






from __future__ import annotations

from collections.abc import Callable

_UpperCamelCase			:	Tuple								=list[list[float | int]]



def  a__ (__lowercase							:Matrix					,  __lowercase							:Matrix   )		-> Matrix:
				_A	:				int   =      len(__lowercase   )
				_A	:				Matrix   =      [[0 for _ in range(size + 1   )] for _ in range(__lowercase   )]
				_A	:				int
				_A	:				int
				_A	:				int
				_A	:				int
				_A	:				int
				_A	:				float

				for row in range(__lowercase   ):
								for col in range(__lowercase   ):
												_A	:				List[Any]   =      matrix[row][col]

								_A	:				List[str]   =      vector[row][0]

				_A	:				Optional[int]   =      0
				_A	:				List[str]   =      0
				while row < size and col < size:
								# pivoting
								_A	:				str   =      max((abs(augmented[rowa][col]   ), rowa) for rowa in range(__lowercase					,  __lowercase   )   )[
								    1
								]
								if augmented[pivot_row][col] == 0:
												col += 1
												continue
								else:
												_A  ,				_A	:				str   =      augmented[pivot_row], augmented[row]

								for rowa in range(row + 1					,  __lowercase   ):
												_A	:				str   =      augmented[rowa][col] / augmented[row][col]
												_A	:				Tuple   =      0
												for cola in range(col + 1					,  size + 1   ):
																augmented[rowa][cola] -= augmented[row][cola] * ratio

								row += 1
								col += 1

				# back substitution
				for col in range(1					,  __lowercase   ):
								for row in range(__lowercase   ):
												_A	:				Dict   =      augmented[row][col] / augmented[col][col]
												for cola in range(__lowercase					,  size + 1   ):
																augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
				return [
				    [round(augmented[row][size] / augmented[row][row]					,  10   )] for row in range(__lowercase   )
				]



def  a__ (__lowercase							:list[int]   )		-> Callable[[int], int]:
				_A	:				int   =      len(__lowercase   )
				_A	:				Matrix   =      [[0 for _ in range(__lowercase   )] for _ in range(__lowercase   )]
				_A	:				Matrix   =      [[0] for _ in range(__lowercase   )]
				_A	:				Matrix
				_A	:				int
				_A	:				int
				_A	:				int

				for x_val, y_val in enumerate(__lowercase   ):
								for col in range(__lowercase   ):
												_A	:				int   =      (x_val + 1) ** (size - col - 1)
								_A	:				Tuple   =      y_val

				_A	:				Tuple   =      solve(__lowercase					,  __lowercase   )

				def interpolated_func(__lowercase							:int   ) -> int:
								return sum(
								    round(coeffs[x_val][0]   ) * (var ** (size - x_val - 1))
								    for x_val in range(__lowercase   )   )

				return interpolated_func



def  a__ (__lowercase							:int   )		-> int:
				return (
				    1
				    - variable
				    + variable**2
				    - variable**3
				    + variable**4
				    - variable**5
				    + variable**6
				    - variable**7
				    + variable**8
				    - variable**9
				    + variable**10
				)



def  a__ (__lowercase							:Callable[[int], int] = question_function					,  __lowercase							:int = 10   )		-> int:
				_A	:				list[int]   =      [func(__lowercase   ) for x_val in range(1					,  order + 1   )]

				_A	:				list[Callable[[int], int]]   =      [
				    interpolate(data_points[:max_coeff]   ) for max_coeff in range(1					,  order + 1   )
				]

				_A	:				int   =      0
				_A	:				Callable[[int], int]
				_A	:				int

				for poly in polynomials:
								_A	:				int   =      1
								while func(__lowercase   ) == poly(__lowercase   ):
												x_val += 1

								ret += poly(__lowercase   )

				return ret


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











from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    convert_to_rgb,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    OPENAI_CLIP_MEAN,
    OPENAI_CLIP_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


_UpperCamelCase			:	Any								=logging.get_logger(__name__)


if is_vision_available():
	import PIL






class 						UpperCAmelCase__ (							__snake_case							):
		__snake_case      :       Union[str, Any]     =   ["pixel_values"]







		def __init__(					self       ,A__ = True       ,A__ = None       ,A__ = PILImageResampling.BICUBIC       ,A__ = True       ,A__ = None       ,A__ = True       ,A__ = 1 / 255       ,A__ = True       ,A__ = None       ,A__ = None       ,A__ = True       ,**A__       ,):
						super().__init__(**A__		)
						_A	:				List[str]   =      size if size is not None else {'''shortest_edge''': 224}
						_A	:				int   =      get_size_dict(A__       ,default_to_square=A__		)
						_A	:				Optional[int]   =      crop_size if crop_size is not None else {'''height''': 224, '''width''': 224}
						_A	:				Dict   =      get_size_dict(A__       ,default_to_square=A__       ,param_name='''crop_size'''		)

