
from __future__ import annotations

from collections.abc import Callable

lowerCamelCase__          =		list[list[float | int]]
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		Matrix:
			lowerCAmelCase__      :      int         =		len(SCREAMING_SNAKE_CASE_     )
			lowerCAmelCase__      :      Matrix         =		[[0 for _ in range(size + 1     )] for _ in range(SCREAMING_SNAKE_CASE_     )]
			lowerCAmelCase__      :      int
			lowerCAmelCase__      :      int
			lowerCAmelCase__      :      int
			lowerCAmelCase__      :      int
			lowerCAmelCase__      :      int
			lowerCAmelCase__      :      float

			for row in range(SCREAMING_SNAKE_CASE_     ):
						for col in range(SCREAMING_SNAKE_CASE_     ):
									lowerCAmelCase__      :      Dict         =		matrix[row][col]

						lowerCAmelCase__      :      Optional[int]         =		vector[row][0]

			lowerCAmelCase__      :      List[Any]         =		0
			lowerCAmelCase__      :      str         =		0
			while row < size and col < size:
						# pivoting
						lowerCAmelCase__      :      str         =		max((abs(augmented[rowa][col]     ), rowa) for rowa in range(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )     )[
						    1
						]
						if augmented[pivot_row][col] == 0:
									col += 1
									continue
						else:
									lowerCAmelCase__      ,				lowerCAmelCase__      :      Optional[Any]         =		augmented[pivot_row], augmented[row]

						for rowa in range(row + 1       ,							SCREAMING_SNAKE_CASE_     ):
									lowerCAmelCase__      :      Optional[int]         =		augmented[rowa][col] / augmented[row][col]
									lowerCAmelCase__      :      Dict         =		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       ,							SCREAMING_SNAKE_CASE_     ):
						for row in range(SCREAMING_SNAKE_CASE_     ):
									lowerCAmelCase__      :      Union[str, Any]         =		augmented[row][col] / augmented[col][col]
									for cola in range(SCREAMING_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(SCREAMING_SNAKE_CASE_     )
			]
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		Callable[[int], int]:
			lowerCAmelCase__      :      int         =		len(SCREAMING_SNAKE_CASE_     )
			lowerCAmelCase__      :      Matrix         =		[[0 for _ in range(SCREAMING_SNAKE_CASE_     )] for _ in range(SCREAMING_SNAKE_CASE_     )]
			lowerCAmelCase__      :      Matrix         =		[[0] for _ in range(SCREAMING_SNAKE_CASE_     )]
			lowerCAmelCase__      :      Matrix
			lowerCAmelCase__      :      int
			lowerCAmelCase__      :      int
			lowerCAmelCase__      :      int

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

			lowerCAmelCase__      :      int         =		solve(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )

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

			return interpolated_func
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		int:
			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_ = question_function       ,							SCREAMING_SNAKE_CASE_ = 10     )				->		int:
			lowerCAmelCase__      :      list[int]         =		[func(SCREAMING_SNAKE_CASE_     ) for x_val in range(1       ,							order + 1     )]

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

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

			for poly in polynomials:
						lowerCAmelCase__      :      List[str]         =		1
						while func(SCREAMING_SNAKE_CASE_     ) == poly(SCREAMING_SNAKE_CASE_     ):
									x_val += 1

						ret += poly(SCREAMING_SNAKE_CASE_     )

			return ret


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

import json
import os
import unittest

from transformers import BatchEncoding, MvpTokenizer, MvpTokenizerFast
from transformers.models.roberta.tokenization_roberta import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers, require_torch
from transformers.utils import cached_property

from ...test_tokenization_common import TokenizerTesterMixin, filter_roberta_detectors







@require_tokenizers
class      A__							(     __magic_name__						,   unittest.TestCase	):
				lowercase			    =  MvpTokenizer
				lowercase			    =  MvpTokenizerFast
				lowercase			    =  True
				lowercase			    =  filter_roberta_detectors






				def 							_lowerCamelCase		(						self					:      int   ):






