


from __future__ import annotations

from collections.abc import Callable

snake_case__			 =						list[list[float | int]]


def 				lowerCamelCase__	(      a	:   Matrix	,  a	:   Matrix				)    ->	Matrix:





			"""simple docstring"""
			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__ :Optional[int]						  =    matrix[row][col]

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

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

						for rowa in range(row + 1	,  a				):
									a__ :Dict						  =    augmented[rowa][col] / augmented[row][col]
									a__ :Tuple						  =    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__ :Union[str, 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 				lowerCamelCase__	(      a	:   list[int]				)    ->	Callable[[int], int]:





			"""simple docstring"""
			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__ :Optional[Any]						  =    (x_val + 1) ** (size - col - 1)
						a__ :List[str]						  =    y_val

			a__ :str						  =    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 				lowerCamelCase__	(      a	:   int				)    ->	int:





			"""simple docstring"""
			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)


def 				lowerCamelCase__	(      a	:   Callable[[int], int] = question_function	,  a	:   int = 10				)    ->	int:





			"""simple docstring"""
			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() = }''')






import datasets

from .evaluate import evaluate


snake_case__			 =						'''\
@inproceedings{Rajpurkar2016SQuAD10,
  title={SQuAD: 100, 000+ Questions for Machine Comprehension of Text},
  author={Pranav Rajpurkar and Jian Zhang and Konstantin Lopyrev and Percy Liang},
  booktitle={EMNLP},
  year={2016}
}
'''

snake_case__			 =						'''
This metric wrap the official scoring script for version 1 of the Stanford Question Answering Dataset (SQuAD).

Stanford Question Answering Dataset (SQuAD) is a reading comprehension dataset, consisting of questions posed by
crowdworkers on a set of Wikipedia articles, where the answer to every question is a segment of text, or span,
from the corresponding reading passage, or the question might be unanswerable.
'''

snake_case__			 =						'''
Computes SQuAD scores (F1 and EM).
Args:
    predictions: List of question-answers dictionaries with the following key-values:
        - \'id\': id of the question-answer pair as given in the references (see below)
        - \'prediction_text\': the text of the answer
    references: List of question-answers dictionaries with the following key-values:
        - \'id\': id of the question-answer pair (see above),
        - \'answers\': a Dict in the SQuAD dataset format
            {
                \'text\': list of possible texts for the answer, as a list of strings
                \'answer_start\': list of start positions for the answer, as a list of ints
            }
            Note that answer_start values are not taken into account to compute the metric.
Returns:
    \'exact_match\': Exact match (the normalized answer exactly match the gold answer)
    \'f1\': The F-score of predicted tokens versus the gold answer
Examples:

    >>> predictions = [{\'prediction_text\': \'1976\', \'id\': \'56e10a3be3433e1400422b22\'}]
    >>> references = [{\'answers\': {\'answer_start\': [97], \'text\': [\'1976\']}, \'id\': \'56e10a3be3433e1400422b22\'}]
    >>> squad_metric = datasets.load_metric("squad")
    >>> results = squad_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {\'exact_match\': 100.0, \'f1\': 100.0}
'''


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




						def  _snake_case					(	self						:   List[str]						)      ->Union[str, Any]:






									"""simple docstring"""






									return datasets.MetricInfo(
									    description=_DESCRIPTION   ,     citation=_CITATION   ,     inputs_description=_KWARGS_DESCRIPTION   ,     features=datasets.Features(
									        {
									            "predictions": {"id": datasets.Value("string"						), "prediction_text": datasets.Value("string"						)},
									            "references": {
									                "id": datasets.Value("string"						),
									                "answers": datasets.features.Sequence(
									                    {
									                        "text": datasets.Value("string"						),
									                        "answer_start": datasets.Value("int32"						),
									                    }						),
									            },
									        }						)   ,     codebase_urls=["https://rajpurkar.github.io/SQuAD-explorer/"]   ,     reference_urls=["https://rajpurkar.github.io/SQuAD-explorer/"]   ,     )






						def  _snake_case					(	self						:   Dict   ,     __A						:   List[Any]   ,     __A						:   Optional[int]						)      ->str:






									"""simple docstring"""






									a__ :Optional[int]						  =    {prediction["id"]: prediction["prediction_text"] for prediction in predictions}
									a__ :Optional[Any]						  =    [
									    {
									        "paragraphs": [
									            {
									                "qas": [
									                    {
									                        "answers": [{"text": answer_text} for answer_text in ref["answers"]["text"]],
									                        "id": ref["id"],
									                    }
									                    for ref in references
									                ]
									            }
									        ]
									    }
									]
									a__ :Union[str, Any]						  =    evaluate(dataset=__A   ,     predictions=__A						)
									return score


