





"""simple docstring"""






from __future__ import annotations

from collections.abc import Callable

A 			=  list[list[float | int]]

def     __A      (			a_						:Matrix   ,       a_						:Matrix)		->		Matrix:
    __a :						int			       =  len(a_)
    __a :						Matrix			       =  [[0 for _ in range(size + 1)] for _ in range(a_)]
    __a :						int
    __a :						int
    __a :						int
    __a :						int
    __a :						int
    __a :						float

    for row in range(a_):
        for col in range(a_):
            __a :						Any			       =  matrix[row][col]

        __a :						Optional[Any]			       =  vector[row][0]

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

        for rowa in range(row + 1   ,       a_):
            __a :						Tuple			       =  augmented[rowa][col] / augmented[row][col]
            __a :						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   ,       a_):
        for row in range(a_):
            __a :						List[Any]			       =  augmented[row][col] / augmented[col][col]
            for cola in range(a_   ,       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(a_)
    ]

def     __A      (			a_						:list[int])		->		Callable[[int], int]:
    __a :						int			       =  len(a_)
    __a :						Matrix			       =  [[0 for _ in range(a_)] for _ in range(a_)]
    __a :						Matrix			       =  [[0] for _ in range(a_)]
    __a :						Matrix
    __a :						int
    __a :						int
    __a :						int

    for x_val, y_val in enumerate(a_):
        for col in range(a_):
            __a :						str			       =  (x_val + 1) ** (size - col - 1)
        __a :						Dict			       =  y_val

    __a :						Union[str, Any]			       =  solve(a_   ,       a_)

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

    return interpolated_func

def     __A      (			a_						: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      (			a_						:Callable[[int], int] = question_function   ,       a_						:int = 10)		->		int:
    __a :						list[int]			       =  [func(a_) 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 :						Tuple			       =  1
        while func(a_) == poly(a_):
            x_val += 1

        ret += poly(a_)

    return ret


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






"""simple docstring"""






import json
import os
import unittest

from transformers import OpenAIGPTTokenizer, OpenAIGPTTokenizerFast
from transformers.models.openai.tokenization_openai import VOCAB_FILES_NAMES
from transformers.testing_utils import require_ftfy, require_spacy, require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin




@require_tokenizers
class 				__lowercase			(			_UpperCamelCase   ,      unittest.TestCase							):







					'''simple docstring'''




					__lowerCAmelCase  =  OpenAIGPTTokenizer
					__lowerCAmelCase  =  OpenAIGPTTokenizerFast
					__lowerCAmelCase  =  True
					__lowerCAmelCase  =  False







					def  _lowerCamelCase		(						self     ):
									super().setUp()

									# Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
									__a :						List[str]			       =  [
									    '''l''',
									    '''o''',
									    '''w''',
									    '''e''',
									    '''r''',
									    '''s''',
									    '''t''',
									    '''i''',
									    '''d''',
									    '''n''',
									    '''w</w>''',
									    '''r</w>''',
									    '''t</w>''',
									    '''lo''',
									    '''low''',
									    '''er</w>''',
									    '''low</w>''',
									    '''lowest</w>''',
									    '''newer</w>''',
									    '''wider</w>''',
									    '''<unk>''',
									]
									__a :						str			       =  dict(zip(_UpperCAmelCase	,			range(len(_UpperCAmelCase     )     )     )     )
									__a :						List[Any]			       =  ['''#version: 0.2''', '''l o''', '''lo w''', '''e r</w>''', '''''']

									__a :						Union[str, Any]			       =  os.path.join(self.tmpdirname	,			VOCAB_FILES_NAMES['''vocab_file''']     )
									__a :						Dict			       =  os.path.join(self.tmpdirname	,			VOCAB_FILES_NAMES['''merges_file''']     )
									with open(self.vocab_file	,			'''w'''     ) as fp:
													fp.write(json.dumps(_UpperCAmelCase     )     )
									with open(self.merges_file	,			'''w'''     ) as fp:
													fp.write('''\n'''.join(_UpperCAmelCase     )     )







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase     ):
									return "lower newer", "lower newer"







					def  _lowerCamelCase		(						self     ):
									__a :						Tuple			       =  OpenAIGPTTokenizer(self.vocab_file	,			self.merges_file     )

									__a :						Tuple			       =  '''lower'''
									__a :						Union[str, Any]			       =  ['''low''', '''er</w>''']
									__a :						str			       =  tokenizer.tokenize(_UpperCAmelCase     )
									self.assertListEqual(_UpperCAmelCase	,			_UpperCAmelCase     )

									__a :						List[Any]			       =  tokens + ['''<unk>''']
									__a :						Tuple			       =  [14, 15, 20]
									self.assertListEqual(tokenizer.convert_tokens_to_ids(_UpperCAmelCase     )	,			_UpperCAmelCase     )







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase=15     ):
									for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
													with self.subTest(f"""{tokenizer.__class__.__name__} ({pretrained_name})"""     ):
																	__a :						Any			       =  self.rust_tokenizer_class.from_pretrained(_UpperCAmelCase	,			**_UpperCAmelCase     )

																	# Simple input
																	__a :						str			       =  '''This is a simple input'''
																	__a :						Dict			       =  ['''This is a simple input 1''', '''This is a simple input 2''']
																	__a :						List[Any]			       =  ('''This is a simple input''', '''This is a pair''')
																	__a :						Optional[Any]			       =  [
																	    ('''This is a simple input 1''', '''This is a simple input 2'''),
																	    ('''This is a simple pair 1''', '''This is a simple pair 2'''),
																	]

																	# Simple input tests
																	self.assertRaises(_UpperCAmelCase	,			tokenizer_r.encode	,			_UpperCAmelCase	,			max_length=_UpperCAmelCase	,			padding='''max_length'''     )

																	# Simple input
																	self.assertRaises(_UpperCAmelCase	,			tokenizer_r.encode_plus	,			_UpperCAmelCase	,			max_length=_UpperCAmelCase	,			padding='''max_length'''     )

																	# Simple input
																	self.assertRaises(
																	    _UpperCAmelCase	,			tokenizer_r.batch_encode_plus	,			_UpperCAmelCase	,			max_length=_UpperCAmelCase	,			padding='''max_length'''	,			)

																	# Pair input
																	self.assertRaises(_UpperCAmelCase	,			tokenizer_r.encode	,			_UpperCAmelCase	,			max_length=_UpperCAmelCase	,			padding='''max_length'''     )

																	# Pair input
																	self.assertRaises(_UpperCAmelCase	,			tokenizer_r.encode_plus	,			_UpperCAmelCase	,			max_length=_UpperCAmelCase	,			padding='''max_length'''     )

																	# Pair input
																	self.assertRaises(
																	    _UpperCAmelCase	,			tokenizer_r.batch_encode_plus	,			_UpperCAmelCase	,			max_length=_UpperCAmelCase	,			padding='''max_length'''	,			)







					def  _lowerCamelCase		(						self     ):
									pass






@require_ftfy
@require_spacy
@require_tokenizers
class 				__lowercase			(			_UpperCamelCase							):







					'''simple docstring'''




					pass