

import json
import os
import shutil
import sys
import tempfile
import unittest
from unittest import TestCase
from unittest.mock import patch

import faiss
import numpy as np
from datasets import Dataset

from transformers import BartConfig, BartTokenizer, DPRConfig, DPRQuestionEncoderTokenizer, RagConfig
from transformers.file_utils import is_datasets_available, is_faiss_available, is_psutil_available, is_torch_available
from transformers.integrations import is_ray_available
from transformers.models.bert.tokenization_bert import VOCAB_FILES_NAMES as DPR_VOCAB_FILES_NAMES
from transformers.models.rag.retrieval_rag import CustomHFIndex, RagRetriever
from transformers.models.roberta.tokenization_roberta import VOCAB_FILES_NAMES as BART_VOCAB_FILES_NAMES
from transformers.testing_utils import require_ray


sys.path.append(os.path.join(os.getcwd()))  # noqa: E402 # noqa: E402 # isort:skip

if is_torch_available():
  from distributed_pytorch_retriever import RagPyTorchDistributedRetriever  # noqa: E402 # isort:skip
else:
  _UpperCAmelCase    	=			None

if is_ray_available():
  import ray  # noqa: E402 # isort:skip
  from distributed_ray_retriever import RagRayDistributedRetriever, RayRetriever  # noqa: E402 # isort:skip
else:
  _UpperCAmelCase    	=			None
  _UpperCAmelCase    	=			None
  _UpperCAmelCase    	=			None


def 			__UpperCamelCase    (lowerCAmelCase					:  Union[str, Any]     )     ->  str:
      if not (is_datasets_available() and is_faiss_available() and is_psutil_available()):
            A    =				unittest.skip('test requires Datasets, Faiss, psutil'     )(lowerCAmelCase     )
      return test_case







@require_distributed_retrieval
class        _UpperCAmelCase (   __lowercase			):
  '''simple docstring'''







  def 	UpperCamelCase       ( self	: Optional[Any] ):
        A    =				tempfile.mkdtemp()
        A    =				8

        # DPR tok
        A    =				[
            '[UNK]',
            '[CLS]',
            '[SEP]',
            '[PAD]',
            '[MASK]',
            'want',
            '##want',
            '##ed',
            'wa',
            'un',
            'runn',
            '##ing',
            ',',
            'low',
            'lowest',
        ]
        A    =				os.path.join(self.tmpdirname		,						'dpr_tokenizer' )
        os.makedirs(UpperCamelCase__		,						exist_ok=UpperCamelCase__ )
        A    =				os.path.join(UpperCamelCase__		,						DPR_VOCAB_FILES_NAMES['vocab_file'] )
        with open(self.vocab_file		,						'w'		,						encoding='utf-8' ) as vocab_writer:
              vocab_writer.write(''.join([x + '\n' for x in vocab_tokens] ) )

        # BART tok
        A    =				[
            'l',
            'o',
            'w',
            'e',
            'r',
            's',
            't',
            'i',
            'd',
            'n',
            '\u0120',
            '\u0120l',
            '\u0120n',
            '\u0120lo',
            '\u0120low',
            'er',
            '\u0120lowest',
            '\u0120newer',
            '\u0120wider',
            '<unk>',
        ]
        A    =				dict(zip(UpperCamelCase__		,						range(len(UpperCamelCase__ ) ) ) )
        A    =				['#version: 0.2', '\u0120 l', '\u0120l o', '\u0120lo w', 'e r', '']
        A    =				{'unk_token': '<unk>'}

