





"""simple docstring"""


def SCREAMING_SNAKE_CASE_   (       snake_case   :					str = 10**6		)->		Optional[int]:

       if n <= 0:
              raise ValueError('Please enter an integer greater than 0'		)

       _lowerCamelCase    	=					list(range(n + 1		)		)
       for number in range(2						,  n + 1		):
              if phi[number] == number:
                     phi[number] -= 1
                     for multiple in range(number * 2						,  n + 1						,  __lowerCamelCase		):
                            _lowerCamelCase    	=					(phi[multiple] // number) * (number - 1)

       _lowerCamelCase    	=					1
       for number in range(1						,  n + 1		):
              if (answer / phi[answer]) < (number / phi[number]):
                     _lowerCamelCase    	=					number

       return answer


if __name__ == "__main__":
      print(solution())







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,
)


lowerCamelCase_				:		Union[str, Any]       						=       logging.getLogger(__name__)
torch.set_grad_enabled(False)
lowerCamelCase_				:		List[Any]       						=       """cuda""" if torch.cuda.is_available() else """cpu"""
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase=100      ,				__lowerCamelCase=" "						):
					__a							=   text.split(__lowerCamelCase						)
					return [character.join(text[i : i + n]						).strip() for i in range(0      ,				len(__lowerCamelCase						)      ,				__lowerCamelCase						)]
def 							lowerCAmelCase(	__lowerCamelCase						):
					__a					,      __a							=   [], []
					for title, text in zip(documents['title']      ,				documents['text']						):
										if text is not None:
															for passage in split_text(__lowerCamelCase						):
																				titles.append(title if title is not None else ''						)
																				texts.append(__lowerCamelCase						)
					return {"title": titles, "text": texts}
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase						):
					__a							=   ctx_tokenizer(
					    documents['title']      ,				documents['text']      ,				truncation=__lowerCamelCase      ,				padding='longest'      ,				return_tensors='pt'						)['input_ids']
					__a							=   ctx_encoder(input_ids.to(device=__lowerCamelCase						)      ,				return_dict=__lowerCamelCase						).pooler_output
					return {"embeddings": embeddings.detach().cpu().numpy()}
def 							lowerCAmelCase(	__lowerCamelCase      ,				__lowerCamelCase      ,				__lowerCamelCase      ,				):
					######################################
					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(__lowerCamelCase      ,				batched=__lowerCamelCase      ,				num_proc=processing_args.num_proc						)

					# And compute the embeddings
					__a							=   DPRContextEncoder.from_pretrained(rag_example_args.dpr_ctx_encoder_model_name						).to(device=__lowerCamelCase						)
					__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(__lowerCamelCase      ,				ctx_encoder=__lowerCamelCase      ,				ctx_tokenizer=__lowerCamelCase						)      ,				batched=__lowerCamelCase      ,				batch_size=processing_args.batch_size      ,				features=__lowerCamelCase      ,				)

					# And finally save your dataset
					__a							=   os.path.join(rag_example_args.output_dir      ,				'my_knowledge_dataset'						)
					dataset.save_to_disk(__lowerCamelCase						)
					# 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=__lowerCamelCase						)

					# And save the index
					__a							=   os.path.join(rag_example_args.output_dir      ,				'my_knowledge_dataset_hnsw_index.faiss'						)
					dataset.get_index('embeddings'						).save(__lowerCamelCase						)
					# 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=__lowerCamelCase						)
					__a							=   RagSequenceForGeneration.from_pretrained(rag_example_args.rag_model_name      ,				retriever=__lowerCamelCase						)
					__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(__lowerCamelCase      ,				return_tensors='pt'						)['input_ids']
					__a							=   model.generate(__lowerCamelCase						)
					__a							=   tokenizer.batch_decode(__lowerCamelCase      ,				skip_special_tokens=__lowerCamelCase						)[0]
					logger.info('Q: ' + question						)
					logger.info('A: ' + generated_string						)


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






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






@dataclass
class 						a__							:
			A__				:   int								=			field(
			    default=7_68      ,						metadata={'help': 'The dimension of the embeddings to pass to the HNSW Faiss index.'}      ,						)
			A__				:   int								=			field(
			    default=1_28      ,						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)

	lowerCamelCase_				:		Tuple       						=       HfArgumentParser((RagExampleArguments, ProcessingArguments, IndexHnswArguments))
	lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_				:		Union[str, Any]       						=       parser.parse_args_into_dataclasses()
	with TemporaryDirectory() as tmp_dir:
		lowerCamelCase_				:		Union[str, Any]       						=       rag_example_args.output_dir or tmp_dir
		main(rag_example_args, processing_args, index_hnsw_args)




