






from __future__ import annotations

from collections.abc import Callable

SCREAMING_SNAKE_CASE__   :      Optional[Any]				=		list[list[float | int]]

def   __lowercase       (			snake_case,	snake_case			):







				"""simple docstring"""






				__magic_name__		:int   =   len(snake_case			)
				__magic_name__		:Matrix   =   [[0 for _ in range(size + 1			)] for _ in range(snake_case			)]
				__magic_name__		:int
				__magic_name__		:int
				__magic_name__		:int
				__magic_name__		:int
				__magic_name__		:int
				__magic_name__		:float

				for row in range(snake_case			):
								for col in range(snake_case			):
												__magic_name__		:Optional[Any]   =   matrix[row][col]

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

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

								for rowa in range(row + 1,	snake_case			):
												__magic_name__		:List[Any]   =   augmented[rowa][col] / augmented[row][col]
												__magic_name__		: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,	snake_case			):
								for row in range(snake_case			):
												__magic_name__		:int   =   augmented[row][col] / augmented[col][col]
												for cola in range(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],	1_0			)] for row in range(snake_case			)
				]

def   __lowercase       (			snake_case			):







				"""simple docstring"""






				__magic_name__		:int   =   len(snake_case			)
				__magic_name__		:Matrix   =   [[0 for _ in range(snake_case			)] for _ in range(snake_case			)]
				__magic_name__		:Matrix   =   [[0] for _ in range(snake_case			)]
				__magic_name__		:Matrix
				__magic_name__		:int
				__magic_name__		:int
				__magic_name__		:int

				for x_val, y_val in enumerate(snake_case			):
								for col in range(snake_case			):
												__magic_name__		:Union[str, Any]   =   (x_val + 1) ** (size - col - 1)
								__magic_name__		:Optional[int]   =   y_val

				__magic_name__		:List[str]   =   solve(snake_case,	snake_case			)

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

				return interpolated_func

def   __lowercase       (			snake_case			):







				"""simple docstring"""






				return (
				    1
				    - variable
				    + variable**2
				    - variable**3
				    + variable**4
				    - variable**5
				    + variable**6
				    - variable**7
				    + variable**8
				    - variable**9
				    + variable**1_0
				)

def   __lowercase       (			snake_case = question_function,	snake_case = 1_0			):







				"""simple docstring"""






				__magic_name__		:list[int]   =   [func(snake_case			) for x_val in range(1,	order + 1			)]

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

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

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

								ret += poly(snake_case			)

				return ret


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








'''simple docstring'''
import comet  # From: unbabel-comet
import torch

import datasets


lowercase__											=datasets.logging.get_logger(__name__)

lowercase__											='\\n@inproceedings{rei-EtAl:2020:WMT,\n   author    = {Rei, Ricardo  and  Stewart, Craig  and  Farinha, Ana C  and  Lavie, Alon},\n   title     = {Unbabel\'s Participation in the WMT20 Metrics Shared Task},\n   booktitle      = {Proceedings of the Fifth Conference on Machine Translation},\n   month          = {November},\n   year           = {2020},\n   address        = {Online},\n   publisher      = {Association for Computational Linguistics},\n   pages     = {909--918},\n}\n@inproceedings{rei-etal-2020-comet,\n   title = "{COMET}: A Neural Framework for {MT} Evaluation",\n   author = "Rei, Ricardo  and\n      Stewart, Craig  and\n      Farinha, Ana C  and\n      Lavie, Alon",\n   booktitle = "Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP)",\n   month = nov,\n   year = "2020",\n   address = "Online",\n   publisher = "Association for Computational Linguistics",\n   url = "https://www.aclweb.org/anthology/2020.emnlp-main.213",\n   pages = "2685--2702",\n}\n'

lowercase__											='\\nCrosslingual Optimized Metric for Evaluation of Translation (COMET) is an open-source framework used to train Machine Translation metrics that achieve high levels of correlation with different types of human judgments (HTER, DA\'s or MQM).\nWith the release of the framework the authors also released fully trained models that were used to compete in the WMT20 Metrics Shared Task achieving SOTA in that years competition.\n\nSee the [README.md] file at https://unbabel.github.io/COMET/html/models.html for more information.\n'

lowercase__											='\nCOMET score.\n\nArgs:\n\n`sources` (list of str): Source sentences\n`predictions` (list of str): candidate translations\n`references` (list of str): reference translations\n`cuda` (bool): If set to True, runs COMET using GPU\n`show_progress` (bool): Shows progress\n`model`: COMET model to be used. Will default to `wmt-large-da-estimator-1719` if None.\n\nReturns:\n    `samples`: List of dictionaries with `src`, `mt`, `ref` and `score`.\n    `scores`: List of scores.\n\nExamples:\n\n    >>> comet_metric = datasets.load_metric(\'comet\')\n    >>> # comet_metric = load_metric(\'comet\', \'wmt20-comet-da\')  # you can also choose which model to use\n    >>> source = ["Dem Feuer konnte Einhalt geboten werden", "Schulen und Kindergärten wurden eröffnet."]\n    >>> hypothesis = ["The fire could be stopped", "Schools and kindergartens were open"]\n    >>> reference = ["They were able to control the fire.", "Schools and kindergartens opened"]\n    >>> results = comet_metric.compute(predictions=hypothesis, references=reference, sources=source)\n    >>> print([round(v, 2) for v in results["scores"]])\n    [0.19, 0.92]\n'







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION		,  _KWARGS_DESCRIPTION					)
class   a_ (      datasets.Metric					):




			def 					lowerCAmelCase__					(       self	):
				return datasets.MetricInfo(
				    description=_DESCRIPTION					,   citation=_CITATION					,   homepage="""https://unbabel.github.io/COMET/html/index.html"""					,   inputs_description=_KWARGS_DESCRIPTION					,   features=datasets.Features(
				        {
				            """sources""": datasets.Value("""string"""					,   id="""sequence"""	),
				            """predictions""": datasets.Value("""string"""					,   id="""sequence"""	),
				            """references""": datasets.Value("""string"""					,   id="""sequence"""	),
				        }	)					,   codebase_urls=["""https://github.com/Unbabel/COMET"""]					,   reference_urls=[
				        """https://github.com/Unbabel/COMET""",
				        """https://www.aclweb.org/anthology/2020.emnlp-main.213/""",
				        """http://www.statmt.org/wmt20/pdf/2020.wmt-1.101.pdf6""",
				    ]					,   )




			def 					lowerCAmelCase__					(       self					,   UpperCAmelCase	):
				if self.config_name == "default":
					a_      				=						comet.load_from_checkpoint(comet.download_model("""wmt20-comet-da"""	)	)
				else:
					a_      				=						comet.load_from_checkpoint(comet.download_model(self.config_name	)	)






			def 					lowerCAmelCase__					(       self					,   UpperCAmelCase					,   UpperCAmelCase					,   UpperCAmelCase					,   UpperCAmelCase=None					,   UpperCAmelCase=False	):
				if gpus is None:
					a_      				=						1 if torch.cuda.is_available() else 0
				a_      				=						{"""src""": sources, """mt""": predictions, """ref""": references}
				a_      				=						[dict(zip(UpperCAmelCase					,   UpperCAmelCase	)	) for t in zip(*data.values()	)]
				a_				,  a_      				=						self.scorer.predict(UpperCAmelCase					,   gpus=UpperCAmelCase					,   progress_bar=UpperCAmelCase	)
				return {"mean_score": mean_score, "scores": scores}
