

from __future__ import annotations

from collections.abc import Callable

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

def 		UpperCamelCase      (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__							:					List[str]       =	matrix[row][col]

		A__							:					int       =	vector[row][0]

	A__							:					Optional[int]       =	0
	A__							:					str       =	0
	while row < size and col < size:
		# pivoting
		A__							:					int       =	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__							:					List[Any]       =	augmented[rowa][col] / augmented[row][col]
			A__							:					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					,   lowercase_      ):
		for row in range(lowercase_      ):
			A__							:					List[str]       =	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 		UpperCamelCase      (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__							:					Dict       =	(x_val + 1) ** (size - col - 1)
		A__							:					Any       =	y_val

	A__							:					Union[str, Any]       =	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 		UpperCamelCase      (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 		UpperCamelCase      (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__							:					List[str]       =	1
		while func(lowercase_      ) == poly(lowercase_      ):
			x_val += 1

		ret += poly(lowercase_      )

	return ret


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






import os
import tempfile
import unittest
from pathlib import Path

from transformers import AutoConfig, is_torch_available
from transformers.testing_utils import require_torch, torch_device


if is_torch_available():
	from transformers import PyTorchBenchmark, PyTorchBenchmarkArguments



@require_torch
class 					_a		(unittest.TestCase       ):


					'''simple docstring'''






					def 						__A    (				self					, A__    ):
						for model_result in results.values():
							for batch_size, sequence_length in zip(model_result["""bs"""]					, model_result["""ss"""]    ):
								A__							:					str       =	model_result["""result"""][batch_size][sequence_length]
								self.assertIsNotNone(A__    )






					def 						__A    (				self    ):
						A__							:					Dict       =	"""sshleifer/tiny-gpt2"""
						A__							:					Tuple       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					int       =	PyTorchBenchmark(A__    )
						A__							:					List[Any]       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_inference_result    )
						self.check_results_dict_not_empty(results.memory_inference_result    )






					def 						__A    (				self    ):
						A__							:					Dict       =	"""sgugger/tiny-distilbert-classification"""
						A__							:					Dict       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, only_pretrain_model=A__					, )
						A__							:					str       =	PyTorchBenchmark(A__    )
						A__							:					List[str]       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_inference_result    )
						self.check_results_dict_not_empty(results.memory_inference_result    )






					def 						__A    (				self    ):
						A__							:					Any       =	"""sshleifer/tiny-gpt2"""
						A__							:					List[Any]       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, torchscript=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					Tuple       =	PyTorchBenchmark(A__    )
						A__							:					str       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_inference_result    )
						self.check_results_dict_not_empty(results.memory_inference_result    )






					@unittest.skipIf(torch_device == """cpu"""					, """Cant do half precision"""    )
					def 						__A    (				self    ):
						A__							:					Optional[Any]       =	"""sshleifer/tiny-gpt2"""
						A__							:					Optional[Any]       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, fpaa=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					str       =	PyTorchBenchmark(A__    )
						A__							:					Any       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_inference_result    )
						self.check_results_dict_not_empty(results.memory_inference_result    )






					def 						__A    (				self    ):
						A__							:					Optional[Any]       =	"""sshleifer/tiny-gpt2"""
						A__							:					Tuple       =	AutoConfig.from_pretrained(A__    )
						# set architectures equal to `None`
						A__							:					List[Any]       =	None
						A__							:					str       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					List[str]       =	PyTorchBenchmark(A__					, configs=[config]    )
						A__							:					Any       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_inference_result    )
						self.check_results_dict_not_empty(results.memory_inference_result    )






					def 						__A    (				self    ):
						A__							:					Optional[int]       =	"""sshleifer/tiny-gpt2"""
						A__							:					Optional[int]       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					Any       =	PyTorchBenchmark(A__    )
						A__							:					Dict       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_train_result    )
						self.check_results_dict_not_empty(results.memory_train_result    )