        A    =				os.path.join(self.tmpdirname		,						'bart_tokenizer' )
        os.makedirs(UpperCamelCase__		,						exist_ok=UpperCamelCase__ )
        A    =				os.path.join(UpperCamelCase__		,						BART_VOCAB_FILES_NAMES['vocab_file'] )
        A    =				os.path.join(UpperCamelCase__		,						BART_VOCAB_FILES_NAMES['merges_file'] )
        with open(self.vocab_file		,						'w'		,						encoding='utf-8' ) as fp:
              fp.write(json.dumps(UpperCamelCase__ ) + '\n' )
        with open(self.merges_file		,						'w'		,						encoding='utf-8' ) as fp:
              fp.write('\n'.join(UpperCamelCase__ ) )







  def 	UpperCamelCase       ( self	: Dict ):
        return DPRQuestionEncoderTokenizer.from_pretrained(os.path.join(self.tmpdirname		,						'dpr_tokenizer' ) )







  def 	UpperCamelCase       ( self	: Union[str, Any] ):
        return BartTokenizer.from_pretrained(os.path.join(self.tmpdirname		,						'bart_tokenizer' ) )







  def 	UpperCamelCase       ( self	: Optional[int] ):
        shutil.rmtree(self.tmpdirname )







  def 	UpperCamelCase       ( self	: Union[str, Any] ):
        A    =				Dataset.from_dict(
            {
                'id': ['0', '1'],
                'text': ['foo', 'bar'],
                'title': ['Foo', 'Bar'],
                'embeddings': [np.ones(self.retrieval_vector_size ), 2 * np.ones(self.retrieval_vector_size )],
            } )
        dataset.add_faiss_index('embeddings'		,						string_factory='Flat'		,						metric_type=faiss.METRIC_INNER_PRODUCT )
        return dataset







  def 	UpperCamelCase       ( self	: Optional[Any]		,						UpperCamelCase__	: bool		,						UpperCamelCase__	: List[Any]=12345 ):
        A    =				self.get_dummy_dataset()
        A    =				RagConfig(
            retrieval_vector_size=self.retrieval_vector_size		,						question_encoder=DPRConfig().to_dict()		,						generator=BartConfig().to_dict()		,						)
        with patch('transformers.models.rag.retrieval_rag.load_dataset' ) as mock_load_dataset:
              A    =				dataset
              A    =				RagPyTorchDistributedRetriever(
                  UpperCamelCase__		,						question_encoder_tokenizer=self.get_dpr_tokenizer()		,						generator_tokenizer=self.get_bart_tokenizer()		,						)
              if init_retrieval:
                    retriever.init_retrieval(UpperCamelCase__ )
        return retriever







  def 	UpperCamelCase       ( self	: Tuple		,						UpperCamelCase__	: bool ):
        # Have to run in local mode because sys.path modifications at top of
        # file are not propogated to remote workers.
        # https://stackoverflow.com/questions/54338013/parallel-import-a-python-file-from-sibling-folder
        ray.init(local_mode=UpperCamelCase__ )
        A    =				RagConfig(
            retrieval_vector_size=self.retrieval_vector_size		,						question_encoder=DPRConfig().to_dict()		,						generator=BartConfig().to_dict()		,						)
        A    =				ray.remote(UpperCamelCase__ )
        A    =				[remote_cls.remote() for _ in range(1 )]
        with patch('transformers.models.rag.retrieval_rag.load_dataset' ) as mock_load_dataset:
              A    =				self.get_dummy_dataset()
              A    =				RagRayDistributedRetriever(
                  UpperCamelCase__		,						question_encoder_tokenizer=self.get_dpr_tokenizer()		,						generator_tokenizer=self.get_bart_tokenizer()		,						retrieval_workers=UpperCamelCase__		,						)
              if init_retrieval:
                    retriever.init_retrieval()
        return retriever







