from __future__ import annotations

from collections.abc import Callable

lowerCamelCase_    :		Dict							=	list[list[float | int]]
def 							lowerCAmelCase(     __lowerCamelCase				,    __lowerCamelCase						):
					__a		 =       len(__lowerCamelCase						)
					__a		 =       [[0 for _ in range(size + 1						)] for _ in range(__lowerCamelCase						)]
					__a		 =       42
					__a		 =       42
					__a		 =       42
					__a		 =       42
					__a		 =       42
					__a		 =       42

					for row in range(__lowerCamelCase						):
										for col in range(__lowerCamelCase						):
															__a		 =       matrix[row][col]

										__a		 =       vector[row][0]

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

										for rowa in range(row + 1				,    __lowerCamelCase						):
															__a		 =       augmented[rowa][col] / augmented[row][col]
															__a		 =       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						):
															__a		 =       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 							lowerCAmelCase(     __lowerCamelCase						):
					__a		 =       len(__lowerCamelCase						)
					__a		 =       [[0 for _ in range(__lowerCamelCase						)] for _ in range(__lowerCamelCase						)]
					__a		 =       [[0] for _ in range(__lowerCamelCase						)]
					__a		 =       42
					__a		 =       42
					__a		 =       42
					__a		 =       42

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

					__a		 =       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 							lowerCAmelCase(     __lowerCamelCase						):
					return (
					    1
					    - variable
					    + variable**2
					    - variable**3
					    + variable**4
					    - variable**5
					    + variable**6
					    - variable**7
					    + variable**8
					    - variable**9
					    + variable**10
					)
def 							lowerCAmelCase(     __lowerCamelCase = question_function				,    __lowerCamelCase = 10						):
					__a		 =       [func(__lowerCamelCase						) for x_val in range(1				,    order + 1						)]

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

					__a		 =       0
					__a		 =       42
					__a		 =       42

					for poly in polynomials:
										__a		 =       1
										while func(__lowerCamelCase						) == poly(__lowerCamelCase						):
															x_val += 1

										ret += poly(__lowerCamelCase						)

					return ret


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





def 							lowerCAmelCase(     __lowerCamelCase						):
					if not all(char in '01' for char in bin_string						):
										raise ValueError('Non-binary value was passed to the function'						)
					if not bin_string:
										raise ValueError('Empty string was passed to the function'						)
					__a		 =       ''
					while len(__lowerCamelCase						) % 3 != 0:
										__a		 =       '0' + bin_string
					__a		 =       [
					    bin_string[index : index + 3]
					    for index in range(len(__lowerCamelCase						)						)
					    if index % 3 == 0
					]
					for bin_group in bin_string_in_3_list:
										__a		 =       0
										for index, val in enumerate(__lowerCamelCase						):
															oct_val += int(2 ** (2 - index) * int(__lowerCamelCase						)						)
										oct_string += str(__lowerCamelCase						)
					return oct_string


if __name__ == "__main__":
	from doctest import testmod

	testmod()




