


import mpmath  # for roots of unity
import numpy as np





class   SCREAMING_SNAKE_CASE_			:




       '''simple docstring'''



       def __init__(						self				:				Dict		,				__a				:				int=None		,				__a				:				Dict=None							)					->Optional[int]:
          # Input as list
          lowerCamelCase_						:   List[str]		= list(poly_a or [0]							)[:]
          lowerCamelCase_						:   Tuple		= list(poly_b or [0]							)[:]

          # Remove leading zero coefficients
          while self.polyA[-1] == 0:
             self.polyA.pop()
          lowerCamelCase_						:   int		= len(self.polyA							)

          while self.polyB[-1] == 0:
             self.polyB.pop()
          lowerCamelCase_						:   Optional[int]		= len(self.polyB							)

          # Add 0 to make lengths equal a power of 2
          lowerCamelCase_						:   str		= int(
              2 ** np.ceil(np.loga(len(self.polyA							) + len(self.polyB							) - 1							)							)							)

          while len(self.polyA							) < self.c_max_length:
             self.polyA.append(0							)
          while len(self.polyB							) < self.c_max_length:
             self.polyB.append(0							)
          # A complex root used for the fourier transform
          lowerCamelCase_						:   List[Any]		= complex(mpmath.root(x=1		,				n=self.c_max_length		,				k=1							)							)

          # The product
          lowerCamelCase_						:   Optional[int]		= self.__multiply()



       def 				_lowerCAmelCase							(						self				:				Tuple		,				__a				:				Any							)					->List[Any]:
          lowerCamelCase_						:   Any		= [[x] for x in self.polyA] if which == """A""" else [[x] for x in self.polyB]
          # Corner case
          if len(__a							) <= 1:
             return dft[0]
          #
          lowerCamelCase_						:   Union[str, Any]		= self.c_max_length // 2
          while next_ncol > 0:
             lowerCamelCase_						:   Tuple		= [[] for i in range(__a							)]
             lowerCamelCase_						:   Optional[int]		= self.root**next_ncol

             # First half of next step
             lowerCamelCase_						:   Union[str, Any]		= 1
             for j in range(self.c_max_length // (next_ncol * 2)							):
                for i in range(__a							):
                   new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]							)
                current_root *= root
             # Second half of next step
             lowerCamelCase_						:   str		= 1
             for j in range(self.c_max_length // (next_ncol * 2)							):
                for i in range(__a							):
                   new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]							)
                current_root *= root
             # Update
             lowerCamelCase_						:   Optional[Any]		= new_dft
             lowerCamelCase_						:   Any		= next_ncol // 2
          return dft[0]



       def 				_lowerCAmelCase							(						self				:				Any							)					->str:
          lowerCamelCase_						:   int		= self.__dft("""A"""							)
          lowerCamelCase_						:   str		= self.__dft("""B"""							)
          lowerCamelCase_						:   int		= [[dft_a[i] * dft_b[i] for i in range(self.c_max_length							)]]
          del dft_a
          del dft_b

          # Corner Case
          if len(inverce_c[0]							) <= 1:
             return inverce_c[0]
          # Inverse DFT
          lowerCamelCase_						:   Union[str, Any]		= 2
          while next_ncol <= self.c_max_length:
             lowerCamelCase_						:   Union[str, Any]		= [[] for i in range(__a							)]
             lowerCamelCase_						:   Optional[int]		= self.root ** (next_ncol // 2)
             lowerCamelCase_						:   List[str]		= 1
             # First half of next step
             for j in range(self.c_max_length // next_ncol							):
                for i in range(next_ncol // 2							):
                   # Even positions
                   new_inverse_c[i].append(
                       (
                           inverce_c[i][j]
                           + inverce_c[i][j + self.c_max_length // next_ncol]
                       )
                       / 2							)
                   # Odd positions
                   new_inverse_c[i + next_ncol // 2].append(
                       (
                           inverce_c[i][j]
                           - inverce_c[i][j + self.c_max_length // next_ncol]
                       )
                       / (2 * current_root)							)
                current_root *= root
             # Update
             lowerCamelCase_						:   Any		= new_inverse_c
             next_ncol *= 2
          # Unpack
          lowerCamelCase_						:   Dict		= [round(x[0].real		,				8							) + round(x[0].imag		,				8							) * 1j for x in inverce_c]