  def 	UpperCamelCase       ( self	: Optional[int]		,						UpperCamelCase__	: bool		,						UpperCamelCase__	: bool		,						UpperCamelCase__	: str=12345 ):
        A    =				self.get_dummy_dataset()
        A    =				RagConfig(
            retrieval_vector_size=self.retrieval_vector_size		,						question_encoder=DPRConfig().to_dict()		,						generator=BartConfig().to_dict()		,						index_name='custom'		,						)
        if from_disk:
              A    =				os.path.join(self.tmpdirname		,						'dataset' )
              A    =				os.path.join(self.tmpdirname		,						'index.faiss' )
              dataset.get_index('embeddings' ).save(os.path.join(self.tmpdirname		,						'index.faiss' ) )
              dataset.drop_index('embeddings' )
              dataset.save_to_disk(os.path.join(self.tmpdirname		,						'dataset' ) )
              del dataset
              A    =				RagPyTorchDistributedRetriever(
                  UpperCamelCase__		,						question_encoder_tokenizer=self.get_dpr_tokenizer()		,						generator_tokenizer=self.get_bart_tokenizer()		,						)
        else:
              A    =				RagPyTorchDistributedRetriever(
                  UpperCamelCase__		,						question_encoder_tokenizer=self.get_dpr_tokenizer()		,						generator_tokenizer=self.get_bart_tokenizer()		,						index=CustomHFIndex(config.retrieval_vector_size		,						UpperCamelCase__ )		,						)
        if init_retrieval:
              retriever.init_retrieval(UpperCamelCase__ )
        return retriever







  def 	UpperCamelCase       ( self	: Dict		,						UpperCamelCase__	: bool		,						UpperCamelCase__	: bool ):
        # Have to run in local mode because sys.path modifications at top of
        # file are not propogated to remote workers.
        # https://stackoverflow.com/questions/54338013/parallel-import-a-python-file-from-sibling-folder
        ray.init(local_mode=UpperCamelCase__ )
        A    =				self.get_dummy_dataset()
        A    =				RagConfig(
            retrieval_vector_size=self.retrieval_vector_size		,						question_encoder=DPRConfig().to_dict()		,						generator=BartConfig().to_dict()		,						index_name='custom'		,						)
        A    =				ray.remote(UpperCamelCase__ )
        A    =				[remote_cls.remote() for _ in range(1 )]
        if from_disk:
              A    =				os.path.join(self.tmpdirname		,						'dataset' )
              A    =				os.path.join(self.tmpdirname		,						'index.faiss' )
              dataset.get_index('embeddings' ).save(os.path.join(self.tmpdirname		,						'index.faiss' ) )
              dataset.drop_index('embeddings' )
              dataset.save_to_disk(os.path.join(self.tmpdirname		,						'dataset' ) )
              del dataset
              A    =				RagRayDistributedRetriever(
                  UpperCamelCase__		,						question_encoder_tokenizer=self.get_dpr_tokenizer()		,						generator_tokenizer=self.get_bart_tokenizer()		,						retrieval_workers=UpperCamelCase__		,						index=CustomHFIndex.load_from_disk(
                      vector_size=config.retrieval_vector_size		,						dataset_path=config.passages_path		,						index_path=config.index_path		,						)		,						)
        else:
              A    =				RagRayDistributedRetriever(
                  UpperCamelCase__		,						question_encoder_tokenizer=self.get_dpr_tokenizer()		,						generator_tokenizer=self.get_bart_tokenizer()		,						retrieval_workers=UpperCamelCase__		,						index=CustomHFIndex(config.retrieval_vector_size		,						UpperCamelCase__ )		,						)
        if init_retrieval:
              retriever.init_retrieval()
        return retriever







  def 	UpperCamelCase       ( self	: Optional[Any]		,						UpperCamelCase__	: RagRetriever		,						UpperCamelCase__	: np.array		,						UpperCamelCase__	: int ):
        A ,	A ,	A    =				retriever.retrieve(UpperCamelCase__		,						n_docs=UpperCamelCase__ )
        self.assertEqual(retrieved_doc_embeds.shape		,						(2, n_docs, self.retrieval_vector_size) )
        self.assertEqual(len(UpperCamelCase__ )		,						2 )
        self.assertEqual(sorted(doc_dicts[0] )		,						['embeddings', 'id', 'text', 'title'] )
        self.assertEqual(len(doc_dicts[0]['id'] )		,						UpperCamelCase__ )
        self.assertEqual(doc_dicts[0]['id'][0]		,						'1' )  # max inner product is reached with second doc
        self.assertEqual(doc_dicts[1]['id'][0]		,						'0' )  # max inner product is reached with first doc
        self.assertListEqual(doc_ids.tolist()		,						[[1], [0]] )







