


from __future__ import annotations

from collections.abc import Callable

SCREAMING_SNAKE_CASE :   int							      =				list[list[float | int]]



def        UpperCamelCase_(   lowerCamelCase_							,				lowerCamelCase_				)					->		Matrix:
    _lowercase :							int   	=	len(lowerCamelCase_				)
    _lowercase :							Matrix   	=	[[0 for _ in range(size + 1				)] for _ in range(lowerCamelCase_				)]
    _lowercase :							int
    _lowercase :							int
    _lowercase :							int
    _lowercase :							int
    _lowercase :							int
    _lowercase :							float

    for row in range(lowerCamelCase_				):
        for col in range(lowerCamelCase_				):
            _lowercase :							Optional[Any]   	=	matrix[row][col]

        _lowercase :							Union[str, Any]   	=	vector[row][0]

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

        for rowa in range(row + 1							,				lowerCamelCase_				):
            _lowercase :							Optional[Any]   	=	augmented[rowa][col] / augmented[row][col]
            _lowercase :							Optional[int]   	=	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							,				lowerCamelCase_				):
        for row in range(lowerCamelCase_				):
            _lowercase :							Union[str, Any]   	=	augmented[row][col] / augmented[col][col]
            for cola in range(lowerCamelCase_							,				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(lowerCamelCase_				)
    ]



def        UpperCamelCase_(   lowerCamelCase_				)					->		Callable[[int], int]:
    _lowercase :							int   	=	len(lowerCamelCase_				)
    _lowercase :							Matrix   	=	[[0 for _ in range(lowerCamelCase_				)] for _ in range(lowerCamelCase_				)]
    _lowercase :							Matrix   	=	[[0] for _ in range(lowerCamelCase_				)]
    _lowercase :							Matrix
    _lowercase :							int
    _lowercase :							int
    _lowercase :							int

    for x_val, y_val in enumerate(lowerCamelCase_				):
        for col in range(lowerCamelCase_				):
            _lowercase :							Optional[int]   	=	(x_val + 1) ** (size - col - 1)
        _lowercase :							Dict   	=	y_val

    _lowercase :							Optional[Any]   	=	solve(lowerCamelCase_							,				lowerCamelCase_				)

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

    return interpolated_func



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



def        UpperCamelCase_(   lowerCamelCase_ = question_function							,				lowerCamelCase_ = 10				)					->		int:
    _lowercase :							list[int]   	=	[func(lowerCamelCase_				) for x_val in range(1							,				order + 1				)]

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

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

    for poly in polynomials:
        _lowercase :							str   	=	1
        while func(lowerCamelCase_				) == poly(lowerCamelCase_				):
            x_val += 1

        ret += poly(lowerCamelCase_				)

    return ret


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






import warnings

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding






class _lowerCamelCase(		_a     ):
       lowercase_				:			int									=    ["""image_processor""", """tokenizer"""]
       lowercase_				:			List[str]									=    """CLIPImageProcessor"""
       lowercase_				:			Union[str, Any]									=    ("""CLIPTokenizer""", """CLIPTokenizerFast""")
       def __init__(      self,   lowerCamelCase=None,   lowerCamelCase=None,   **lowerCamelCase) ->     Dict:




           """simple docstring"""

           _lowercase :							List[Any]   	=	None
           if "feature_extractor" in kwargs:
               warnings.warn(
                   'The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`'
                   ' instead.',   lowerCamelCase,   )
               _lowercase :							Dict   	=	kwargs.pop('feature_extractor')

           _lowercase :							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,   lowerCamelCase=None,   lowerCamelCase=None,   lowerCamelCase=None,   **lowerCamelCase) ->     Tuple:




           """simple docstring"""

           if text is None and images is None:
               raise ValueError('You have to specify either text or images. Both cannot be none.')

           if text is not None:
               _lowercase :							Optional[Any]   	=	self.tokenizer(lowerCamelCase,   return_tensors=lowerCamelCase,   **lowerCamelCase)

           if images is not None:
               _lowercase :							List[Any]   	=	self.image_processor(lowerCamelCase,   return_tensors=lowerCamelCase,   **lowerCamelCase)

           if text is not None and images is not None:
               _lowercase :							int   	=	image_features.pixel_values
               return encoding
           elif text is not None:
               return encoding
           else:
               return BatchEncoding(data=dict(**lowerCamelCase),   tensor_type=lowerCamelCase)
       def     UpperCamelCase  (      self,   *lowerCamelCase,   **lowerCamelCase) ->     Union[str, Any]:




           """simple docstring"""

           return self.tokenizer.batch_decode(*lowerCamelCase,   **lowerCamelCase)
       def     UpperCamelCase  (      self,   *lowerCamelCase,   **lowerCamelCase) ->     int:




           """simple docstring"""

           return self.tokenizer.decode(*lowerCamelCase,   **lowerCamelCase)
       @property
       def     UpperCamelCase  (      self) ->     int:




           """simple docstring"""

           _lowercase :							int   	=	self.tokenizer.model_input_names
           _lowercase :							Dict   	=	self.image_processor.model_input_names
           return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names))
       @property
       def     UpperCamelCase  (      self) ->     List[str]:




           """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) ->     Optional[Any]:




           """simple docstring"""

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


