



import logging
import os
from dataclasses import dataclass, field
from functools import partial
from pathlib import Path
from tempfile import TemporaryDirectory
from typing import List, Optional

import faiss
import torch
from datasets import Features, Sequence, Value, load_dataset

from transformers import (
    DPRContextEncoder,
    DPRContextEncoderTokenizerFast,
    HfArgumentParser,
    RagRetriever,
    RagSequenceForGeneration,
    RagTokenizer,
)


__snake_case		:Dict 						=	logging.getLogger(__name__)
torch.set_grad_enabled(False)
__snake_case		:Any 						=	'''cuda''' if torch.cuda.is_available() else '''cpu'''





def 	__snake_case      (     _UpperCAmelCase  ,					_UpperCAmelCase=100  ,					_UpperCAmelCase=" "							):
    __a					=							text.split(_UpperCAmelCase							)
    return [character.join(text[i : i + n]							).strip() for i in range(0  ,					len(_UpperCAmelCase							)  ,					_UpperCAmelCase							)]





def 	__snake_case      (     _UpperCAmelCase							):
    __a			,  __a					=							[], []
    for title, text in zip(documents['''title''']  ,					documents['''text''']							):
        if text is not None:
            for passage in split_text(_UpperCAmelCase							):
                titles.append(title if title is not None else ''''''							)
                texts.append(_UpperCAmelCase							)
    return {"title": titles, "text": texts}





def 	__snake_case      (     _UpperCAmelCase  ,					_UpperCAmelCase  ,					_UpperCAmelCase							):
    __a					=							ctx_tokenizer(
        documents['''title''']  ,					documents['''text''']  ,					truncation=_UpperCAmelCase  ,					padding='''longest'''  ,					return_tensors='''pt'''							)['''input_ids''']
    __a					=							ctx_encoder(input_ids.to(device=_UpperCAmelCase							)  ,					return_dict=_UpperCAmelCase							).pooler_output
    return {"embeddings": embeddings.detach().cpu().numpy()}





def 	__snake_case      (     _UpperCAmelCase  ,					_UpperCAmelCase  ,					_UpperCAmelCase  ,					):
    ######################################
    logger.info('''Step 1 - Create the dataset'''							)
    ######################################

    # The dataset needed for RAG must have three columns:
    # - title (string): title of the document
    # - text (string): text of a passage of the document
    # - embeddings (array of dimension d): DPR representation of the passage

    # Let's say you have documents in tab-separated csv files with columns "title" and "text"
    assert os.path.isfile(rag_example_args.csv_path							), "Please provide a valid path to a csv file"

    # You can load a Dataset object this way
    __a					=							load_dataset(
        '''csv'''  ,					data_files=[rag_example_args.csv_path]  ,					split='''train'''  ,					delimiter='''\t'''  ,					column_names=['''title''', '''text''']							)

    # More info about loading csv files in the documentation: https://huggingface.co/docs/datasets/loading_datasets.html?highlight=csv#csv-files

    # Then split the documents into passages of 100 words
    __a					=							dataset.map(_UpperCAmelCase  ,					batched=_UpperCAmelCase  ,					num_proc=processing_args.num_proc							)

    # And compute the embeddings
    __a					=							DPRContextEncoder.from_pretrained(rag_example_args.dpr_ctx_encoder_model_name							).to(device=_UpperCAmelCase							)
    __a					=							DPRContextEncoderTokenizerFast.from_pretrained(rag_example_args.dpr_ctx_encoder_model_name							)
    __a					=							Features(
        {'''text''': Value('''string'''							), '''title''': Value('''string'''							), '''embeddings''': Sequence(Value('''float32'''							)							)}							)  # optional, save as float32 instead of float64 to save space
    __a					=							dataset.map(
        partial(_UpperCAmelCase  ,					ctx_encoder=_UpperCAmelCase  ,					ctx_tokenizer=_UpperCAmelCase							)  ,					batched=_UpperCAmelCase  ,					batch_size=processing_args.batch_size  ,					features=_UpperCAmelCase  ,					)

    # And finally save your dataset
    __a					=							os.path.join(rag_example_args.output_dir  ,					'''my_knowledge_dataset'''							)
    dataset.save_to_disk(_UpperCAmelCase							)
    # from datasets import load_from_disk
    # dataset = load_from_disk(passages_path)  # to reload the dataset

    ######################################
    logger.info('''Step 2 - Index the dataset'''							)
    ######################################

    # Let's use the Faiss implementation of HNSW for fast approximate nearest neighbor search
    __a					=							faiss.IndexHNSWFlat(index_hnsw_args.d  ,					index_hnsw_args.m  ,					faiss.METRIC_INNER_PRODUCT							)
    dataset.add_faiss_index('''embeddings'''  ,					custom_index=_UpperCAmelCase							)

    # And save the index
    __a					=							os.path.join(rag_example_args.output_dir  ,					'''my_knowledge_dataset_hnsw_index.faiss'''							)
    dataset.get_index('''embeddings'''							).save(_UpperCAmelCase							)
    # dataset.load_faiss_index("embeddings", index_path)  # to reload the index

