



'''simple docstring'''

from sklearn.metrics import fa_score, matthews_corrcoef

import datasets

from .record_evaluation import evaluate as evaluate_record


__lowerCAmelCase						      =       '''\
@article{wang2019superglue,
  title={SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems},
  author={Wang, Alex and Pruksachatkun, Yada and Nangia, Nikita and Singh, Amanpreet and Michael, Julian and Hill, Felix and Levy, Omer and Bowman, Samuel R},
  journal={arXiv preprint arXiv:1905.00537},
  year={2019}
}
'''

__lowerCAmelCase						      =       '''\
SuperGLUE (https://super.gluebenchmark.com/) is a new benchmark styled after
GLUE with a new set of more difficult language understanding tasks, improved
resources, and a new public leaderboard.
'''

__lowerCAmelCase						      =       '''
Compute SuperGLUE evaluation metric associated to each SuperGLUE dataset.
Args:
    predictions: list of predictions to score. Depending on the SuperGlUE subset:
        - for \'record\': list of question-answer dictionaries with the following keys:
            - \'idx\': index of the question as specified by the dataset
            - \'prediction_text\': the predicted answer text
        - for \'multirc\': list of question-answer dictionaries with the following keys:
            - \'idx\': index of the question-answer pair as specified by the dataset
            - \'prediction\': the predicted answer label
        - otherwise: list of predicted labels
    references: list of reference labels. Depending on the SuperGLUE subset:
        - for \'record\': list of question-answers dictionaries with the following keys:
            - \'idx\': index of the question as specified by the dataset
            - \'answers\': list of possible answers
        - otherwise: list of reference labels
Returns: depending on the SuperGLUE subset:
    - for \'record\':
        - \'exact_match\': Exact match between answer and gold answer
        - \'f1\': F1 score
    - for \'multirc\':
        - \'exact_match\': Exact match between answer and gold answer
        - \'f1_m\': Per-question macro-F1 score
        - \'f1_a\': Average F1 score over all answers
    - for \'axb\':
        \'matthews_correlation\': Matthew Correlation
    - for \'cb\':
        - \'accuracy\': Accuracy
        - \'f1\': F1 score
    - for all others:
        - \'accuracy\': Accuracy
Examples:

    >>> super_glue_metric = datasets.load_metric(\'super_glue\', \'copa\')  # any of [\"copa\", \"rte\", \"wic\", \"wsc\", \"wsc.fixed\", \"boolq\", \"axg\"]
    >>> predictions = [0, 1]
    >>> references = [0, 1]
    >>> results = super_glue_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {\'accuracy\': 1.0}

    >>> super_glue_metric = datasets.load_metric(\'super_glue\', \'cb\')
    >>> predictions = [0, 1]
    >>> references = [0, 1]
    >>> results = super_glue_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {\'accuracy\': 1.0, \'f1\': 1.0}

    >>> super_glue_metric = datasets.load_metric(\'super_glue\', \'record\')
    >>> predictions = [{\'idx\': {\'passage\': 0, \'query\': 0}, \'prediction_text\': \'answer\'}]
    >>> references = [{\'idx\': {\'passage\': 0, \'query\': 0}, \'answers\': [\'answer\', \'another_answer\']}]
    >>> results = super_glue_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {\'exact_match\': 1.0, \'f1\': 1.0}

    >>> super_glue_metric = datasets.load_metric(\'super_glue\', \'multirc\')
    >>> predictions = [{\'idx\': {\'answer\': 0, \'paragraph\': 0, \'question\': 0}, \'prediction\': 0}, {\'idx\': {\'answer\': 1, \'paragraph\': 2, \'question\': 3}, \'prediction\': 1}]
    >>> references = [0, 1]
    >>> results = super_glue_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {\'exact_match\': 1.0, \'f1_m\': 1.0, \'f1_a\': 1.0}

    >>> super_glue_metric = datasets.load_metric(\'super_glue\', \'axb\')
    >>> references = [0, 1]
    >>> predictions = [0, 1]
    >>> results = super_glue_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {\'matthews_correlation\': 1.0}
'''



def        __lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_  )      ->				Any:
		return float((preds == labels).mean()  )



def        __lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_						,      lowerCAmelCase_="binary"  )      ->				List[str]:
		_a					:				Any				=							simple_accuracy(lowerCAmelCase_						,      lowerCAmelCase_  )
		_a					:				Optional[Any]				=							float(fa_score(y_true=lowerCAmelCase_						,      y_pred=lowerCAmelCase_						,      average=lowerCAmelCase_  )  )
		return {
		    "accuracy": acc,
		    "f1": fa,
		}