						_A	:				List[str]   =      do_resize
						_A	:				List[str]   =      size
						_A	:				Tuple   =      resample
						_A	:				List[Any]   =      do_center_crop
						_A	:				Dict   =      crop_size
						_A	:				Any   =      do_rescale
						_A	:				Optional[Any]   =      rescale_factor
						_A	:				Dict   =      do_normalize
						_A	:				Optional[int]   =      image_mean if image_mean is not None else OPENAI_CLIP_MEAN
						_A	:				Optional[int]   =      image_std if image_std is not None else OPENAI_CLIP_STD
						_A	:				Any   =      do_convert_rgb







		def  A__      (					self       ,A__       ,A__       ,A__ = PILImageResampling.BICUBIC       ,A__ = None       ,**A__       ,):
						_A	:				List[Any]   =      get_size_dict(A__       ,default_to_square=A__		)
						if "shortest_edge" not in size:
										raise ValueError(f"""The `size` parameter must contain the key `shortest_edge`. Got {size.keys()}"""		)
						_A	:				Any   =      get_resize_output_image_size(A__       ,size=size['''shortest_edge''']       ,default_to_square=A__		)
						return resize(A__       ,size=A__       ,resample=A__       ,data_format=A__       ,**A__		)







		def  A__      (					self       ,A__       ,A__       ,A__ = None       ,**A__       ,):
						_A	:				Union[str, Any]   =      get_size_dict(A__		)
						if "height" not in size or "width" not in size:
										raise ValueError(f"""The `size` parameter must contain the keys (height, width). Got {size.keys()}"""		)
						return center_crop(A__       ,size=(size['''height'''], size['''width'''])       ,data_format=A__       ,**A__		)







		def  A__      (					self       ,A__       ,A__       ,A__ = None       ,**A__       ,):
						return rescale(A__       ,scale=A__       ,data_format=A__       ,**A__		)







		def  A__      (					self       ,A__       ,A__       ,A__       ,A__ = None       ,**A__       ,):
						return normalize(A__       ,mean=A__       ,std=A__       ,data_format=A__       ,**A__		)







		def  A__      (					self       ,A__       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = None       ,A__ = ChannelDimension.FIRST       ,**A__       ,):
						_A	:				str   =      do_resize if do_resize is not None else self.do_resize
						_A	:				List[str]   =      size if size is not None else self.size
						_A	:				List[str]   =      get_size_dict(A__       ,param_name='''size'''       ,default_to_square=A__		)
						_A	:				Optional[Any]   =      resample if resample is not None else self.resample
						_A	:				int   =      do_center_crop if do_center_crop is not None else self.do_center_crop
						_A	:				Any   =      crop_size if crop_size is not None else self.crop_size
						_A	:				int   =      get_size_dict(A__       ,param_name='''crop_size'''       ,default_to_square=A__		)
						_A	:				int   =      do_rescale if do_rescale is not None else self.do_rescale
						_A	:				List[str]   =      rescale_factor if rescale_factor is not None else self.rescale_factor
						_A	:				Tuple   =      do_normalize if do_normalize is not None else self.do_normalize
						_A	:				Union[str, Any]   =      image_mean if image_mean is not None else self.image_mean
						_A	:				int   =      image_std if image_std is not None else self.image_std
						_A	:				Optional[Any]   =      do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb

						_A	:				Optional[Any]   =      make_list_of_images(A__		)

						if not valid_images(A__		):
										raise ValueError(
										    '''Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '''
										    '''torch.Tensor, tf.Tensor or jax.ndarray.'''		)

						if do_resize and size is None:
										raise ValueError('''Size must be specified if do_resize is True.'''		)

						if do_center_crop and crop_size is None:
										raise ValueError('''Crop size must be specified if do_center_crop is True.'''		)

						if do_rescale and rescale_factor is None:
										raise ValueError('''Rescale factor must be specified if do_rescale is True.'''		)

						if do_normalize and (image_mean is None or image_std is None):
										raise ValueError('''Image mean and std must be specified if do_normalize is True.'''		)

						# PIL RGBA images are converted to RGB
						if do_convert_rgb:
										_A	:				int   =      [convert_to_rgb(A__		) for image in images]

						# All transformations expect numpy arrays.
						_A	:				int   =      [to_numpy_array(A__		) for image in images]

						if do_resize:
										_A	:				List[str]   =      [self.resize(image=A__       ,size=A__       ,resample=A__		) for image in images]

						if do_center_crop:
										_A	:				Union[str, Any]   =      [self.center_crop(image=A__       ,size=A__		) for image in images]

						if do_rescale:
										_A	:				Tuple   =      [self.rescale(image=A__       ,scale=A__		) for image in images]

						if do_normalize:
										_A	:				Dict   =      [self.normalize(image=A__       ,mean=A__       ,std=A__		) for image in images]

						_A	:				Dict   =      [to_channel_dimension_format(A__       ,A__		) for image in images]

						_A	:				Dict   =      {'''pixel_values''': images}
						return BatchFeature(data=A__       ,tensor_type=A__		)



