"""simple docstring"""






from collections import OrderedDict
from typing import TYPE_CHECKING, Any, List, Mapping, Optional, Union

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import TensorType, logging


if TYPE_CHECKING:
						from ...onnx.config import PatchingSpec
						from ...tokenization_utils_base import PreTrainedTokenizerBase


lowerCAmelCase__						:						Union[str, Any]		  =			logging.get_logger(__name__)

lowerCAmelCase__						:						str		  =			{
    'allenai/longformer-base-4096': 'https://huggingface.co/allenai/longformer-base-4096/resolve/main/config.json',
    'allenai/longformer-large-4096': 'https://huggingface.co/allenai/longformer-large-4096/resolve/main/config.json',
    'allenai/longformer-large-4096-finetuned-triviaqa': (
        'https://huggingface.co/allenai/longformer-large-4096-finetuned-triviaqa/resolve/main/config.json'
    ),
    'allenai/longformer-base-4096-extra.pos.embd.only': (
        'https://huggingface.co/allenai/longformer-base-4096-extra.pos.embd.only/resolve/main/config.json'
    ),
    'allenai/longformer-large-4096-extra.pos.embd.only': (
        'https://huggingface.co/allenai/longformer-large-4096-extra.pos.embd.only/resolve/main/config.json'
    ),
}
class        snake_case (				UpperCAmelCase_       ):




					"""simple docstring"""

					snake_case__       					=				"longformer"







					def __init__(       self     :			int					,lowerCamelCase__     :			Union[List[int], int] = 512					,lowerCamelCase__     :			int = 2					,lowerCamelCase__     :			int = 1					,lowerCamelCase__     :			int = 0					,lowerCamelCase__     :			int = 2					,lowerCamelCase__     :			int = 30_522					,lowerCamelCase__     :			int = 768					,lowerCamelCase__     :			int = 12					,lowerCamelCase__     :			int = 12					,lowerCamelCase__     :			int = 3_072					,lowerCamelCase__     :			str = "gelu"					,lowerCamelCase__     :			float = 0.1					,lowerCamelCase__     :			float = 0.1					,lowerCamelCase__     :			int = 512					,lowerCamelCase__     :			int = 2					,lowerCamelCase__     :			float = 0.0_2					,lowerCamelCase__     :			float = 1e-12					,lowerCamelCase__     :			bool = False					,**lowerCamelCase__     :			str					,):
									super().__init__(pad_token_id=_snake_case					,**_snake_case    )

									UpperCAmelCase__    =							attention_window
									UpperCAmelCase__    =							sep_token_id
									UpperCAmelCase__    =							bos_token_id
									UpperCAmelCase__    =							eos_token_id
									UpperCAmelCase__    =							vocab_size
									UpperCAmelCase__    =							hidden_size
									UpperCAmelCase__    =							num_hidden_layers
									UpperCAmelCase__    =							num_attention_heads
									UpperCAmelCase__    =							hidden_act
									UpperCAmelCase__    =							intermediate_size
									UpperCAmelCase__    =							hidden_dropout_prob
									UpperCAmelCase__    =							attention_probs_dropout_prob
									UpperCAmelCase__    =							max_position_embeddings
									UpperCAmelCase__    =							type_vocab_size
									UpperCAmelCase__    =							initializer_range
									UpperCAmelCase__    =							layer_norm_eps
									UpperCAmelCase__    =							onnx_export






class        snake_case (				UpperCAmelCase_       ):




					"""simple docstring"""

					def __init__(       self     :			str					,lowerCamelCase__     :			"PretrainedConfig"					,lowerCamelCase__     :			str = "default"					,lowerCamelCase__     :			"List[PatchingSpec]" = None    ):
									super().__init__(_snake_case					,_snake_case					,_snake_case    )
									UpperCAmelCase__    =							True







					@property
					def 	__lowerCAmelCase		(       self     :			str    ):


									if self.task == "multiple-choice":
													UpperCAmelCase__    =							{0: 'batch', 1: 'choice', 2: 'sequence'}
									else:
													UpperCAmelCase__    =							{0: 'batch', 1: 'sequence'}
									return OrderedDict(
									    [
									        ('input_ids', dynamic_axis),
									        ('attention_mask', dynamic_axis),
									        ('global_attention_mask', dynamic_axis),
									    ]    )







					@property
					def 	__lowerCAmelCase		(       self     :			int    ):
									UpperCAmelCase__    =							super().outputs
									if self.task == "default":
													UpperCAmelCase__    =							{0: 'batch'}
									return outputs







					@property
					def 	__lowerCAmelCase		(       self     :			str    ):
									return 1e-4







					@property
					def 	__lowerCAmelCase		(       self     :			str    ):
									return max(super().default_onnx_opset					,14    )







					def 	__lowerCAmelCase		(       self     :			Tuple					,lowerCamelCase__     :			"PreTrainedTokenizerBase"					,lowerCamelCase__     :			int = -1					,lowerCamelCase__     :			int = -1					,lowerCamelCase__     :			bool = False					,lowerCamelCase__     :			Optional[TensorType] = None					,):
									UpperCAmelCase__    =							super().generate_dummy_inputs(
									    preprocessor=_snake_case					,batch_size=_snake_case					,seq_length=_snake_case					,is_pair=_snake_case					,framework=_snake_case    )
									import torch

									# for some reason, replacing this code by inputs["global_attention_mask"] = torch.randint(2, inputs["input_ids"].shape, dtype=torch.int64)
									# makes the export fail randomly
									UpperCAmelCase__    =							torch.zeros_like(inputs['input_ids']    )
									# make every second token global
									UpperCAmelCase__    =							1

									return inputs




"""simple docstring"""






from __future__ import annotations

from math import ceil, floor, sqrt



def 						a_		(      lowerCamelCase = 2_0_0_0_0_0_0 ):
				UpperCAmelCase__    =							[0]
				UpperCAmelCase__    =							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
				UpperCAmelCase__    =							0
				# the area corresponding to the grid that gives the product closest to target
				UpperCAmelCase__    =							0
				# an estimate of b, using the quadratic formula
				UpperCAmelCase__    =							42
				# the largest integer less than b_estimate
				UpperCAmelCase__    =							42
				# the largest integer less than b_estimate
				UpperCAmelCase__    =							42
				# the triangle number corresponding to b_floor
				UpperCAmelCase__    =							42
				# the triangle number corresponding to b_ceil
				UpperCAmelCase__    =							42

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

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

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

				return area


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



