"""simple docstring"""






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tokenizers_available,
    is_torch_available,
    is_vision_available,
)


lowerCAmelCase__						:						int		  =			{
    'configuration_layoutlmv2': ['LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP', 'LayoutLMv2Config'],
    'processing_layoutlmv2': ['LayoutLMv2Processor'],
    'tokenization_layoutlmv2': ['LayoutLMv2Tokenizer'],
}

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__						:						int		  =			['LayoutLMv2TokenizerFast']

try:
						if not is_vision_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__						:						Optional[Any]		  =			['LayoutLMv2FeatureExtractor']
						lowerCAmelCase__						:						Union[str, Any]		  =			['LayoutLMv2ImageProcessor']

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__						:						Optional[Any]		  =			[
						    'LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'LayoutLMv2ForQuestionAnswering',
						    'LayoutLMv2ForSequenceClassification',
						    'LayoutLMv2ForTokenClassification',
						    'LayoutLMv2Layer',
						    'LayoutLMv2Model',
						    'LayoutLMv2PreTrainedModel',
						]

if TYPE_CHECKING:
						from .configuration_layoutlmva import LAYOUTLMV2_PRETRAINED_CONFIG_ARCHIVE_MAP, LayoutLMvaConfig
						from .processing_layoutlmva import LayoutLMvaProcessor
						from .tokenization_layoutlmva import LayoutLMvaTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_layoutlmva_fast import LayoutLMvaTokenizerFast

						try:
												if not is_vision_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .feature_extraction_layoutlmva import LayoutLMvaFeatureExtractor, LayoutLMvaImageProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_layoutlmva import (
												    LAYOUTLMV2_PRETRAINED_MODEL_ARCHIVE_LIST,
												    LayoutLMvaForQuestionAnswering,
												    LayoutLMvaForSequenceClassification,
												    LayoutLMvaForTokenClassification,
												    LayoutLMvaLayer,
												    LayoutLMvaModel,
												    LayoutLMvaPreTrainedModel,
												)
else:
						import sys

						lowerCAmelCase__						:						Tuple		  =			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




"""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() = }""")



