

from __future__ import annotations

from collections.abc import Callable

a		=list[list[float | int]]






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__      )  ->					Matrix:
	__lowerCamelCase    :    int 	=			len(lowerCamelCase__      )
	__lowerCamelCase    :    Matrix 	=			[[0 for _ in range(size + 1      )] for _ in range(lowerCamelCase__      )]
	__lowerCamelCase    :    int
	__lowerCamelCase    :    int
	__lowerCamelCase    :    int
	__lowerCamelCase    :    int
	__lowerCamelCase    :    int
	__lowerCamelCase    :    float

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

		__lowerCamelCase    :    Union[str, Any] 	=			vector[row][0]

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

		for rowa in range(row + 1     ,			lowerCamelCase__      ):
			__lowerCamelCase    :    Optional[int] 	=			augmented[rowa][col] / augmented[row][col]
			__lowerCamelCase    :    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__      ):
			__lowerCamelCase    :    str 	=			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]     ,			1_0      )] for row in range(lowerCamelCase__      )
	]






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					Callable[[int], int]:
	__lowerCamelCase    :    int 	=			len(lowerCamelCase__      )
	__lowerCamelCase    :    Matrix 	=			[[0 for _ in range(lowerCamelCase__      )] for _ in range(lowerCamelCase__      )]
	__lowerCamelCase    :    Matrix 	=			[[0] for _ in range(lowerCamelCase__      )]
	__lowerCamelCase    :    Matrix
	__lowerCamelCase    :    int
	__lowerCamelCase    :    int
	__lowerCamelCase    :    int

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

	__lowerCamelCase    :    str 	=			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        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					int:
	return (
	    1
	    - variable
	    + variable**2
	    - variable**3
	    + variable**4
	    - variable**5
	    + variable**6
	    - variable**7
	    + variable**8
	    - variable**9
	    + variable**1_0
	)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__ = question_function     ,			lowerCamelCase__ = 1_0      )  ->					int:
	__lowerCamelCase    :    list[int] 	=			[func(lowerCamelCase__      ) 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    :    Dict 	=			1
		while func(lowerCamelCase__      ) == poly(lowerCamelCase__      ):
			x_val += 1

		ret += poly(lowerCamelCase__      )

	return ret


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







import unittest
from pathlib import Path
from tempfile import TemporaryDirectory

from transformers import AutoConfig, TFGPTaLMHeadModel, is_keras_nlp_available, is_tf_available
from transformers.models.gpta.tokenization_gpta import GPTaTokenizer
from transformers.testing_utils import require_keras_nlp, require_tf, slow


if is_tf_available():
					import tensorflow as tf

if is_keras_nlp_available():
					from transformers.models.gpta import TFGPTaTokenizer


a		=["""gpt2"""]
a		="""gpt2"""

if is_tf_available():






					class 	A_		(	tf.Module    ):
												def __init__(		self		:      Tuple       ,SCREAMING_SNAKE_CASE__		:      Tuple):
													super().__init__()
													__lowerCamelCase    :    List[Any] 	=			tokenizer
													__lowerCamelCase    :    str 	=			AutoConfig.from_pretrained(SCREAMING_SNAKE_CASE__)
													__lowerCamelCase    :    Tuple 	=			TFGPTaLMHeadModel.from_config(SCREAMING_SNAKE_CASE__)


												@tf.function(input_signature=(tf.TensorSpec((None,)       ,tf.string       ,name='text'),))
												def    lowerCAmelCase					(		self		:      int       ,SCREAMING_SNAKE_CASE__		:      Optional[int]):
													__lowerCamelCase    :    str 	=			self.tokenizer(SCREAMING_SNAKE_CASE__)
													__lowerCamelCase    :    Dict 	=			tokenized['input_ids'].to_tensor()

													__lowerCamelCase    :    List[Any] 	=			tf.cast(input_ids_dense > 0       ,tf.intaa)
													# input_mask = tf.reshape(input_mask, [-1, MAX_SEQ_LEN])

													__lowerCamelCase    :    Union[str, Any] 	=			self.model(input_ids=SCREAMING_SNAKE_CASE__       ,attention_mask=SCREAMING_SNAKE_CASE__)['logits']

													return outputs






@require_tf
@require_keras_nlp
class 	A_		(	unittest.TestCase    ):
							def    lowerCAmelCase					(		self		:      List[str]):
								super().setUp()

								__lowerCamelCase    :    str 	=			[GPTaTokenizer.from_pretrained(SCREAMING_SNAKE_CASE__) for checkpoint in (TOKENIZER_CHECKPOINTS)]
								__lowerCamelCase    :    List[Any] 	=			[TFGPTaTokenizer.from_pretrained(SCREAMING_SNAKE_CASE__) for checkpoint in TOKENIZER_CHECKPOINTS]
								assert len(self.tokenizers) == len(self.tf_tokenizers)