							'''simple docstring'''







							super().setUp()
							lowerCAmelCase__      :      Dict         =		[
							    'l',
							    'o',
							    'w',
							    'e',
							    'r',
							    's',
							    't',
							    'i',
							    'd',
							    'n',
							    '\u0120',
							    '\u0120l',
							    '\u0120n',
							    '\u0120lo',
							    '\u0120low',
							    'er',
							    '\u0120lowest',
							    '\u0120newer',
							    '\u0120wider',
							    '<unk>',
							]
							lowerCAmelCase__      :      Any         =		dict(zip(a    ,     range(len(a   )   )   )   )
							lowerCAmelCase__      :      Union[str, Any]         =		['#version: 0.2', '\u0120 l', '\u0120l o', '\u0120lo w', 'e r', '']
							lowerCAmelCase__      :      Any         =		{'unk_token': '<unk>'}

							lowerCAmelCase__      :      int         =		os.path.join(self.tmpdirname    ,     VOCAB_FILES_NAMES['vocab_file']   )
							lowerCAmelCase__      :      Optional[int]         =		os.path.join(self.tmpdirname    ,     VOCAB_FILES_NAMES['merges_file']   )
							with open(self.vocab_file    ,     'w'    ,     encoding='utf-8'   ) as fp:
										fp.write(json.dumps(a   ) + '\n'   )
							with open(self.merges_file    ,     'w'    ,     encoding='utf-8'   ) as fp:
										fp.write('\n'.join(a   )   )






				def 							_lowerCamelCase		(						self					:      str    ,     **a					:      Tuple   ):






							'''simple docstring'''







							kwargs.update(self.special_tokens_map   )
							return self.tokenizer_class.from_pretrained(self.tmpdirname    ,     **a   )






				def 							_lowerCamelCase		(						self					:      Dict    ,     **a					:      Optional[int]   ):






							'''simple docstring'''







							kwargs.update(self.special_tokens_map   )
							return self.rust_tokenizer_class.from_pretrained(self.tmpdirname    ,     **a   )






				def 							_lowerCamelCase		(						self					:      Tuple    ,     a					:      Dict   ):






							'''simple docstring'''







							return "lower newer", "lower newer"






				@cached_property
				def 							_lowerCamelCase		(						self					:      List[str]   ):






							'''simple docstring'''







							return MvpTokenizer.from_pretrained('RUCAIBox/mvp'   )






				@cached_property
				def 							_lowerCamelCase		(						self					:      Dict   ):






							'''simple docstring'''







							return MvpTokenizerFast.from_pretrained('RUCAIBox/mvp'   )






				@require_torch
				def 							_lowerCamelCase		(						self					:      Optional[int]   ):






							'''simple docstring'''







							lowerCAmelCase__      :      List[Any]         =		['A long paragraph for summarization.', 'Another paragraph for summarization.']
							lowerCAmelCase__      :      List[Any]         =		[0, 250, 251, 17_818, 13, 39_186, 1_938, 4, 2]

							for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
										lowerCAmelCase__      :      int         =		tokenizer(a    ,     max_length=len(a   )    ,     padding=a    ,     return_tensors='pt'   )
										self.assertIsInstance(a    ,     a   )

										self.assertEqual((2, 9)    ,     batch.input_ids.shape   )
										self.assertEqual((2, 9)    ,     batch.attention_mask.shape   )
										lowerCAmelCase__      :      List[Any]         =		batch.input_ids.tolist()[0]
										self.assertListEqual(a    ,     a   )
										# Test that special tokens are reset






				@require_torch
				def 							_lowerCamelCase		(						self					:      str   ):






							'''simple docstring'''







							lowerCAmelCase__      :      List[Any]         =		['A long paragraph for summarization.', 'Another paragraph for summarization.']
							for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
										lowerCAmelCase__      :      Any         =		tokenizer(a    ,     padding=a    ,     return_tensors='pt'   )
										# check if input_ids are returned and no labels
										self.assertIn('input_ids'    ,     a   )
										self.assertIn('attention_mask'    ,     a   )
										self.assertNotIn('labels'    ,     a   )
										self.assertNotIn('decoder_attention_mask'    ,     a   )






				@require_torch
				def 							_lowerCamelCase		(						self					:      Optional[int]   ):






