





from collections import defaultdict
from math import gcd
def      A__       (    SCREAMING_SNAKE_CASE_   :      int = 1_50_00_00						)  ->  int:






   """simple docstring"""







   _UpperCAmelCase           =   defaultdict(SCREAMING_SNAKE_CASE_						)
   _UpperCAmelCase           =   2
   while 2 * euclid_m * (euclid_m + 1) <= limit:
      for euclid_n in range((euclid_m % 2) + 1				,	SCREAMING_SNAKE_CASE_				,	2						):
         if gcd(SCREAMING_SNAKE_CASE_				,	SCREAMING_SNAKE_CASE_						) > 1:
            continue
         _UpperCAmelCase           =   2 * euclid_m * (euclid_m + euclid_n)
         for perimeter in range(SCREAMING_SNAKE_CASE_				,	limit + 1				,	SCREAMING_SNAKE_CASE_						):
            frequencies[perimeter] += 1
      euclid_m += 1
   return sum(1 for frequency in frequencies.values() if frequency == 1						)


if __name__ == "__main__":
   print(f'''{solution() = }''')

"""simple docstring"""




import datasets

from .evaluate import evaluate


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

lowerCAmelCase__				=					'\nThis metric wrap the official scoring script for version 1 of the Stanford Question Answering Dataset (SQuAD).\n\nStanford Question Answering Dataset (SQuAD) is a reading comprehension dataset, consisting of questions posed by\ncrowdworkers on a set of Wikipedia articles, where the answer to every question is a segment of text, or span,\nfrom the corresponding reading passage, or the question might be unanswerable.\n'

lowerCAmelCase__				=					'\nComputes SQuAD scores (F1 and EM).\nArgs:\n    predictions: List of question-answers dictionaries with the following key-values:\n        - \'id\': id of the question-answer pair as given in the references (see below)\n        - \'prediction_text\': the text of the answer\n    references: List of question-answers dictionaries with the following key-values:\n        - \'id\': id of the question-answer pair (see above),\n        - \'answers\': a Dict in the SQuAD dataset format\n            {\n                \'text\': list of possible texts for the answer, as a list of strings\n                \'answer_start\': list of start positions for the answer, as a list of ints\n            }\n            Note that answer_start values are not taken into account to compute the metric.\nReturns:\n    \'exact_match\': Exact match (the normalized answer exactly match the gold answer)\n    \'f1\': The F-score of predicted tokens versus the gold answer\nExamples:\n\n    >>> predictions = [{\'prediction_text\': \'1976\', \'id\': \'56e10a3be3433e1400422b22\'}]\n    >>> references = [{\'answers\': {\'answer_start\': [97], \'text\': [\'1976\']}, \'id\': \'56e10a3be3433e1400422b22\'}]\n    >>> squad_metric = datasets.load_metric("squad")\n    >>> results = squad_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'exact_match\': 100.0, \'f1\': 100.0}\n'





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

							def _lowercase       (self     ):

									"""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 _lowercase       (self							,							SCREAMING_SNAKE_CASE_							,							SCREAMING_SNAKE_CASE_     ):

									"""simple docstring"""







									SCREAMING_SNAKE_CASE_    			=			{prediction['''id''']: prediction['''prediction_text'''] for prediction in predictions}
									SCREAMING_SNAKE_CASE_    			=			[
									    {
									        '''paragraphs''': [
									            {
									                '''qas''': [
									                    {
									                        '''answers''': [{'''text''': answer_text} for answer_text in ref['''answers''']['''text''']],
									                        '''id''': ref['''id'''],
									                    }
									                    for ref in references
									                ]
									            }
									        ]
									    }
									]
									SCREAMING_SNAKE_CASE_    			=			evaluate(dataset=SCREAMING_SNAKE_CASE_							,							predictions=SCREAMING_SNAKE_CASE_     )
									return score