								__lowerCamelCase    :    Optional[int] 	=			[
								    'This is a straightforward English test sentence.',
								    'This one has some weird characters\rto\nsee\r\nif  those\u00E9break things.',
								    'Now we\'re going to add some Chinese: 一 二 三 一二三',
								    'And some much more rare Chinese: 齉 堃 齉堃',
								    'Je vais aussi écrire en français pour tester les accents',
								    'Classical Irish also has some unusual characters, so in they go: Gaelaċ, ꝼ',
								]
								__lowerCamelCase    :    List[str] 	=			list(zip(self.test_sentences       ,self.test_sentences[::-1]))
							def    lowerCAmelCase					(		self		:      Optional[int]):
								for tokenizer, tf_tokenizer in zip(self.tokenizers       ,self.tf_tokenizers):
									for test_inputs in self.test_sentences:
										__lowerCamelCase    :    Union[str, Any] 	=			tokenizer([test_inputs]       ,return_tensors='tf')
										__lowerCamelCase    :    Dict 	=			tf_tokenizer([test_inputs])

										for key in python_outputs.keys():
											# convert them to numpy to avoid messing with ragged tensors
											__lowerCamelCase    :    List[str] 	=			python_outputs[key].numpy()
											__lowerCamelCase    :    Optional[Any] 	=			tf_outputs[key].numpy()

											self.assertTrue(tf.reduce_all(python_outputs_values.shape == tf_outputs_values.shape))
											self.assertTrue(tf.reduce_all(tf.cast(SCREAMING_SNAKE_CASE__       ,tf.intaa) == tf_outputs_values))
							@slow
							def    lowerCAmelCase					(		self		:      Optional[Any]):
								for tf_tokenizer in self.tf_tokenizers:
									__lowerCamelCase    :    Dict 	=			tf.function(SCREAMING_SNAKE_CASE__)
									for test_inputs in self.test_sentences:
										__lowerCamelCase    :    Any 	=			tf.constant(SCREAMING_SNAKE_CASE__)
										__lowerCamelCase    :    Dict 	=			compiled_tokenizer(SCREAMING_SNAKE_CASE__)
										__lowerCamelCase    :    Dict 	=			tf_tokenizer(SCREAMING_SNAKE_CASE__)

										for key in eager_outputs.keys():
											self.assertTrue(tf.reduce_all(eager_outputs[key] == compiled_outputs[key]))
							@slow
							def    lowerCAmelCase					(		self		:      str):
								for tf_tokenizer in self.tf_tokenizers:
									__lowerCamelCase    :    Any 	=			ModelToSave(tokenizer=SCREAMING_SNAKE_CASE__)
									__lowerCamelCase    :    Tuple 	=			tf.convert_to_tensor([self.test_sentences[0]])
									__lowerCamelCase    :    str 	=			model.serving(SCREAMING_SNAKE_CASE__)  # Build model with some sample inputs
									with TemporaryDirectory() as tempdir:
										__lowerCamelCase    :    Optional[Any] 	=			Path(SCREAMING_SNAKE_CASE__) / 'saved.model'
										tf.saved_model.save(SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__       ,signatures={'serving_default': model.serving})
										__lowerCamelCase    :    Tuple 	=			tf.saved_model.load(SCREAMING_SNAKE_CASE__)
									__lowerCamelCase    :    Optional[int] 	=			loaded_model.signatures['serving_default'](SCREAMING_SNAKE_CASE__)['output_0']
									# We may see small differences because the loaded model is compiled, so we need an epsilon for the test
									self.assertTrue(tf.reduce_all(out == loaded_output))
							@slow
							def    lowerCAmelCase					(		self		:      int):
								for tf_tokenizer in self.tf_tokenizers:
									__lowerCamelCase    :    Optional[int] 	=			tf.convert_to_tensor([self.test_sentences[0]])
									__lowerCamelCase    :    Optional[Any] 	=			tf_tokenizer(SCREAMING_SNAKE_CASE__)  # Build model with some sample inputs

									__lowerCamelCase    :    str 	=			tf_tokenizer.get_config()
									__lowerCamelCase    :    List[str] 	=			TFGPTaTokenizer.from_config(SCREAMING_SNAKE_CASE__)
									__lowerCamelCase    :    Optional[int] 	=			model_from_config(SCREAMING_SNAKE_CASE__)

									for key in from_config_output.keys():
										self.assertTrue(tf.reduce_all(from_config_output[key] == out[key]))


							@slow
							def    lowerCAmelCase					(		self		:      Dict):
								for tf_tokenizer in self.tf_tokenizers:
									# for the test to run
									__lowerCamelCase    :    List[Any] 	=			1_2_3_1_2_3

									for max_length in [3, 5, 1_0_2_4]:
										__lowerCamelCase    :    Dict 	=			tf.convert_to_tensor([self.test_sentences[0]])
										__lowerCamelCase    :    Union[str, Any] 	=			tf_tokenizer(SCREAMING_SNAKE_CASE__       ,max_length=SCREAMING_SNAKE_CASE__)

										__lowerCamelCase    :    List[Any] 	=			out['input_ids'].numpy().shape[1]

										assert out_length == max_length