          # Remove leading 0's
          while inverce_c[-1] == 0:
             inverce_c.pop()
          return inverce_c




       def __str__(						self				:				List[str]							)					->Any:
          lowerCamelCase_						:   Optional[Any]		= """A = """ + """ + """.join(
              F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]							)							)
          lowerCamelCase_						:   int		= """B = """ + """ + """.join(
              F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]							)							)
          lowerCamelCase_						:   List[str]		= """A*B = """ + """ + """.join(
              F'''{coef}*x^{i}''' for coef, i in enumerate(self.product							)							)

          return F'''{a}\n{b}\n{c}'''


# Unit tests
if __name__ == "__main__":
      import doctest

      doctest.testmod()









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_			(a__						):




       '''simple docstring'''



       _a   							=							["image_processor", "tokenizer"]
       _a   							=							"LayoutLMv2ImageProcessor"
       _a   							=							("LayoutXLMTokenizer", "LayoutXLMTokenizerFast")



       def __init__(						self				:				Any		,				__a				:				str=None		,				__a				:				List[Any]=None		,				**__a				:				Optional[int]							)					->int:
          if "feature_extractor" in kwargs:
             warnings.warn(
                 """The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"""
                 """ instead."""		,				__a		,				)
             lowerCamelCase_						:   str		= kwargs.pop("""feature_extractor"""							)

          lowerCamelCase_						:   List[Any]		= 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__(__a		,				__a							)



       def __call__(						self				:				List[str]		,				__a				:				List[Any]		,				__a				:				Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None		,				__a				:				Optional[Union[PreTokenizedInput, List[PreTokenizedInput]]] = None		,				__a				:				Union[List[List[int]], List[List[List[int]]]] = None		,				__a				:				Optional[Union[List[int], List[List[int]]]] = None		,				__a				:				bool = True		,				__a				:				Union[bool, str, PaddingStrategy] = False		,				__a				:				Union[bool, str, TruncationStrategy] = None		,				__a				:				Optional[int] = None		,				__a				:				int = 0		,				__a				:				Optional[int] = None		,				__a				:				Optional[bool] = None		,				__a				:				Optional[bool] = None		,				__a				:				bool = False		,				__a				:				bool = False		,				__a				:				bool = False		,				__a				:				bool = False		,				__a				:				bool = True		,				__a				:				Optional[Union[str, TensorType]] = None		,				**__a				:				Any		,				)					->BatchEncoding:
          # 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
          lowerCamelCase_						:   Tuple		= self.image_processor(images=__a		,				return_tensors=__a							)

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

          lowerCamelCase_						:   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=__a		,				add_special_tokens=__a		,				padding=__a		,				truncation=__a		,				max_length=__a		,				stride=__a		,				pad_to_multiple_of=__a		,				return_token_type_ids=__a		,				return_attention_mask=__a		,				return_overflowing_tokens=__a		,				return_special_tokens_mask=__a		,				return_offsets_mapping=__a		,				return_length=__a		,				verbose=__a		,				return_tensors=__a		,				**__a		,				)

          # add pixel values
          lowerCamelCase_						:   Any		= features.pop("""pixel_values"""							)
          if return_overflowing_tokens is True:
             lowerCamelCase_						:   Dict		= self.get_overflowing_images(__a		,				encoded_inputs["""overflow_to_sample_mapping"""]							)
          lowerCamelCase_						:   Optional[int]		= images

          return encoded_inputs



       def 				_lowerCAmelCase							(						self				:				Optional[Any]		,				__a				:				str		,				__a				:				Union[str, Any]							)					->List[str]:
          # in case there's an overflow, ensure each `input_ids` sample is mapped to its corresponding image
          lowerCamelCase_						:   Dict		= []
          for sample_idx in overflow_to_sample_mapping:
             images_with_overflow.append(images[sample_idx]							)

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

          return images_with_overflow



       def 				_lowerCAmelCase							(						self				:				Dict		,				*__a				:				Dict		,				**__a				:				int							)					->int:
          return self.tokenizer.batch_decode(*__a		,				**__a							)



       def 				_lowerCAmelCase							(						self				:				List[Any]		,				*__a				:				List[str]		,				**__a				:				int							)					->List[Any]:
          return self.tokenizer.decode(*__a		,				**__a							)



       @property
       def 				_lowerCAmelCase							(						self				:				int							)					->List[str]:
          return ["input_ids", "bbox", "attention_mask", "image"]



       @property
       def 				_lowerCAmelCase							(						self				:				int							)					->str:
          warnings.warn(
              """`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."""		,				__a		,				)
          return self.image_processor_class




       @property
       def 				_lowerCAmelCase							(						self				:				int							)					->List[Any]:
          warnings.warn(
              """`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."""		,				__a		,				)
          return self.image_processor





