
from __future__ import annotations

from collections.abc import Callable

_snake_case      = list[list[float | int]]

def  __lowerCamelCase					( _lowercase						,     _lowercase			)       ->      Matrix:
     UpperCamelCase						    =					len(_lowercase			)
     UpperCamelCase						    =					[[0 for _ in range(size + 1			)] for _ in range(_lowercase			)]
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42

     for row in range(_lowercase			):
          for col in range(_lowercase			):
               UpperCamelCase						    =					matrix[row][col]

          UpperCamelCase						    =					vector[row][0]

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

          for rowa in range(row + 1						,     _lowercase			):
               UpperCamelCase						    =					augmented[rowa][col] / augmented[row][col]
               UpperCamelCase						    =					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			):
               UpperCamelCase						    =					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  __lowerCamelCase					( _lowercase			)       ->      Callable[[int], int]:
     UpperCamelCase						    =					len(_lowercase			)
     UpperCamelCase						    =					[[0 for _ in range(_lowercase			)] for _ in range(_lowercase			)]
     UpperCamelCase						    =					[[0] for _ in range(_lowercase			)]
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42

     for x_val, y_val in enumerate(_lowercase			):
          for col in range(_lowercase			):
               UpperCamelCase						    =					(x_val + 1) ** (size - col - 1)
          UpperCamelCase						    =					y_val

     UpperCamelCase						    =					solve(_lowercase						,     _lowercase			)

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

     return interpolated_func

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

def  __lowerCamelCase					( _lowercase = question_function						,     _lowercase = 10			)       ->      int:
     UpperCamelCase						    =					[func(_lowercase			) for x_val in range(1						,     order + 1			)]

     UpperCamelCase						    =					[
         interpolate(data_points[:max_coeff]			) for max_coeff in range(1						,     order + 1			)
     ]

     UpperCamelCase						    =					0
     UpperCamelCase						    =					42
     UpperCamelCase						    =					42

     for poly in polynomials:
          UpperCamelCase						    =					1
          while func(_lowercase			) == poly(_lowercase			):
               x_val += 1

          ret += poly(_lowercase			)

     return ret


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




from ...utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_torch_available,
    is_transformers_available,
)


try:
 if not (is_transformers_available() and is_torch_available()):
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
 from .multicontrolnet import MultiControlNetModel
 from .pipeline_controlnet import StableDiffusionControlNetPipeline
 from .pipeline_controlnet_imgaimg import StableDiffusionControlNetImgaImgPipeline
 from .pipeline_controlnet_inpaint import StableDiffusionControlNetInpaintPipeline


if is_transformers_available() and is_flax_available():
 from .pipeline_flax_controlnet import FlaxStableDiffusionControlNetPipeline