  def 	UpperCamelCase       ( self	: int ):
        A    =				1
        A    =				np.array(
            [np.ones(self.retrieval_vector_size ), -np.ones(self.retrieval_vector_size )]		,						dtype=np.floataa )

        self.distributed_retriever_check(
            self.get_dummy_pytorch_distributed_retriever(init_retrieval=UpperCamelCase__ )		,						UpperCamelCase__		,						UpperCamelCase__ )







  def 	UpperCamelCase       ( self	: Union[str, Any] ):
        A    =				1
        A    =				np.array(
            [np.ones(self.retrieval_vector_size ), -np.ones(self.retrieval_vector_size )]		,						dtype=np.floataa )

        self.distributed_retriever_check(
            self.get_dummy_custom_hf_index_pytorch_retriever(init_retrieval=UpperCamelCase__		,						from_disk=UpperCamelCase__ )		,						UpperCamelCase__		,						UpperCamelCase__		,						)







  def 	UpperCamelCase       ( self	: List[Any] ):
        A    =				1
        A    =				np.array(
            [np.ones(self.retrieval_vector_size ), -np.ones(self.retrieval_vector_size )]		,						dtype=np.floataa )

        self.distributed_retriever_check(
            self.get_dummy_custom_hf_index_pytorch_retriever(init_retrieval=UpperCamelCase__		,						from_disk=UpperCamelCase__ )		,						UpperCamelCase__		,						UpperCamelCase__		,						)







  @require_ray
  def 	UpperCamelCase       ( self	: Dict ):
        A    =				1
        A    =				np.array(
            [np.ones(self.retrieval_vector_size ), -np.ones(self.retrieval_vector_size )]		,						dtype=np.floataa )

        self.distributed_retriever_check(
            self.get_dummy_ray_distributed_retriever(init_retrieval=UpperCamelCase__ )		,						UpperCamelCase__		,						UpperCamelCase__ )
        ray.shutdown()







  @require_ray
  def 	UpperCamelCase       ( self	: int ):
        A    =				1
        A    =				np.array(
            [np.ones(self.retrieval_vector_size ), -np.ones(self.retrieval_vector_size )]		,						dtype=np.floataa )
        with self.assertRaises(UpperCamelCase__ ):
              self.distributed_retriever_check(
                  self.get_dummy_custom_hf_index_ray_retriever(init_retrieval=UpperCamelCase__		,						from_disk=UpperCamelCase__ )		,						UpperCamelCase__		,						UpperCamelCase__		,						)
        ray.shutdown()







  @require_ray
  def 	UpperCamelCase       ( self	: Any ):
        A    =				1
        A    =				np.array(
            [np.ones(self.retrieval_vector_size ), -np.ones(self.retrieval_vector_size )]		,						dtype=np.floataa )

        self.distributed_retriever_check(
            self.get_dummy_custom_hf_index_ray_retriever(init_retrieval=UpperCamelCase__		,						from_disk=UpperCamelCase__ )		,						UpperCamelCase__		,						UpperCamelCase__ )
        ray.shutdown()






from math import floor, sqrt


def 			__UpperCamelCase    (lowerCAmelCase					:  int     )     ->  int:
      A    =				0.0
      A    =				1.0
      A    =				int(sqrt(lowerCAmelCase     )     )
      A    =				root
      A    =				0
      while integer_part != 2 * root:
            A    =				denominator * integer_part - numerator
            A    =				(n - numerator**2) / denominator
            A    =				int((root + numerator) / denominator     )
            period += 1
      return period


def 			__UpperCamelCase    (lowerCAmelCase					:  int = 10_000     )     ->  int:
      A    =				0
      for i in range(2,    n + 1     ):
            A    =				sqrt(lowerCAmelCase     )
            if sr - floor(lowerCAmelCase     ) != 0 and continuous_fraction_period(lowerCAmelCase     ) % 2 == 1:
                  count_odd_periods += 1
      return count_odd_periods


if __name__ == "__main__":
  print(F'''{solution(int(input().strip()))}''')



