


from __future__ import annotations

from collections.abc import Callable

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





def   _lowerCAmelCase				(   UpperCamelCase__:     Matrix							,					UpperCamelCase__:     Matrix						) ->   Matrix:





	"""simple docstring"""







	A								=				len(UpperCamelCase__						)
	A								=				[[0 for _ in range(size + 1						)] for _ in range(UpperCamelCase__						)]
	A								=				42
	A								=				42
	A								=				42
	A								=				42
	A								=				42
	A								=				42

	for row in range(UpperCamelCase__						):
		for col in range(UpperCamelCase__						):
			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(UpperCamelCase__							,					UpperCamelCase__						)						)[
		    1
		]
		if augmented[pivot_row][col] == 0:
			col += 1
			continue
		else:
			A					,			A								=				augmented[pivot_row], augmented[row]

		for rowa in range(row + 1							,					UpperCamelCase__						):
			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							,					UpperCamelCase__						):
		for row in range(UpperCamelCase__						):
			A								=				augmented[row][col] / augmented[col][col]
			for cola in range(UpperCamelCase__							,					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(UpperCamelCase__						)
	]





def   _lowerCAmelCase				(   UpperCamelCase__:     list[int]						) ->   Callable[[int], int]:





	"""simple docstring"""







	A								=				len(UpperCamelCase__						)
	A								=				[[0 for _ in range(UpperCamelCase__						)] for _ in range(UpperCamelCase__						)]
	A								=				[[0] for _ in range(UpperCamelCase__						)]
	A								=				42
	A								=				42
	A								=				42
	A								=				42

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

	A								=				solve(UpperCamelCase__							,					UpperCamelCase__						)

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

	return interpolated_func





def   _lowerCAmelCase				(   UpperCamelCase__:     int						) ->   int:





	"""simple docstring"""







	return (
	    1
	    - variable
	    + variable**2
	    - variable**3
	    + variable**4
	    - variable**5
	    + variable**6
	    - variable**7
	    + variable**8
	    - variable**9
	    + variable**10
	)





def   _lowerCAmelCase				(   UpperCamelCase__:     Callable[[int], int] = question_function							,					UpperCamelCase__:     int = 10						) ->   int:





	"""simple docstring"""







	A								=				[func(UpperCamelCase__						) 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(UpperCamelCase__						) == poly(UpperCamelCase__						):
			x_val += 1

		ret += poly(UpperCamelCase__						)

	return ret


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







def   _lowerCAmelCase				(   UpperCamelCase__:     int						) ->   bool:





	"""simple docstring"""







	return str(UpperCamelCase__						) == str(UpperCamelCase__						)[::-1]





def   _lowerCAmelCase				(   UpperCamelCase__:     int						) ->   int:





	"""simple docstring"""







	return int(UpperCamelCase__						) + int(str(UpperCamelCase__						)[::-1]						)





def   _lowerCAmelCase				(   UpperCamelCase__:     int = 1_00_00						) ->   int:





	"""simple docstring"""







	A								=				[]
	for num in range(1							,					UpperCamelCase__						):
		A								=				0
		A								=				num
		while iterations < 50:
			A								=				sum_reverse(UpperCamelCase__						)
			iterations += 1
			if is_palindrome(UpperCamelCase__						):
				break
		else:
			lychrel_nums.append(UpperCamelCase__						)
	return len(UpperCamelCase__						)


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



