
'''simple docstring'''




from __future__ import annotations

from collections.abc import Callable

lowercase     :							Union[str, Any]       						=     list[list[float | int]]







def 						lowerCAmelCase_							(  snake_case__						,							snake_case__		):




    '''simple docstring'''



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

    for row in range(snake_case__		):
        for col in range(snake_case__		):
            A			:  Union[str, Any]   =		matrix[row][col]

        A			:  List[str]   =		vector[row][0]

    A			:  Optional[Any]   =		0
    A			:  Union[str, Any]   =		0
    while row < size and col < size:
        # pivoting
        A			:  Optional[Any]   =		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:
            A,    A			:  Any   =		augmented[pivot_row], augmented[row]

        for rowa in range(row + 1						,							snake_case__		):
            A			:  Optional[Any]   =		augmented[rowa][col] / augmented[row][col]
            A			:  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__		):
            A			:  List[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 						lowerCAmelCase_							(  snake_case__		):




    '''simple docstring'''



    A			:  int   =		len(snake_case__		)
    A			:  Matrix   =		[[0 for _ in range(snake_case__		)] for _ in range(snake_case__		)]
    A			:  Matrix   =		[[0] for _ in range(snake_case__		)]
    A			:  Matrix
    A			:  int
    A			:  int
    A			:  int

    for x_val, y_val in enumerate(snake_case__		):
        for col in range(snake_case__		):
            A			:  List[str]   =		(x_val + 1) ** (size - col - 1)
        A			:  List[str]   =		y_val

    A			:  Union[str, Any]   =		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 						lowerCAmelCase_							(  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 						lowerCAmelCase_							(  snake_case__ = question_function						,							snake_case__ = 10		):




    '''simple docstring'''



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

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

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

    for poly in polynomials:
        A			:  Dict   =		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'''




def 						lowerCAmelCase_							(  snake_case__		):




    '''simple docstring'''



    if len(snake_case__		) <= 1:
        return [tuple(snake_case__		)]

    A			:  int   =		[]

    def generate(snake_case__						,							snake_case__		):
        if k == 1:
            res.append(tuple(arr[:]		)		)
            return

        generate(k - 1						,							snake_case__		)

        for i in range(k - 1		):
            if k % 2 == 0:  # k is even
                A,    A			:  Any   =		arr[k - 1], arr[i]
            else:  # k is odd
                A,    A			:  List[str]   =		arr[k - 1], arr[0]
            generate(k - 1						,							snake_case__		)

    generate(len(snake_case__		)						,							snake_case__		)
    return res


if __name__ == "__main__":
      lowercase     :							int       						=     input('Enter numbers separated by a comma:\n').strip()
      lowercase     :							Dict       						=     [int(item) for item in user_input.split(',')]
      print(heaps(arr))




