42
			# the triangle number corresponding to b_floor
			lowercase__   					=			42
			# the triangle number corresponding to b_ceil
			lowercase__   					=			42

			for idx_a, triangle_a in enumerate(triangle_numbers[1:]  ,					1					):
						lowercase__   					=			(-1 + sqrt(1 + 8 * target / triangle_a					)) / 2
						lowercase__   					=			floor(SCREAMING_SNAKE_CASE_					)
						lowercase__   					=			ceil(SCREAMING_SNAKE_CASE_					)
						lowercase__   					=			triangle_numbers[b_floor]
						lowercase__   					=			triangle_numbers[b_ceil]

						if abs(target - triangle_b_first_guess * triangle_a					) < abs(
						    target - best_product					):
									lowercase__   					=			triangle_b_first_guess * triangle_a
									lowercase__   					=			idx_a * b_floor

						if abs(target - triangle_b_second_guess * triangle_a					) < abs(
						    target - best_product					):
									lowercase__   					=			triangle_b_second_guess * triangle_a
									lowercase__   					=			idx_a * b_ceil

			return area


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




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


lowercase_						=       logging.get_logger(__name__)

lowercase_						=       {
    """facebook/dpr-ctx_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-ctx_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-multiset-base""": (
        """https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/config.json"""
    ),
}
class 			_snake_case     (   lowercase__):
				UpperCamelCase__			:   str       						="""dpr"""




				def __init__(  self   :  int,   __lowercase   :  List[str]=3_0522,   __lowercase   :  Any=768,   __lowercase   :  Union[str, Any]=12,   __lowercase   :  Optional[int]=12,   __lowercase   :  List[Any]=3072,   __lowercase   :  List[str]="gelu",   __lowercase   :  Union[str, Any]=0.1,   __lowercase   :  str=0.1,   __lowercase   :  List[str]=512,   __lowercase   :  Optional[int]=2,   __lowercase   :  Dict=0.02,   __lowercase   :  Any=1e-1_2,   __lowercase   :  List[Any]=0,   __lowercase   :  str="absolute",   __lowercase   :  int = 0,   **__lowercase   :  str,   ):
							super().__init__(pad_token_id=__lowercase,   **__lowercase  )

							lowercase__   					=			vocab_size
							lowercase__   					=			hidden_size
							lowercase__   					=			num_hidden_layers
							lowercase__   					=			num_attention_heads
							lowercase__   					=			hidden_act
							lowercase__   					=			intermediate_size
							lowercase__   					=			hidden_dropout_prob
							lowercase__   					=			attention_probs_dropout_prob
							lowercase__   					=			max_position_embeddings
							lowercase__   					=			type_vocab_size
							lowercase__   					=			initializer_range
							lowercase__   					=			layer_norm_eps
							lowercase__   					=			projection_dim
							lowercase__   					=			position_embedding_type




