



UpperCamelCase__    =						"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"






def  UpperCAmelCase__    (    lowercase__   ) ->      bytes:
						# Make sure the supplied data is a bytes-like object
						if not isinstance(lowercase__						,       lowercase__   ):
												__lowercase					=				F"a bytes-like object is required, not '{data.__class__.__name__}'"
												raise TypeError(lowercase__   )

						__lowercase					=				"""""".join(bin(lowercase__   )[2:].zfill(8   ) for byte in data   )

						__lowercase					=				len(lowercase__   ) % 6 != 0

						if padding_needed:
												# The padding that will be added later
												__lowercase					=				B"""=""" * ((6 - len(lowercase__   ) % 6) // 2)

												# Append binary_stream with arbitrary binary digits (0's by default) to make its
												# length a multiple of 6.
												binary_stream += "0" * (6 - len(lowercase__   ) % 6)
						else:
												__lowercase					=				B""""""

						# Encode every 6 binary digits to their corresponding Base64 character
						return (
						    "".join(
						        B64_CHARSET[int(binary_stream[index : index + 6]						,       2   )]
						        for index in range(0						,       len(lowercase__   )						,       6   )   ).encode()
						    + padding
						)






def  UpperCAmelCase__    (    lowercase__   ) ->      bytes:
						# Make sure encoded_data is either a string or a bytes-like object
						if not isinstance(lowercase__						,       lowercase__   ) and not isinstance(lowercase__						,       lowercase__   ):
												__lowercase					=				(
												    """argument should be a bytes-like object or ASCII string, """
												    F"not '{encoded_data.__class__.__name__}'"
												)
												raise TypeError(lowercase__   )

						# In case encoded_data is a bytes-like object, make sure it contains only
						# ASCII characters so we convert it to a string object
						if isinstance(lowercase__						,       lowercase__   ):
												try:
																		__lowercase					=				encoded_data.decode("""utf-8"""   )
												except UnicodeDecodeError:
																		raise ValueError("""base64 encoded data should only contain ASCII characters"""   )

						__lowercase					=				encoded_data.count("""="""   )

						# Check if the encoded string contains non base64 characters
						if padding:
												assert all(
												    char in B64_CHARSET for char in encoded_data[:-padding]   ), "Invalid base64 character(s) found."
						else:
												assert all(
												    char in B64_CHARSET for char in encoded_data   ), "Invalid base64 character(s) found."

						# Check the padding
						assert len(lowercase__   ) % 4 == 0 and padding < 3, "Incorrect padding"

						if padding:
												# Remove padding if there is one
												__lowercase					=				encoded_data[:-padding]

												__lowercase					=				"""""".join(
												    bin(B64_CHARSET.index(lowercase__   )   )[2:].zfill(6   ) for char in encoded_data   )[: -padding * 2]
						else:
												__lowercase					=				"""""".join(
												    bin(B64_CHARSET.index(lowercase__   )   )[2:].zfill(6   ) for char in encoded_data   )

						__lowercase					=				[
						    int(binary_stream[index : index + 8]						,       2   )
						    for index in range(0						,       len(lowercase__   )						,       8   )
						]

						return bytes(lowercase__   )


if __name__ == "__main__":
			import doctest

			doctest.testmod()










from __future__ import annotations

from collections.abc import Callable

UpperCamelCase__ =						list[list[float | int]]






def  UpperCAmelCase__    (    lowercase__						,       lowercase__   ) ->      Matrix:
						__lowercase					=				len(lowercase__   )
						__lowercase					=				[[0 for _ in range(size + 1   )] for _ in range(lowercase__   )]
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42

						for row in range(lowercase__   ):
												for col in range(lowercase__   ):
																		__lowercase					=				matrix[row][col]

												__lowercase					=				vector[row][0]

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

												for rowa in range(row + 1						,       lowercase__   ):
																		__lowercase					=				augmented[rowa][col] / augmented[row][col]
																		__lowercase					=				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__   ):
																		__lowercase					=				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  UpperCAmelCase__    (    lowercase__   ) ->      Callable[[int], int]:
						__lowercase					=				len(lowercase__   )
						__lowercase					=				[[0 for _ in range(lowercase__   )] for _ in range(lowercase__   )]
						__lowercase					=				[[0] for _ in range(lowercase__   )]
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42
						__lowercase					=				42

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

						__lowercase					=				solve(lowercase__						,       lowercase__   )

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

						return interpolated_func






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






def  UpperCAmelCase__    (    lowercase__ = question_function						,       lowercase__ = 10   ) ->      int:
						__lowercase					=				[func(lowercase__   ) for x_val in range(1						,       order + 1   )]

						__lowercase					=				[
						    interpolate(data_points[:max_coeff]   ) for max_coeff in range(1						,       order + 1   )
						]

						__lowercase					=				0
						__lowercase					=				42
						__lowercase					=				42

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

												ret += poly(lowercase__   )

						return ret


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





