from __future__ import annotations

from collections.abc import Callable

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







def     _a				(      lowercase__  :			Matrix     ,  lowercase__  :			Matrix ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				int			=		len(lowercase__ )
     SCREAMING_SNAKE_CASE__				:				Matrix			=		[[0 for _ in range(size + 1 )] for _ in range(lowercase__ )]
     SCREAMING_SNAKE_CASE__				:				int
     SCREAMING_SNAKE_CASE__				:				int
     SCREAMING_SNAKE_CASE__				:				int
     SCREAMING_SNAKE_CASE__				:				int
     SCREAMING_SNAKE_CASE__				:				int
     SCREAMING_SNAKE_CASE__				:				float

     for row in range(lowercase__ ):
          for col in range(lowercase__ ):
               SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		matrix[row][col]

          SCREAMING_SNAKE_CASE__				:				List[Any]			=		vector[row][0]

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

          for rowa in range(row + 1     ,  lowercase__ ):
               SCREAMING_SNAKE_CASE__				:				int			=		augmented[rowa][col] / augmented[row][col]
               SCREAMING_SNAKE_CASE__				:				List[str]			=		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__ ):
               SCREAMING_SNAKE_CASE__				:				Tuple			=		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     _a				(      lowercase__  :			list[int] ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				int			=		len(lowercase__ )
     SCREAMING_SNAKE_CASE__				:				Matrix			=		[[0 for _ in range(lowercase__ )] for _ in range(lowercase__ )]
     SCREAMING_SNAKE_CASE__				:				Matrix			=		[[0] for _ in range(lowercase__ )]
     SCREAMING_SNAKE_CASE__				:				Matrix
     SCREAMING_SNAKE_CASE__				:				int
     SCREAMING_SNAKE_CASE__				:				int
     SCREAMING_SNAKE_CASE__				:				int

     for x_val, y_val in enumerate(lowercase__ ):
          for col in range(lowercase__ ):
               SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		(x_val + 1) ** (size - col - 1)
          SCREAMING_SNAKE_CASE__				:				Tuple			=		y_val

     SCREAMING_SNAKE_CASE__				:				Tuple			=		solve(lowercase__     ,  lowercase__ )

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

     return interpolated_func







def     _a				(      lowercase__  :			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     _a				(      lowercase__  :			Callable[[int], int] = question_function     ,  lowercase__  :			int = 10 ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				list[int]			=		[func(lowercase__ ) for x_val in range(1     ,  order + 1 )]

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

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

     for poly in polynomials:
          SCREAMING_SNAKE_CASE__				:				Optional[int]			=		1
          while func(lowercase__ ) == poly(lowercase__ ):
               x_val += 1

          ret += poly(lowercase__ )

     return ret


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




import requests

SCREAMING_SNAKE_CASE__		:					int						=					"https://newsapi.org/v1/articles?source=bbc-news&sortBy=top&apiKey="







def     _a				(      lowercase__  :			str ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		requests.get(_NEWS_API + bbc_news_api_key ).json()
     # each article in the list is a dict
     for i, article in enumerate(bbc_news_page['articles']     ,  1 ):
          print(f'''{i}.) {article['title']}''' )


if __name__ == "__main__":
      fetch_bbc_news(bbc_news_api_key="<Your BBC News API key goes here>")



