






from __future__ import annotations

import bisect





def 						__UpperCAmelCase			(     a_							,     a_							,     a_ = 0							,     a_ = -1):
							if hi < 0:
														snake_case_				=							len(lowercase__)

							while lo < hi:
														snake_case_				=							lo + (hi - lo) // 2
														if sorted_collection[mid] < item:
																					snake_case_				=							mid + 1
														else:
																					snake_case_				=							mid

							return lo





def 						__UpperCAmelCase			(     a_							,     a_							,     a_ = 0							,     a_ = -1):
							if hi < 0:
														snake_case_				=							len(lowercase__)

							while lo < hi:
														snake_case_				=							lo + (hi - lo) // 2
														if sorted_collection[mid] <= item:
																					snake_case_				=							mid + 1
														else:
																					snake_case_				=							mid

							return lo





def 						__UpperCAmelCase			(     a_							,     a_							,     a_ = 0							,     a_ = -1):
							sorted_collection.insert(bisect_left(lowercase__							,     lowercase__							,     lowercase__							,     lowercase__)							,     lowercase__)





def 						__UpperCAmelCase			(     a_							,     a_							,     a_ = 0							,     a_ = -1):
							sorted_collection.insert(bisect_right(lowercase__							,     lowercase__							,     lowercase__							,     lowercase__)							,     lowercase__)





def 						__UpperCAmelCase			(     a_							,     a_):
							snake_case_				=							0
							snake_case_				=							len(lowercase__) - 1

							while left <= right:
														snake_case_				=							left + (right - left) // 2
														snake_case_				=							sorted_collection[midpoint]
														if current_item == item:
																					return midpoint
														elif item < current_item:
																					snake_case_				=							midpoint - 1
														else:
																					snake_case_				=							midpoint + 1
							return None





def 						__UpperCAmelCase			(     a_							,     a_):
							snake_case_				=							bisect.bisect_left(lowercase__							,     lowercase__)
							if index != len(lowercase__) and sorted_collection[index] == item:
														return index
							return None





def 						__UpperCAmelCase			(     a_							,     a_							,     a_							,     a_):
							if right < left:
														return None

							snake_case_				=							left + (right - left) // 2

							if sorted_collection[midpoint] == item:
														return midpoint
							elif sorted_collection[midpoint] > item:
														return binary_search_by_recursion(lowercase__							,     lowercase__							,     lowercase__							,     midpoint - 1)
							else:
														return binary_search_by_recursion(lowercase__							,     lowercase__							,     midpoint + 1							,     lowercase__)


if __name__ == "__main__":
	lowercase  							=					input("Enter numbers separated by comma:\n").strip()
	lowercase  							=					sorted(int(item) for item in user_input.split(","))
	lowercase  							=					int(input("Enter a single number to be found in the list:\n"))
	lowercase  							=					binary_search(collection, target)
	if result is None:
		print(f'{target} was not found in {collection}.')
	else:
		print(f'{target} was found at position {result} in {collection}.')









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

import datasets


__lowerCAmelCase	: Optional[Any]  				='\\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'


__lowerCAmelCase	: Any  				='\\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'


__lowerCAmelCase	: Optional[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        _lowercase      (			datasets.Metric       ):






				'''simple docstring'''



				def 		__magic_name__(       self			:Optional[Any]	)		->			List[str]:
										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 		__magic_name__(       self			:Any			,			lowerCAmelCase__			:Optional[int]			,			lowerCAmelCase__			:Any	)		->			Optional[int]:
										__SCREAMING_SNAKE_CASE						:     Tuple					=		0.0
										for i, j in zip(lowerCAmelCase__			,			lowerCAmelCase__	):
																n_correct += 1.0 if math_equivalence.is_equiv(lowerCAmelCase__			,			lowerCAmelCase__	) else 0.0
										__SCREAMING_SNAKE_CASE						:     str					=		n_correct / len(lowerCAmelCase__	)
										return {
										    "accuracy": accuracy,
										}
