



from __future__ import annotations

from collections.abc import Callable

a_			=					list[list[float | int]]





def 		a__			(		_UpperCamelCase			: Matrix ,_UpperCamelCase			: Matrix							):
			__lowerCamelCase													=    len(_UpperCamelCase							)
			__lowerCamelCase													=    [[0 for _ in range(size + 1							)] for _ in range(_UpperCamelCase							)]
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42

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

						__lowerCamelCase													=    vector[row][0]

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

						for rowa in range(row + 1 ,_UpperCamelCase							):
									__lowerCamelCase													=    augmented[rowa][col] / augmented[row][col]
									__lowerCamelCase													=    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							):
									__lowerCamelCase													=    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 		a__			(		_UpperCamelCase			: list[int]							):
			__lowerCamelCase													=    len(_UpperCamelCase							)
			__lowerCamelCase													=    [[0 for _ in range(_UpperCamelCase							)] for _ in range(_UpperCamelCase							)]
			__lowerCamelCase													=    [[0] for _ in range(_UpperCamelCase							)]
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42

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

			__lowerCamelCase													=    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 		a__			(		_UpperCamelCase			: int							):
			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)





def 		a__			(		_UpperCamelCase			: Callable[[int], int] = question_function ,_UpperCamelCase			: int = 10							):
			__lowerCamelCase													=    [func(_UpperCamelCase							) for x_val in range(1 ,order + 1							)]

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

			__lowerCamelCase													=    0
			__lowerCamelCase													=    42
			__lowerCamelCase													=    42

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

						ret += poly(_UpperCamelCase							)

			return ret


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











from collections import namedtuple

import requests
from lxml import html  # type: ignore

a_			=					namedtuple("""covid_data""", """cases deaths recovered""")





def 		a__			(		_UpperCamelCase			: str = "https://www.worldometers.info/coronavirus/"							):
   __lowerCamelCase													=    '''//div[@class = "maincounter-number"]/span/text()'''
   return covid_data(*html.fromstring(requests.get(_UpperCamelCase							).content							).xpath(_UpperCamelCase							)							)


a_			=					"""Total COVID-19 cases in the world: {}
Total deaths due to COVID-19 in the world: {}
Total COVID-19 patients recovered in the world: {}"""





print(fmt.format(*covid_stats()))