							'''simple docstring'''







							lowerCAmelCase__      :      Union[str, Any]         =		[
							    'Summary of the text.',
							    'Another summary.',
							]
							for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
										lowerCAmelCase__      :      Tuple         =		tokenizer(text_target=a    ,     max_length=32    ,     padding='max_length'    ,     return_tensors='pt'   )
										self.assertEqual(32    ,     targets['input_ids'].shape[1]   )






				@require_torch
				def 							_lowerCamelCase		(						self					:      Optional[int]   ):






							'''simple docstring'''







							for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
										lowerCAmelCase__      :      str         =		tokenizer(
										    ['I am a small frog' * 1_024, 'I am a small frog']    ,     padding=a    ,     truncation=a    ,     return_tensors='pt'   )
										self.assertIsInstance(a    ,     a   )
										self.assertEqual(batch.input_ids.shape    ,     (2, 1_024)   )






				@require_torch
				def 							_lowerCamelCase		(						self					:      Any   ):






							'''simple docstring'''







							lowerCAmelCase__      :      Union[str, Any]         =		['A long paragraph for summarization.']
							lowerCAmelCase__      :      Any         =		[
							    'Summary of the text.',
							]
							for tokenizer in [self.default_tokenizer, self.default_tokenizer_fast]:
										lowerCAmelCase__      :      List[Any]         =		tokenizer(a    ,     text_target=a    ,     return_tensors='pt'   )
										lowerCAmelCase__      :      Optional[int]         =		inputs['input_ids']
										lowerCAmelCase__      :      str         =		inputs['labels']
										self.assertTrue((input_ids[:, 0] == tokenizer.bos_token_id).all().item()   )
										self.assertTrue((labels[:, 0] == tokenizer.bos_token_id).all().item()   )
										self.assertTrue((input_ids[:, -1] == tokenizer.eos_token_id).all().item()   )
										self.assertTrue((labels[:, -1] == tokenizer.eos_token_id).all().item()   )






				def 							_lowerCamelCase		(						self					:      Any   ):






							'''simple docstring'''







							pass






				def 							_lowerCamelCase		(						self					:      Tuple   ):






							'''simple docstring'''







							for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
										with self.subTest(f'''{tokenizer.__class__.__name__} ({pretrained_name})'''   ):
													lowerCAmelCase__      :      str         =		self.rust_tokenizer_class.from_pretrained(a    ,     **a   )
													lowerCAmelCase__      :      List[str]         =		self.tokenizer_class.from_pretrained(a    ,     **a   )
													lowerCAmelCase__      :      Optional[int]         =		'A, <mask> AllenNLP sentence.'
													lowerCAmelCase__      :      int         =		tokenizer_r.encode_plus(a    ,     add_special_tokens=a    ,     return_token_type_ids=a   )
													lowerCAmelCase__      :      Optional[int]         =		tokenizer_p.encode_plus(a    ,     add_special_tokens=a    ,     return_token_type_ids=a   )

													# token_type_ids should put 0 everywhere
													self.assertEqual(sum(tokens_r['token_type_ids']   )    ,     sum(tokens_p['token_type_ids']   )   )

													# attention_mask should put 1 everywhere, so sum over length should be 1
													self.assertEqual(
													    sum(tokens_r['attention_mask']   ) / len(tokens_r['attention_mask']   )    ,     sum(tokens_p['attention_mask']   ) / len(tokens_p['attention_mask']   )    ,     )

													lowerCAmelCase__      :      List[Any]         =		tokenizer_r.convert_ids_to_tokens(tokens_r['input_ids']   )
													lowerCAmelCase__      :      Dict         =		tokenizer_p.convert_ids_to_tokens(tokens_p['input_ids']   )

													# Rust correctly handles the space before the mask while python doesnt
													self.assertSequenceEqual(tokens_p['input_ids']    ,     [0, 250, 6, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]   )
													self.assertSequenceEqual(tokens_r['input_ids']    ,     [0, 250, 6, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]   )

													self.assertSequenceEqual(
													    a    ,     ['<s>', 'A', ',', '<mask>', 'ĠAllen', 'N', 'LP', 'Ġsentence', '.', '</s>']   )
													self.assertSequenceEqual(
													    a    ,     ['<s>', 'A', ',', '<mask>', 'ĠAllen', 'N', 'LP', 'Ġsentence', '.', '</s>']   )