code: 
  
  
  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 		_SCREAMING_SNAKE_CASE    (	lowerCamelCase__    ):
  					__SCREAMING_SNAKE_CASE    				=						['''image_processor''', '''tokenizer''']
  					__SCREAMING_SNAKE_CASE    				=						'''LayoutLMv2ImageProcessor'''
  					__SCREAMING_SNAKE_CASE    				=						('''LayoutLMv2Tokenizer''', '''LayoutLMv2TokenizerFast''')
  
  
  					def __init__(     self       ,				A_=None       ,				A_=None       ,				**A_						):
  							_UpperCAmelCase		:       Dict       =    None
  							if "feature_extractor" in kwargs:
  									warnings.warn(
  									    """The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"""
  									    """ instead."""       ,				SCREAMING_SNAKE_CASE_       ,				)
  									_UpperCAmelCase		:       int       =    kwargs.pop("""feature_extractor"""						)
  
  							_UpperCAmelCase		:       Dict       =    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__(SCREAMING_SNAKE_CASE_       ,				SCREAMING_SNAKE_CASE_						)
  
  
  					def __call__(     self       ,				A_       ,				A_ = None       ,				A_ = None       ,				A_ = None       ,				A_ = None       ,				A_ = True       ,				A_ = False       ,				A_ = False       ,				A_ = None       ,				A_ = 0       ,				A_ = None       ,				A_ = None       ,				A_ = None       ,				A_ = False       ,				A_ = False       ,				A_ = False       ,				A_ = False       ,				A_ = True       ,				A_ = None       ,				**A_       ,				):
  							# verify input
  							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
  							_UpperCAmelCase		:       str       =    self.image_processor(images=SCREAMING_SNAKE_CASE_       ,				return_tensors=SCREAMING_SNAKE_CASE_						)
  
  							# second, apply the tokenizer
  							if text is not None and self.image_processor.apply_ocr and text_pair is None:
  									if isinstance(SCREAMING_SNAKE_CASE_       ,				SCREAMING_SNAKE_CASE_						):
  											_UpperCAmelCase		:       Optional[Any]       =    [text]  # add batch dimension (as the image processor always adds a batch dimension)
  									_UpperCAmelCase		:       int       =    features["""words"""]
  
  							_UpperCAmelCase		:       Optional[int]       =    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=SCREAMING_SNAKE_CASE_       ,				add_special_tokens=SCREAMING_SNAKE_CASE_       ,				padding=SCREAMING_SNAKE_CASE_       ,				truncation=SCREAMING_SNAKE_CASE_       ,				max_length=SCREAMING_SNAKE_CASE_       ,				stride=SCREAMING_SNAKE_CASE_       ,				pad_to_multiple_of=SCREAMING_SNAKE_CASE_       ,				return_token_type_ids=SCREAMING_SNAKE_CASE_       ,				return_attention_mask=SCREAMING_SNAKE_CASE_       ,				return_overflowing_tokens=SCREAMING_SNAKE_CASE_       ,				return_special_tokens_mask=SCREAMING_SNAKE_CASE_       ,				return_offsets_mapping=SCREAMING_SNAKE_CASE_       ,				return_length=SCREAMING_SNAKE_CASE_       ,				verbose=SCREAMING_SNAKE_CASE_       ,				return_tensors=SCREAMING_SNAKE_CASE_       ,				**SCREAMING_SNAKE_CASE_       ,				)
  
  							# add pixel values
  							_UpperCAmelCase		:       Union[str, Any]       =    features.pop("""pixel_values"""						)
  							if return_overflowing_tokens is True:
  									_UpperCAmelCase		:       Dict       =    self.get_overflowing_images(SCREAMING_SNAKE_CASE_       ,				encoded_inputs["""overflow_to_sample_mapping"""]						)
  							_UpperCAmelCase		:       Dict       =    images
  
  							return encoded_inputs
  
  
  					def 					__snake_case(     self       ,				A_       ,				A_						):
  							# in case there's an overflow, ensure each `input_ids` sample is mapped to its corresponding image
  							_UpperCAmelCase		:       Optional[int]       =    []
  							for sample_idx in overflow_to_sample_mapping:
  									images_with_overflow.append(images[sample_idx]						)
  
  							if len(SCREAMING_SNAKE_CASE_						) != len(SCREAMING_SNAKE_CASE_						):
  									raise ValueError(
  									    """Expected length of images to be the same as the length of `overflow_to_sample_mapping`, but got"""
  									    F''' {len(SCREAMING_SNAKE_CASE_						)} and {len(SCREAMING_SNAKE_CASE_						)}'''						)
  
  							return images_with_overflow
  
  
  					def 					__snake_case(     self       ,				*A_       ,				**A_						):
  							return self.tokenizer.batch_decode(*SCREAMING_SNAKE_CASE_       ,				**SCREAMING_SNAKE_CASE_						)
  
  
  					def 					__snake_case(     self       ,				*A_       ,				**A_						):
  							return self.tokenizer.decode(*SCREAMING_SNAKE_CASE_       ,				**SCREAMING_SNAKE_CASE_						)
  
  
  					@property
  					def 					__snake_case(     self						):
  							return ["input_ids", "bbox", "token_type_ids", "attention_mask", "image"]
  
  
  					@property
  					def 					__snake_case(     self						):
  							warnings.warn(
  							    """`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."""       ,				SCREAMING_SNAKE_CASE_       ,				)
  							return self.image_processor_class
  
  
  
  
  					@property
  					def 					__snake_case(     self						):
  							warnings.warn(
  							    """`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."""       ,				SCREAMING_SNAKE_CASE_       ,				)
  							return self.image_processor
  
  
  
  
  
  
style_context: 
  
  
  from itertools import count
  from math import asin, pi, sqrt
  
  
  
  
  def       a__						(		snake_case__				:       float    ):
    return (
        (1 - 2 * point) * sqrt(point - point**2    ) + 2 * point + asin(sqrt(1 - point    )    )
    ) / 4
  
  
  
  
  def       a__						(		snake_case__				:       int    ):
    _UpperCAmelCase		:       int       =    (circles_number + 1 - sqrt(2 * circles_number    )) / (
        2 * (circles_number**2 + 1)
    )
    _UpperCAmelCase		:       Union[str, Any]       =    circles_number * intersection_y
  
    _UpperCAmelCase		:       Tuple       =    intersection_x * intersection_y / 2
    _UpperCAmelCase		:       str       =    circle_bottom_arc_integral(
        1 / 2    ) - circle_bottom_arc_integral(snake_case__    )
  
    return triangle_area + concave_region_area
  
  
  
  
  def       a__						(		snake_case__				:       float = 1 / 1000    ):
    _UpperCAmelCase		:       Dict       =    (1 - pi / 4) / 4
  
    for n in count(1    ):
      if concave_triangle_area(snake_case__    ) / l_section_area < fraction:
        return n
  
    return -1
  
  
  if __name__ == "__main__":
   print(F'{solution() = }')
  
  
  
  
  
  