

'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable

A_							    =				list[list[float | int]]





def  A_	(			snake_case   ,							snake_case			):
  SCREAMING_SNAKE_CASE:int       =       len(snake_case			)
  SCREAMING_SNAKE_CASE:Matrix       =       [[0 for _ in range(size + 1			)] for _ in range(snake_case			)]
  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(snake_case			):
    for col in range(snake_case			):
      SCREAMING_SNAKE_CASE:List[str]       =       matrix[row][col]

    SCREAMING_SNAKE_CASE:Dict       =       vector[row][0]

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

    for rowa in range(row + 1   ,							snake_case			):
      SCREAMING_SNAKE_CASE:Tuple       =       augmented[rowa][col] / augmented[row][col]
      SCREAMING_SNAKE_CASE:int       =       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   ,							snake_case			):
    for row in range(snake_case			):
      SCREAMING_SNAKE_CASE:Any       =       augmented[row][col] / augmented[col][col]
      for cola in range(snake_case   ,							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(snake_case			)
  ]





def  A_	(			snake_case			):
  SCREAMING_SNAKE_CASE:int       =       len(snake_case			)
  SCREAMING_SNAKE_CASE:Matrix       =       [[0 for _ in range(snake_case			)] for _ in range(snake_case			)]
  SCREAMING_SNAKE_CASE:Matrix       =       [[0] for _ in range(snake_case			)]
  SCREAMING_SNAKE_CASE:Matrix
  SCREAMING_SNAKE_CASE:int
  SCREAMING_SNAKE_CASE:int
  SCREAMING_SNAKE_CASE:int

  for x_val, y_val in enumerate(snake_case			):
    for col in range(snake_case			):
      SCREAMING_SNAKE_CASE:Any       =       (x_val + 1) ** (size - col - 1)
    SCREAMING_SNAKE_CASE:Tuple       =       y_val

  SCREAMING_SNAKE_CASE:Tuple       =       solve(snake_case   ,							snake_case			)

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

  return interpolated_func





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





def  A_	(			snake_case = question_function   ,							snake_case = 10			):
  SCREAMING_SNAKE_CASE:list[int]       =       [func(snake_case			) 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:List[Any]       =       1
    while func(snake_case			) == poly(snake_case			):
      x_val += 1

    ret += poly(snake_case			)

  return ret


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







"""simple docstring"""



from __future__ import annotations

def  _A(		lowerCAmelCase							):
							if len(lowerCAmelCase							) == 0:
														return []
							A__				,							A__       :     Dict								=			min(lowerCAmelCase							), max(lowerCAmelCase							)
							A__       :     List[Any]								=			int(max_value - min_value							) + 1
							A__       :     list[list]								=			[[] for _ in range(lowerCAmelCase							)]

							for i in my_list:
														buckets[int(i - min_value							)].append(lowerCAmelCase							)

							return [v for bucket in buckets for v in sorted(lowerCAmelCase							)]


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

				testmod()
				assert bucket_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
				assert bucket_sort([0, 1, -10, 15, 2, -2]) == [-10, -2, 0, 1, 2, 15]





