
from __future__ import annotations

from collections.abc import Callable

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


def     UpperCAmelCase_  (						__lowerCAmelCase	,					__lowerCAmelCase	) ->						Matrix:
    __lowercase		:			int	    =       len(__lowerCAmelCase	)
    __lowercase		:			Matrix	    =       [[0 for _ in range(size + 1	)] for _ in range(__lowerCAmelCase	)]
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			float

    for row in range(__lowerCAmelCase	):
        for col in range(__lowerCAmelCase	):
            __lowercase		:			Optional[Any]	    =       matrix[row][col]

        __lowercase		:			Dict	    =       vector[row][0]

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

        for rowa in range(row + 1	,					__lowerCAmelCase	):
            __lowercase		:			Union[str, Any]	    =       augmented[rowa][col] / augmented[row][col]
            __lowercase		:			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	,					__lowerCAmelCase	):
        for row in range(__lowerCAmelCase	):
            __lowercase		:			int	    =       augmented[row][col] / augmented[col][col]
            for cola in range(__lowerCAmelCase	,					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(__lowerCAmelCase	)
    ]


def     UpperCAmelCase_  (						__lowerCAmelCase	) ->						Callable[[int], int]:
    __lowercase		:			int	    =       len(__lowerCAmelCase	)
    __lowercase		:			Matrix	    =       [[0 for _ in range(__lowerCAmelCase	)] for _ in range(__lowerCAmelCase	)]
    __lowercase		:			Matrix	    =       [[0] for _ in range(__lowerCAmelCase	)]
    __lowercase		:			Matrix
    __lowercase		:			int
    __lowercase		:			int
    __lowercase		:			int

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

    __lowercase		:			Any	    =       solve(__lowerCAmelCase	,					__lowerCAmelCase	)

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

    return interpolated_func


def     UpperCAmelCase_  (						__lowerCAmelCase	) ->						int:
    return (
        1
        - variable
        + variable**2
        - variable**3
        + variable**4
        - variable**5
        + variable**6
        - variable**7
        + variable**8
        - variable**9
        + variable**10
    )


def     UpperCAmelCase_  (						__lowerCAmelCase = question_function	,					__lowerCAmelCase = 10	) ->						int:
    __lowercase		:			list[int]	    =       [func(__lowerCAmelCase	) for x_val in range(1	,					order + 1	)]

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

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

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

        ret += poly(__lowerCAmelCase	)

    return ret


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


import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch


if is_torch_available():
 import torch

 from transformers.activations import gelu_new, gelu_python, get_activation


@require_torch
class 						__lowerCAmelCase	(	unittest.TestCase      ):



      """simple docstring"""







      def 		snake_case_			(      self		:       Optional[Any]				):
          __lowercase		:			Union[str, Any]	    =       torch.tensor([-100, -1, -0.1, 0, 0.1, 1.0, 100]				)
          __lowercase		:			Any	    =       get_activation('''gelu'''				)
          self.assertTrue(torch.allclose(gelu_python(_snake_case				)				,       torch_builtin(_snake_case				)				)				)
          self.assertFalse(torch.allclose(gelu_python(_snake_case				)				,       gelu_new(_snake_case				)				)				)




      def 		snake_case_			(      self		:       Dict				):
          __lowercase		:			Any	    =       torch.tensor([-100, -1, -0.1, 0, 0.1, 1.0, 100]				)
          __lowercase		:			List[str]	    =       get_activation('''gelu'''				)
          __lowercase		:			Optional[Any]	    =       get_activation('''gelu_10'''				)

          __lowercase		:			Tuple	    =       torch_builtin(_snake_case				)
          __lowercase		:			List[Any]	    =       geluaa(_snake_case				)

          __lowercase		:			Tuple	    =       torch.where(y_gelu_aa < 10.0				,       1				,       0				)

          self.assertTrue(torch.max(_snake_case				).item() == 10.0				)
          self.assertTrue(torch.allclose(y_gelu * clipped_mask				,       y_gelu_aa * clipped_mask				)				)




      def 		snake_case_			(      self		:       Any				):
          get_activation('''gelu'''				)
          get_activation('''gelu_10'''				)
          get_activation('''gelu_fast'''				)
          get_activation('''gelu_new'''				)
          get_activation('''gelu_python'''				)
          get_activation('''gelu_pytorch_tanh'''				)
          get_activation('''linear'''				)
          get_activation('''mish'''				)
          get_activation('''quick_gelu'''				)
          get_activation('''relu'''				)
          get_activation('''sigmoid'''				)
          get_activation('''silu'''				)
          get_activation('''swish'''				)
          get_activation('''tanh'''				)
          with self.assertRaises(_snake_case				):
              get_activation('''bogus'''				)
          with self.assertRaises(_snake_case				):
              get_activation(_snake_case				)




      def 		snake_case_			(      self		:       Dict				):
          __lowercase		:			Union[str, Any]	    =       get_activation('''gelu'''				)
          __lowercase		:			List[str]	    =       1
          __lowercase		:			Union[str, Any]	    =       get_activation('''gelu'''				)
          self.assertEqual(acta.a				,       1				)
          with self.assertRaises(_snake_case				):
              __lowercase		:			Tuple	    =       acta.a


