






import mpmath  # for roots of unity
import numpy as np




class 		UpperCAmelCase_						:


						'''simple docstring'''




						def __init__(	self		,				_SCREAMING_SNAKE_CASE=None		,				_SCREAMING_SNAKE_CASE=None				) ->				Union[str, Any]:
								# Input as list
								snake_case_				:							List[str]						 =       list(poly_a or [0]				)[:]
								snake_case_				:							Any						 =       list(poly_b or [0]				)[:]

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

								while self.polyB[-1] == 0:
										self.polyB.pop()
								snake_case_				:							str						 =       len(self.polyB				)

								# Add 0 to make lengths equal a power of 2
								snake_case_				:							Dict						 =       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
								snake_case_				:							Any						 =       complex(mpmath.root(x=1		,				n=self.c_max_length		,				k=1				)				)

								# The product
								snake_case_				:							Union[str, Any]						 =       self.__multiply()






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

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






						def       _lowerCAmelCase       (	self				) ->				Optional[int]:
								snake_case_				:							Tuple						 =       self.__dft("A"				)
								snake_case_				:							Tuple						 =       self.__dft("B"				)
								snake_case_				:							Optional[Any]						 =       [[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
								snake_case_				:							Dict						 =       2
								while next_ncol <= self.c_max_length:
										snake_case_				:							Tuple						 =       [[] for i in range(_SCREAMING_SNAKE_CASE				)]
										snake_case_				:							List[Any]						 =       self.root ** (next_ncol // 2)
										snake_case_				:							Optional[Any]						 =       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
										snake_case_				:							str						 =       new_inverse_c
										next_ncol *= 2
								# Unpack
								snake_case_				:							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				) ->				Tuple:
								snake_case_				:							int						 =       "A = " + " + ".join(
								    f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]				)				)
								snake_case_				:							Optional[int]						 =       "B = " + " + ".join(
								    f'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]				)				)
								snake_case_				:							Tuple						 =       "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 		UpperCAmelCase_						(	SCREAMING_SNAKE_CASE__					):


						'''simple docstring'''




						A     :   Tuple						=					['image_processor', 'tokenizer']
						A     :   List[Any]						=					'ViltImageProcessor'
						A     :   Optional[Any]						=					('BertTokenizer', 'BertTokenizerFast')






						def __init__(	self		,				_SCREAMING_SNAKE_CASE=None		,				_SCREAMING_SNAKE_CASE=None		,				**_SCREAMING_SNAKE_CASE				) ->				int:
								snake_case_				:							str						 =       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		,				)
										snake_case_				:							str						 =       kwargs.pop("feature_extractor"				)

								snake_case_				:							Tuple						 =       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				)
								snake_case_				:							str						 =       self.image_processor






						def __call__(	self		,				_SCREAMING_SNAKE_CASE		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = True		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = 0		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = True		,				_SCREAMING_SNAKE_CASE = None		,				**_SCREAMING_SNAKE_CASE		,				) ->				BatchEncoding:
								snake_case_				:							List[Any]						 =       self.tokenizer(
								    text=_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 + pixel_mask
								snake_case_				:							str						 =       self.image_processor(_SCREAMING_SNAKE_CASE		,				return_tensors=_SCREAMING_SNAKE_CASE				)
								encoding.update(_SCREAMING_SNAKE_CASE				)

								return encoding






						def       _lowerCAmelCase       (	self		,				*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				) ->				List[str]:
								return self.tokenizer.batch_decode(*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				)






						def       _lowerCAmelCase       (	self		,				*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				) ->				Dict:
								return self.tokenizer.decode(*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				)






						@property
						def       _lowerCAmelCase       (	self				) ->				Tuple:
								snake_case_				:							List[Any]						 =       self.tokenizer.model_input_names
								snake_case_				:							Tuple						 =       self.image_processor.model_input_names
								return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names				)				)






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