from __future__ import annotations

from collections.abc import Callable

_lowercase							:      List[Any]      							=list[list[float | int]]



def A__  (			lowercase:     Matrix,		lowercase:     Matrix					)				->		Matrix:
       A						:     int         =len(lowercase					)
       A						:     Matrix         =[[0 for _ in range(size + 1					)] for _ in range(lowercase					)]
       A						:     int
       A						:     int
       A						:     int
       A						:     int
       A						:     int
       A						:     float

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

              A						:     Dict         =vector[row][0]

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

              for rowa in range(row + 1,		lowercase					):
                     A						:     Union[str, Any]         =augmented[rowa][col] / augmented[row][col]
                     A						:     List[str]         =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					):
                     A						:     List[Any]         =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 A__  (			lowercase:     list[int]					)				->		Callable[[int], int]:
       A						:     int         =len(lowercase					)
       A						:     Matrix         =[[0 for _ in range(lowercase					)] for _ in range(lowercase					)]
       A						:     Matrix         =[[0] for _ in range(lowercase					)]
       A						:     Matrix
       A						:     int
       A						:     int
       A						:     int

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

       A						:     Tuple         =solve(lowercase,		lowercase					)

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

       return interpolated_func



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



def A__  (			lowercase:     Callable[[int], int] = question_function,		lowercase:     int = 10					)				->		int:
       A						:     list[int]         =[func(lowercase					) 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						:     Optional[Any]         =1
              while func(lowercase					) == poly(lowercase					):
                     x_val += 1

              ret += poly(lowercase					)

       return ret


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







# Copyright 2021 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import argparse
import os

from accelerate.utils import ComputeEnvironment

from .cluster import get_cluster_input
from .config_args import cache_dir, default_config_file, default_yaml_config_file, load_config_from_file  # noqa: F401
from .config_utils import _ask_field, _ask_options, _convert_compute_environment  # noqa: F401
from .sagemaker import get_sagemaker_input


_lowercase							:      List[str]      							='''Launches a series of prompts to create and save a `default_config.yaml` configuration file for your training system. Should always be ran first on your machine'''



def A__  (			)				->		List[Any]:
       A						:     Any         =_ask_options(
           'In which compute environment are you running?',		['This machine', 'AWS (Amazon SageMaker)'],		_convert_compute_environment,		)
       if compute_environment == ComputeEnvironment.AMAZON_SAGEMAKER:
              A						:     Tuple         =get_sagemaker_input()
       else:
              A						:     str         =get_cluster_input()
       return config



def A__  (			lowercase:     int=None					)				->		str:
       if subparsers is not None:
              A						:     List[str]         =subparsers.add_parser('config',		description=lowercase					)
       else:
              A						:     Union[str, Any]         =argparse.ArgumentParser('Accelerate config command',		description=lowercase					)

       parser.add_argument(
           '--config_file',		default=lowercase,		help=(
               'The path to use to store the config file. Will default to a file named default_config.yaml in the cache '
               'location, which is the content of the environment `HF_HOME` suffixed with \'accelerate\', or if you don\'t have '
               'such an environment variable, your cache directory (\'~/.cache\' or the content of `XDG_CACHE_HOME`) suffixed '
               'with \'huggingface\'.'
           ),		)

       if subparsers is not None:
              parser.set_defaults(func=lowercase					)
       return parser



def A__  (			lowercase:     Tuple					)				->		List[Any]:
       A						:     Union[str, Any]         =get_user_input()
       if args.config_file is not None:
              A						:     Optional[Any]         =args.config_file
       else:
              if not os.path.isdir(lowercase					):
                     os.makedirs(lowercase					)
              A						:     Union[str, Any]         =default_yaml_config_file

       if config_file.endswith('.json'					):
              config.to_json_file(lowercase					)
       else:
              config.to_yaml_file(lowercase					)
       print(F'accelerate configuration saved at {config_file}'					)



def A__  (			)				->		Optional[int]:
       A						:     Any         =config_command_parser()
       A						:     int         =parser.parse_args()
       config_command(lowercase					)


if __name__ == "__main__":
    main()






