



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

import datasets


_lowercase		:				int      		='\\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'


_lowercase		:				int      		='\\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'


_lowercase		:				Union[str, Any]      		=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        snake_case__    (datasets.Metric		):







						"""simple docstring"""




						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				Dict:
									"""simple docstring"""




									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 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase  ) ->				Optional[Any]:
									"""simple docstring"""




									a__       :						List[Any]							=  0.0
									for i, j in zip(_lowercase ,       _lowercase  ):
												n_correct += 1.0 if math_equivalence.is_equiv(_lowercase ,       _lowercase  ) else 0.0
									a__       :						Any							=  n_correct / len(_lowercase  )
									return {
									    "accuracy": accuracy,
									}









from __future__ import annotations

import math

def      lowerCAmelCase_					(  _lowercase    :       int)							->	list[int]:







			"""simple docstring"""

			if num <= 0:
						a__       :						Tuple							=  F'''{num}: Invalid input, please enter a positive integer.'''
						raise ValueError(_lowercase)

			a__       :						List[Any]							=  [True] * (num + 1)
			a__       :						List[str]							=  []
			a__       :						List[Any]							=  2
			a__       :						Optional[int]							=  int(math.sqrt(_lowercase))

			while start <= end:
						# If start is a prime
						if sieve[start] is True:
									prime.append(_lowercase)

									# Set multiples of start be False
									for i in range(start * start						,       num + 1						,       _lowercase):
												if sieve[i] is True:
															a__       :						Optional[int]							=  False

						start += 1

			for j in range(end + 1						,       num + 1):
						if sieve[j] is True:
									prime.append(_lowercase)

			return prime


if __name__ == "__main__":
		print(prime_sieve(int(input("Enter a positive integer: ").strip())))