def        __lowerCamelCase					(				lowerCAmelCase_						,      lowerCAmelCase_  )      ->				Dict:
		_a					:				Tuple				=							{}
		for id_pred, label in zip(lowerCAmelCase_						,      lowerCAmelCase_  ):
				_a					:				Dict				=							f"""{id_pred['idx']['paragraph']}-{id_pred['idx']['question']}"""
				_a					:				int				=							id_pred['prediction']
				if question_id in question_map:
						question_map[question_id].append((pred, label)  )
				else:
						_a					:				Dict				=							[(pred, label)]
		_a	, _a					:				Union[str, Any]				=							[], []
		for question, preds_labels in question_map.items():
				_a	, _a					:				List[Any]				=							zip(*lowerCAmelCase_  )
				_a					:				Union[str, Any]				=							fa_score(y_true=lowerCAmelCase_						,      y_pred=lowerCAmelCase_						,      average='macro'  )
				fas.append(lowerCAmelCase_  )
				_a					:				Union[str, Any]				=							int(sum(pred == label for pred, label in preds_labels  ) == len(lowerCAmelCase_  )  )
				ems.append(lowerCAmelCase_  )
		_a					:				int				=							float(sum(lowerCAmelCase_  ) / len(lowerCAmelCase_  )  )
		_a					:				Union[str, Any]				=							sum(lowerCAmelCase_  ) / len(lowerCAmelCase_  )
		_a					:				Optional[Any]				=							float(fa_score(y_true=lowerCAmelCase_						,      y_pred=[id_pred['prediction'] for id_pred in ids_preds]  )  )
		return {"exact_match": em, "f1_m": fa_m, "f1_a": fa_a}

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







							def 							__lowercase      (							self :	Optional[int]		):
									if self.config_name not in [
									    "boolq",
									    "cb",
									    "copa",
									    "multirc",
									    "record",
									    "rte",
									    "wic",
									    "wsc",
									    "wsc.fixed",
									    "axb",
									    "axg",
									]:
											raise KeyError(
											    'You should supply a configuration name selected in '
											    '["boolq", "cb", "copa", "multirc", "record", "rte", "wic", "wsc", "wsc.fixed", "axb", "axg",]'		)
									return datasets.MetricInfo(
									    description=_DESCRIPTION     ,citation=_CITATION     ,inputs_description=_KWARGS_DESCRIPTION     ,features=datasets.Features(self._get_feature_types()		)     ,codebase_urls=[]     ,reference_urls=[]     ,format='numpy' if not self.config_name == 'record' and not self.config_name == 'multirc' else None     ,)







							def 							__lowercase      (							self :	str		):
									if self.config_name == "record":
											return {
											    "predictions": {
											        "idx": {
											            "passage": datasets.Value('int64'		),
											            "query": datasets.Value('int64'		),
											        },
											        "prediction_text": datasets.Value('string'		),
											    },
											    "references": {
											        "idx": {
											            "passage": datasets.Value('int64'		),
											            "query": datasets.Value('int64'		),
											        },
											        "answers": datasets.Sequence(datasets.Value('string'		)		),
											    },
											}
									elif self.config_name == "multirc":
											return {
											    "predictions": {
											        "idx": {
											            "answer": datasets.Value('int64'		),
											            "paragraph": datasets.Value('int64'		),
											            "question": datasets.Value('int64'		),
											        },
											        "prediction": datasets.Value('int64'		),
											    },
											    "references": datasets.Value('int64'		),
											}
									else:
											return {
											    "predictions": datasets.Value('int64'		),
											    "references": datasets.Value('int64'		),
											}







							def 							__lowercase      (							self :	int     ,_UpperCAmelCase :	List[Any]     ,_UpperCAmelCase :	Optional[int]		):
									if self.config_name == "axb":
											return {"matthews_correlation": matthews_corrcoef(UpperCAmelCase__     ,UpperCAmelCase__		)}
									elif self.config_name == "cb":
											return acc_and_fa(UpperCAmelCase__     ,UpperCAmelCase__     ,fa_avg='macro'		)
									elif self.config_name == "record":
											_a					:				str				=							[
											    {
											        'qas': [
											            {'id': ref['idx']['query'], 'answers': [{'text': ans} for ans in ref['answers']]}
											            for ref in references
											        ]
											    }
											]
											_a					:				Dict				=							{pred['idx']['query']: pred['prediction_text'] for pred in predictions}
											return evaluate_record(UpperCAmelCase__     ,UpperCAmelCase__		)[0]
									elif self.config_name == "multirc":
											return evaluate_multirc(UpperCAmelCase__     ,UpperCAmelCase__		)
									elif self.config_name in ["copa", "rte", "wic", "wsc", "wsc.fixed", "boolq", "axg"]:
											return {"accuracy": simple_accuracy(UpperCAmelCase__     ,UpperCAmelCase__		)}
									else:
											raise KeyError(
											    'You should supply a configuration name selected in '
											    '["boolq", "cb", "copa", "multirc", "record", "rte", "wic", "wsc", "wsc.fixed", "axb", "axg",]'		)









'''simple docstring'''

from math import sqrt



def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				int:
		_a					:				Dict				=							0
		for i in range(1						,      int(sqrt(lowerCAmelCase_  ) + 1  )  ):
				if n % i == 0 and i != sqrt(lowerCAmelCase_  ):
						total += i + n // i
				elif i == sqrt(lowerCAmelCase_  ):
						total += i
		return total - n



def 					__lowerCamelCase					(				lowerCAmelCase_ = 10000  )      ->				int:
		_a					:				Union[str, Any]				=							sum(
		    i
		    for i in range(1						,      lowerCAmelCase_  )
		    if sum_of_divisors(sum_of_divisors(lowerCAmelCase_  )  ) == i and sum_of_divisors(lowerCAmelCase_  ) != i  )
		return total


if __name__ == "__main__":
							print(solution(int(str(input()).strip())))




