
lowerCamelCase__     :		dict[tuple[int, int, int], int]        = {}

def 		UpperCamelCase						(   lowercase_			,			lowercase_			,			lowercase_ )		->						int:


  '''simple docstring'''






  if late == 3 or absent == 2:
    return 0

  # if we have no days left, and have not failed any other rules,
  # we have a prize string
  if days == 0:
    return 1

  # No easy solution, so now we need to do the recursive calculation

  # First, check if the combination is already in the cache, and
  # if yes, return the stored value from there since we already
  # know the number of possible prize strings from this point on
  lowercase__	: Tuple     		=   (days, absent, late)
  if key in cache:
    return cache[key]

  # now we calculate the three possible ways that can unfold from
  # this point on, depending on our attendance today

  # 1) if we are late (but not absent), the "absent" counter stays as
  # it is, but the "late" counter increases by one
  lowercase__	: Union[str, Any]     		=   _calculate(days - 1			,			lowercase_			,			late + 1 )

  # 2) if we are absent, the "absent" counter increases by 1, and the
  # "late" counter resets to 0
  lowercase__	: List[str]     		=   _calculate(days - 1			,			absent + 1			,			0 )

  # 3) if we are on time, this resets the "late" counter and keeps the
  # absent counter
  lowercase__	: Dict     		=   _calculate(days - 1			,			lowercase_			,			0 )

  lowercase__	: List[str]     		=   state_late + state_absent + state_ontime

  lowercase__	: List[Any]     		=   prizestrings
  return prizestrings

def 		UpperCamelCase						(   lowercase_ = 30 )		->						int:


  '''simple docstring'''






  return _calculate(lowercase_			,			absent=0			,			late=0 )


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










'''simple docstring'''
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


__SCREAMING_SNAKE_CASE					:				Optional[int]									=		logging.getLogger(__name__)
torch.set_grad_enabled(False)
__SCREAMING_SNAKE_CASE					:				Dict									=		'''cuda''' if torch.cuda.is_available() else '''cpu'''







def       a_				(	UpperCamelCase_						,  UpperCamelCase_=1_0_0						,  UpperCamelCase_=" " ):
							A_			    =		text.split(UpperCamelCase_ )
							return [character.join(text[i : i + n] ).strip() for i in range(0						,  len(UpperCamelCase_ )						,  UpperCamelCase_ )]







def       a_				(	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       a_				(	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       a_				(	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






@dataclass
class 					__lowerCAmelCase   :

						"""simple docstring"""






						_UpperCAmelCase		:       str   						=field(
						    default=str(Path(lowercase						).parent / "test_run" / "dummy-kb" / "my_knowledge_dataset.csv"						)				,			metadata={"help": "Path to a tab-separated csv file with columns 'title' and 'text'"}				,			)
						_UpperCAmelCase		:       Optional[str]   						=field(
						    default=lowercase				,			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=str(Path(lowercase						).parent / "test_run" / "dummy-kb"						)				,			metadata={"help": "Path to a directory where the dataset passages and the index will be saved"}				,			)






@dataclass
class 					__lowerCAmelCase   :

						"""simple docstring"""






						_UpperCAmelCase		:       Optional[int]   						=field(
						    default=lowercase				,			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 					__lowerCAmelCase   :

						"""simple docstring"""






						_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)

							__SCREAMING_SNAKE_CASE					:				List[str]									=		HfArgumentParser((RagExampleArguments, ProcessingArguments, IndexHnswArguments))
							__SCREAMING_SNAKE_CASE							,						__SCREAMING_SNAKE_CASE							,						__SCREAMING_SNAKE_CASE					:				Dict									=		parser.parse_args_into_dataclasses()
							with TemporaryDirectory() as tmp_dir:
														__SCREAMING_SNAKE_CASE					:				List[str]									=		rag_example_args.output_dir or tmp_dir
														main(rag_example_args, processing_args, index_hnsw_args)





