


from __future__ import annotations

from collections.abc import Callable

_snake_case             =     list[list[float | int]]






def 		lowercase_(  SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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

  for row in range(SCREAMING_SNAKE_CASE_	):
    for col in range(SCREAMING_SNAKE_CASE_	):
      lowerCamelCase :					List[str]    =				matrix[row][col]

    lowerCamelCase :					Any    =				vector[row][0]

  lowerCamelCase :					Dict    =				0
  lowerCamelCase :					List[str]    =				0
  while row < size and col < size:
    # pivoting
    lowerCamelCase :					int    =				max((abs(augmented[rowa][col]	), rowa) for rowa in range(SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	)	)[
        1
    ]
    if augmented[pivot_row][col] == 0:
      col += 1
      continue
    else:
      lowerCamelCase    ,	lowerCamelCase :					Dict    =				augmented[pivot_row], augmented[row]

    for rowa in range(row + 1      ,						SCREAMING_SNAKE_CASE_	):
      lowerCamelCase :					Optional[int]    =				augmented[rowa][col] / augmented[row][col]
      lowerCamelCase :					Union[str, Any]    =				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      ,						SCREAMING_SNAKE_CASE_	):
    for row in range(SCREAMING_SNAKE_CASE_	):
      lowerCamelCase :					List[Any]    =				augmented[row][col] / augmented[col][col]
      for cola in range(SCREAMING_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(SCREAMING_SNAKE_CASE_	)
  ]






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  lowerCamelCase :					int    =				len(SCREAMING_SNAKE_CASE_	)
  lowerCamelCase :					Matrix    =				[[0 for _ in range(SCREAMING_SNAKE_CASE_	)] for _ in range(SCREAMING_SNAKE_CASE_	)]
  lowerCamelCase :					Matrix    =				[[0] for _ in range(SCREAMING_SNAKE_CASE_	)]
  lowerCamelCase :					Matrix
  lowerCamelCase :					int
  lowerCamelCase :					int
  lowerCamelCase :					int

  for x_val, y_val in enumerate(SCREAMING_SNAKE_CASE_	):
    for col in range(SCREAMING_SNAKE_CASE_	):
      lowerCamelCase :					Optional[int]    =				(x_val + 1) ** (size - col - 1)
    lowerCamelCase :					Tuple    =				y_val

  lowerCamelCase :					Optional[int]    =				solve(SCREAMING_SNAKE_CASE_      ,						SCREAMING_SNAKE_CASE_	)

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

  return interpolated_func






def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

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






def 		lowercase_(  SCREAMING_SNAKE_CASE_ = question_function      ,						SCREAMING_SNAKE_CASE_ = 10	):


  '''simple docstring'''

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

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

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

  for poly in polynomials:
    lowerCamelCase :					str    =				1
    while func(SCREAMING_SNAKE_CASE_	) == poly(SCREAMING_SNAKE_CASE_	):
      x_val += 1

    ret += poly(SCREAMING_SNAKE_CASE_	)

  return ret


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







def 		lowercase_(  SCREAMING_SNAKE_CASE_	):


  '''simple docstring'''

  for i in range(len(SCREAMING_SNAKE_CASE_	) - 1      ,						0      ,						-1	):
    lowerCamelCase :					Tuple    =				False

    for j in range(SCREAMING_SNAKE_CASE_      ,						0      ,						-1	):
      if unsorted[j] < unsorted[j - 1]:
        lowerCamelCase    ,	lowerCamelCase :					int    =				unsorted[j - 1], unsorted[j]
        lowerCamelCase :					Optional[int]    =				True

    for j in range(SCREAMING_SNAKE_CASE_	):
      if unsorted[j] > unsorted[j + 1]:
        lowerCamelCase    ,	lowerCamelCase :					Union[str, Any]    =				unsorted[j + 1], unsorted[j]
        lowerCamelCase :					Optional[Any]    =				True

    if not swapped:
      break
  return unsorted


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   _snake_case             =     input('''Enter numbers separated by a comma:\n''').strip()
   _snake_case             =     [int(item) for item in user_input.split(''',''')]
   print(f'''{cocktail_shaker_sort(unsorted) = }''')



