



'''simple docstring'''




import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType






class 						_UpperCamelCase  (							lowerCamelCase__    ):


			'''simple docstring'''

			_A      :		Optional[Any]			    =		['''image_processor''', '''tokenizer''']
			_A      :		List[str]			    =		'''LayoutLMv2ImageProcessor'''
			_A      :		Optional[Any]			    =		('''LayoutXLMTokenizer''', '''LayoutXLMTokenizerFast''')

			def __init__(							self     : Any							,     lowerCAmelCase__     : List[Any]=None							,     lowerCAmelCase__     : Dict=None							,     **lowerCAmelCase__     : int						):





					"""simple docstring"""






					if "feature_extractor" in kwargs:
							warnings.warn(
							    """The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"""
							    """ instead."""							,     lowerCAmelCase__							,     )
							__SCREAMING_SNAKE_CASE       :		int           =		kwargs.pop("""feature_extractor"""						)

					__SCREAMING_SNAKE_CASE       :		Optional[int]           =		image_processor if image_processor is not None else feature_extractor
					if image_processor is None:
							raise ValueError("""You need to specify an `image_processor`."""						)
					if tokenizer is None:
							raise ValueError("""You need to specify a `tokenizer`."""						)

					super().__init__(lowerCAmelCase__							,     lowerCAmelCase__						)

			def __call__(							self     : Optional[int]							,     lowerCAmelCase__     : int							,     lowerCAmelCase__     : Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None							,     lowerCAmelCase__     : Optional[Union[PreTokenizedInput, List[PreTokenizedInput]]] = None							,     lowerCAmelCase__     : Union[List[List[int]], List[List[List[int]]]] = None							,     lowerCAmelCase__     : Optional[Union[List[int], List[List[int]]]] = None							,     lowerCAmelCase__     : bool = True							,     lowerCAmelCase__     : Union[bool, str, PaddingStrategy] = False							,     lowerCAmelCase__     : Union[bool, str, TruncationStrategy] = None							,     lowerCAmelCase__     : Optional[int] = None							,     lowerCAmelCase__     : int = 0							,     lowerCAmelCase__     : Optional[int] = None							,     lowerCAmelCase__     : Optional[bool] = None							,     lowerCAmelCase__     : Optional[bool] = None							,     lowerCAmelCase__     : bool = False							,     lowerCAmelCase__     : bool = False							,     lowerCAmelCase__     : bool = False							,     lowerCAmelCase__     : bool = False							,     lowerCAmelCase__     : bool = True							,     lowerCAmelCase__     : Optional[Union[str, TensorType]] = None							,     **lowerCAmelCase__     : int							,     ):





					"""simple docstring"""






					if self.image_processor.apply_ocr and (boxes is not None):
							raise ValueError(
							    """You cannot provide bounding boxes """
							    """if you initialized the image processor with apply_ocr set to True."""						)

					if self.image_processor.apply_ocr and (word_labels is not None):
							raise ValueError(
							    """You cannot provide word labels if you initialized the image processor with apply_ocr set to True."""						)

					if return_overflowing_tokens is True and return_offsets_mapping is False:
							raise ValueError("""You cannot return overflowing tokens without returning the offsets mapping."""						)

					# first, apply the image processor
					__SCREAMING_SNAKE_CASE       :		Tuple           =		self.image_processor(images=lowerCAmelCase__							,     return_tensors=lowerCAmelCase__						)

					# second, apply the tokenizer
					if text is not None and self.image_processor.apply_ocr and text_pair is None:
							if isinstance(lowerCAmelCase__							,     lowerCAmelCase__						):
									__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		[text]  # add batch dimension (as the image processor always adds a batch dimension)
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		features["""words"""]

					__SCREAMING_SNAKE_CASE       :		Tuple           =		self.tokenizer(
					    text=text if text is not None else features["""words"""]							,     text_pair=text_pair if text_pair is not None else None							,     boxes=boxes if boxes is not None else features["""boxes"""]							,     word_labels=lowerCAmelCase__							,     add_special_tokens=lowerCAmelCase__							,     padding=lowerCAmelCase__							,     truncation=lowerCAmelCase__							,     max_length=lowerCAmelCase__							,     stride=lowerCAmelCase__							,     pad_to_multiple_of=lowerCAmelCase__							,     return_token_type_ids=lowerCAmelCase__							,     return_attention_mask=lowerCAmelCase__							,     return_overflowing_tokens=lowerCAmelCase__							,     return_special_tokens_mask=lowerCAmelCase__							,     return_offsets_mapping=lowerCAmelCase__							,     return_length=lowerCAmelCase__							,     verbose=lowerCAmelCase__							,     return_tensors=lowerCAmelCase__							,     **lowerCAmelCase__							,     )

					# add pixel values
					__SCREAMING_SNAKE_CASE       :		Dict           =		features.pop("""pixel_values"""						)
					if return_overflowing_tokens is True:
							__SCREAMING_SNAKE_CASE       :		Dict           =		self.get_overflowing_images(lowerCAmelCase__							,     encoded_inputs["""overflow_to_sample_mapping"""]						)
					__SCREAMING_SNAKE_CASE       :		Dict           =		images

					return encoded_inputs

			def UpperCamelCase__					(							self     : str							,     lowerCAmelCase__     : str							,     lowerCAmelCase__     : Union[str, Any]						):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		[]
					for sample_idx in overflow_to_sample_mapping:
							images_with_overflow.append(images[sample_idx]						)

					if len(lowerCAmelCase__						) != len(lowerCAmelCase__						):
							raise ValueError(
							    """Expected length of images to be the same as the length of `overflow_to_sample_mapping`, but got"""
							    F" {len(lowerCAmelCase__						)} and {len(lowerCAmelCase__						)}"						)

					return images_with_overflow

			def UpperCamelCase__					(							self     : Union[str, Any]							,     *lowerCAmelCase__     : Optional[Any]							,     **lowerCAmelCase__     : Union[str, Any]						):





					"""simple docstring"""






					return self.tokenizer.batch_decode(*lowerCAmelCase__							,     **lowerCAmelCase__						)

			def UpperCamelCase__					(							self     : Tuple							,     *lowerCAmelCase__     : Optional[Any]							,     **lowerCAmelCase__     : Optional[Any]						):





					"""simple docstring"""






					return self.tokenizer.decode(*lowerCAmelCase__							,     **lowerCAmelCase__						)

			@property
			def UpperCamelCase__					(							self     : int						):





					"""simple docstring"""






					return ["input_ids", "bbox", "attention_mask", "image"]

			@property
			def UpperCamelCase__					(							self     : Any						):





					"""simple docstring"""






					warnings.warn(
					    """`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."""							,     lowerCAmelCase__							,     )
					return self.image_processor_class



			@property
			def UpperCamelCase__					(							self     : Union[str, Any]						):





					"""simple docstring"""






					warnings.warn(
					    """`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."""							,     lowerCAmelCase__							,     )
					return self.image_processor




'''simple docstring'''




from math import ceil, sqrt


def 				lowerCAmelCase_   (	_lowerCamelCase:   int = 1_00_00_00					):
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0

		for outer_width in range(3       ,      (limit // 4) + 2					):
				if outer_width**2 > limit:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		max(ceil(sqrt(outer_width**2 - limit					)					)       ,      1					)
				else:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		1
				if (outer_width - hole_width_lower_bound) % 2:
						hole_width_lower_bound += 1

				answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

		return answer


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