					@unittest.skipIf(torch_device == """cpu"""					, """Can't do half precision"""    )
					def 						__A    (				self    ):
						A__							:					Optional[int]       =	"""sshleifer/tiny-gpt2"""
						A__							:					List[str]       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, fpaa=A__					, multi_process=A__					, )
						A__							:					Dict       =	PyTorchBenchmark(A__    )
						A__							:					Optional[int]       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_train_result    )
						self.check_results_dict_not_empty(results.memory_train_result    )






					def 						__A    (				self    ):
						A__							:					int       =	"""sshleifer/tiny-gpt2"""
						A__							:					Optional[int]       =	AutoConfig.from_pretrained(A__    )
						A__							:					str       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					int       =	PyTorchBenchmark(A__					, configs=[config]    )
						A__							:					Tuple       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_inference_result    )
						self.check_results_dict_not_empty(results.memory_inference_result    )






					def 						__A    (				self    ):
						A__							:					List[str]       =	"""sshleifer/tinier_bart"""
						A__							:					List[str]       =	AutoConfig.from_pretrained(A__    )
						A__							:					List[str]       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					Union[str, Any]       =	PyTorchBenchmark(A__					, configs=[config]    )
						A__							:					str       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_inference_result    )
						self.check_results_dict_not_empty(results.memory_inference_result    )






					def 						__A    (				self    ):
						A__							:					Optional[int]       =	"""sshleifer/tiny-gpt2"""
						A__							:					Union[str, Any]       =	AutoConfig.from_pretrained(A__    )
						A__							:					Tuple       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					int       =	PyTorchBenchmark(A__					, configs=[config]    )
						A__							:					Tuple       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_train_result    )
						self.check_results_dict_not_empty(results.memory_train_result    )






					def 						__A    (				self    ):
						A__							:					Dict       =	"""sshleifer/tinier_bart"""
						A__							:					int       =	AutoConfig.from_pretrained(A__    )
						A__							:					Union[str, Any]       =	PyTorchBenchmarkArguments(
						    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, multi_process=A__					, )
						A__							:					List[Any]       =	PyTorchBenchmark(A__					, configs=[config]    )
						A__							:					Optional[Any]       =	benchmark.run()
						self.check_results_dict_not_empty(results.time_train_result    )
						self.check_results_dict_not_empty(results.memory_train_result    )






					def 						__A    (				self    ):
						A__							:					int       =	"""sshleifer/tiny-gpt2"""
						with tempfile.TemporaryDirectory() as tmp_dir:
							A__							:					Dict       =	PyTorchBenchmarkArguments(
							    models=[MODEL_ID]					, training=A__					, inference=A__					, save_to_csv=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, inference_time_csv_file=os.path.join(A__					, """inf_time.csv"""    )					, train_memory_csv_file=os.path.join(A__					, """train_mem.csv"""    )					, inference_memory_csv_file=os.path.join(A__					, """inf_mem.csv"""    )					, train_time_csv_file=os.path.join(A__					, """train_time.csv"""    )					, env_info_csv_file=os.path.join(A__					, """env.csv"""    )					, multi_process=A__					, )
							A__							:					Optional[Any]       =	PyTorchBenchmark(A__    )
							benchmark.run()
							self.assertTrue(Path(os.path.join(A__					, """inf_time.csv"""    )    ).exists()    )
							self.assertTrue(Path(os.path.join(A__					, """train_time.csv"""    )    ).exists()    )
							self.assertTrue(Path(os.path.join(A__					, """inf_mem.csv"""    )    ).exists()    )
							self.assertTrue(Path(os.path.join(A__					, """train_mem.csv"""    )    ).exists()    )
							self.assertTrue(Path(os.path.join(A__					, """env.csv"""    )    ).exists()    )






					def 						__A    (				self    ):
						A__							:					Optional[int]       =	"""sshleifer/tiny-gpt2"""

						def _check_summary_is_not_empty(A__    ):
							self.assertTrue(hasattr(A__					, """sequential"""    )    )
							self.assertTrue(hasattr(A__					, """cumulative"""    )    )
							self.assertTrue(hasattr(A__					, """current"""    )    )
							self.assertTrue(hasattr(A__					, """total"""    )    )

						with tempfile.TemporaryDirectory() as tmp_dir:
							A__							:					Dict       =	PyTorchBenchmarkArguments(
							    models=[MODEL_ID]					, training=A__					, inference=A__					, sequence_lengths=[8]					, batch_sizes=[1]					, log_filename=os.path.join(A__					, """log.txt"""    )					, log_print=A__					, trace_memory_line_by_line=A__					, multi_process=A__					, )
							A__							:					Dict       =	PyTorchBenchmark(A__    )
							A__							:					str       =	benchmark.run()
							_check_summary_is_not_empty(result.inference_summary    )
							_check_summary_is_not_empty(result.train_summary    )
							self.assertTrue(Path(os.path.join(A__					, """log.txt"""    )    ).exists()    )