    ######################################
    logger.info('''Step 3 - Load RAG'''							)
    ######################################

    # Easy way to load the model
    __a					=							RagRetriever.from_pretrained(
        rag_example_args.rag_model_name  ,					index_name='''custom'''  ,					indexed_dataset=_UpperCAmelCase							)
    __a					=							RagSequenceForGeneration.from_pretrained(rag_example_args.rag_model_name  ,					retriever=_UpperCAmelCase							)
    __a					=							RagTokenizer.from_pretrained(rag_example_args.rag_model_name							)

    # For distributed fine-tuning you'll need to provide the paths instead, as the dataset and the index are loaded separately.
    # retriever = RagRetriever.from_pretrained(rag_model_name, index_name="custom", passages_path=passages_path, index_path=index_path)

    ######################################
    logger.info('''Step 4 - Have fun'''							)
    ######################################

    __a					=							rag_example_args.question or '''What does Moses\' rod turn into ?'''
    __a					=							tokenizer.question_encoder(_UpperCAmelCase  ,					return_tensors='''pt'''							)['''input_ids''']
    __a					=							model.generate(_UpperCAmelCase							)
    __a					=							tokenizer.batch_decode(_UpperCAmelCase  ,					skip_special_tokens=_UpperCAmelCase							)[0]
    logger.info('''Q: ''' + question							)
    logger.info('''A: ''' + generated_string							)

@dataclass
class        _A			:
       UpperCamelCase__    :       str		   =		field(
           default=str(Path(__UpperCAmelCase       ).parent / '''test_data''' / '''my_knowledge_dataset.csv'''       ) ,metadata={'''help''': '''Path to a tab-separated csv file with columns \'title\' and \'text\''''} ,)
       UpperCamelCase__    :       Optional[str]		   =		field(
           default=__UpperCAmelCase ,metadata={'''help''': '''Question that is passed as input to RAG. Default is \'What does Moses\' rod turn into ?\'.'''} ,)
       UpperCamelCase__    :       str		   =		field(
           default='''facebook/rag-sequence-nq''' ,metadata={'''help''': '''The RAG model to use. Either \'facebook/rag-sequence-nq\' or \'facebook/rag-token-nq\''''} ,)
       UpperCamelCase__    :       str		   =		field(
           default='''facebook/dpr-ctx_encoder-multiset-base''' ,metadata={
               '''help''': (
                   '''The DPR context encoder model to use. Either \'facebook/dpr-ctx_encoder-single-nq-base\' or'''
                   ''' \'facebook/dpr-ctx_encoder-multiset-base\''''
               )
           } ,)
       UpperCamelCase__    :       Optional[str]		   =		field(
           default=__UpperCAmelCase ,metadata={'''help''': '''Path to a directory where the dataset passages and the index will be saved'''} ,)


@dataclass
class        _A			:
       UpperCamelCase__    :       Optional[int]		   =		field(
           default=__UpperCAmelCase ,metadata={
               '''help''': '''The number of processes to use to split the documents into passages. Default is single process.'''
           } ,)
       UpperCamelCase__    :       int		   =		field(
           default=16 ,metadata={
               '''help''': '''The batch size to use when computing the passages embeddings using the DPR context encoder.'''
           } ,)


@dataclass
class        _A			:
       UpperCamelCase__    :       int		   =		field(
           default=768 ,metadata={'''help''': '''The dimension of the embeddings to pass to the HNSW Faiss index.'''} ,)
       UpperCamelCase__    :       int		   =		field(
           default=128 ,metadata={
               '''help''': (
                   '''The number of bi-directional links created for every new element during the HNSW index construction.'''
               )
           } ,)


if __name__ == "__main__":
 logging.basicConfig(level=logging.WARNING)
 logger.setLevel(logging.INFO)

 __snake_case		:List[Any] 						=	HfArgumentParser((RagExampleArguments, ProcessingArguments, IndexHnswArguments))
 __snake_case						,__snake_case						,__snake_case		:Tuple 						=	parser.parse_args_into_dataclasses()
 with TemporaryDirectory() as tmp_dir:
  __snake_case		:Optional[int] 						=	rag_example_args.output_dir or tmp_dir
  main(rag_example_args, processing_args, index_hnsw_args)










from math import floor, sqrt





def 	__snake_case      (     _UpperCAmelCase							):
    __a					=							0.0
    __a					=							1.0
    __a					=							int(sqrt(_UpperCAmelCase							)							)
    __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 	__snake_case      (     _UpperCAmelCase = 10000							):
    __a					=							0
    for i in range(2  ,					n + 1							):
        __a					=							sqrt(_UpperCAmelCase							)
        if sr - floor(_UpperCAmelCase							) != 0 and continuous_fraction_period(_UpperCAmelCase							) % 2 == 1:
            count_odd_periods += 1
    return count_odd_periods


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





