



import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


SCREAMING_SNAKE_CASE     				=						"\\n@article{hendrycksmath2021,\n  title={Measuring Mathematical Problem Solving With the MATH Dataset},\n  author={Dan Hendrycks\n    and Collin Burns\n    and Saurav Kadavath\n    and Akul Arora\n    and Steven Basart\n    and Eric Tang\n    and Dawn Song\n    and Jacob Steinhardt},\n  journal={arXiv preprint arXiv:2103.03874},\n  year={2021}\n}\n"


SCREAMING_SNAKE_CASE     				=						"\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting \"1/2\" to \"\\frac{1}{2}\") and then computes accuracy.\n"


SCREAMING_SNAKE_CASE     				=						R"\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")\n\nExamples:\n    >>> metric = datasets.load_metric(\"competition_math\")\n    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])\n    >>> print(results)\n    {'accuracy': 1.0}\n"



@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION,     _KWARGS_DESCRIPTION  )
class 	lowerCamelCase      (						datasets.Metric  ):



					def    A__		(			self     ):
							return datasets.MetricInfo(
							    description=_DESCRIPTION    ,	citation=_CITATION    ,	inputs_description=_KWARGS_DESCRIPTION    ,	features=datasets.Features(
							        {
							            "predictions": datasets.Value("string"     ),
							            "references": datasets.Value("string"     ),
							        }     )    ,	homepage="https://github.com/hendrycks/math"    ,	codebase_urls=["https://github.com/hendrycks/math"]    ,	)



					def    A__		(			self    ,	lowerCAmelCase    ,	lowerCAmelCase     ):
							UpperCAmelCase_						=				0.0
							for i, j in zip(lowerCAmelCase    ,	lowerCAmelCase     ):
									n_correct += 1.0 if math_equivalence.is_equiv(lowerCAmelCase    ,	lowerCAmelCase     ) else 0.0
							UpperCAmelCase_						=				n_correct / len(lowerCAmelCase     )
							return {
							    "accuracy": accuracy,
							}






import math







def snake_case__  (			__SCREAMING_SNAKE_CASE )		->							list[int]:
		UpperCAmelCase_						=				[]
		UpperCAmelCase_						=				2
		UpperCAmelCase_						=				int(math.sqrt(__SCREAMING_SNAKE_CASE ) )  # Size of every segment
		UpperCAmelCase_						=				[True] * (end + 1)
		UpperCAmelCase_						=				[]

		while start <= end:
				if temp[start] is True:
						in_prime.append(__SCREAMING_SNAKE_CASE )
						for i in range(start * start			,     end + 1			,     __SCREAMING_SNAKE_CASE ):
								UpperCAmelCase_						=				False
				start += 1
		prime += in_prime

		UpperCAmelCase_						=				end + 1
		UpperCAmelCase_						=				min(2 * end			,     __SCREAMING_SNAKE_CASE )

		while low <= n:
				UpperCAmelCase_						=				[True] * (high - low + 1)
				for each in in_prime:
						UpperCAmelCase_						=				math.floor(low / each ) * each
						if t < low:
								t += each

						for j in range(__SCREAMING_SNAKE_CASE			,     high + 1			,     __SCREAMING_SNAKE_CASE ):
								UpperCAmelCase_						=				False

				for j in range(len(__SCREAMING_SNAKE_CASE ) ):
						if temp[j] is True:
								prime.append(j + low )

				UpperCAmelCase_						=				high + 1
				UpperCAmelCase_						=				min(high + end			,     __SCREAMING_SNAKE_CASE )

		return prime

print(sieve(10**6))

