



"""simple docstring"""






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

import numpy as np
from datasets import Dataset

from transformers import is_faiss_available
from transformers.models.bart.configuration_bart import BartConfig
from transformers.models.bart.tokenization_bart import BartTokenizer
from transformers.models.bert.tokenization_bert import VOCAB_FILES_NAMES as DPR_VOCAB_FILES_NAMES
from transformers.models.dpr.configuration_dpr import DPRConfig
from transformers.models.dpr.tokenization_dpr import DPRContextEncoderTokenizer, DPRQuestionEncoderTokenizer
from transformers.models.rag.configuration_rag import RagConfig
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_faiss, require_sentencepiece, require_tokenizers, require_torch


if is_faiss_available():
	import faiss



@require_faiss
class      A__  (    __SCREAMING_SNAKE_CASE				):




	'''simple docstring'''





	def 				_SCREAMING_SNAKE_CASE  (	self:						List[Any])							->			List[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    Optional[int]				=			tempfile.mkdtemp()
				__lowerCAmelCase :    List[str]				=			8

				# DPR tok
				__lowerCAmelCase :    List[str]				=			[
				    "[UNK]",
				    "[CLS]",
				    "[SEP]",
				    "[PAD]",
				    "[MASK]",
				    "want",
				    "##want",
				    "##ed",
				    "wa",
				    "un",
				    "runn",
				    "##ing",
				    ",",
				    "low",
				    "lowest",
				]
				__lowerCAmelCase :    List[Any]				=			os.path.join(self.tmpdirname			,     "dpr_tokenizer")
				os.makedirs(_SCREAMING_SNAKE_CASE			,     exist_ok=_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    Dict				=			os.path.join(_SCREAMING_SNAKE_CASE			,     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
				__lowerCAmelCase :    Optional[Any]				=			[
				    "l",
				    "o",
				    "w",
				    "e",
				    "r",
				    "s",
				    "t",
				    "i",
				    "d",
				    "n",
				    "\u0120",
				    "\u0120l",
				    "\u0120n",
				    "\u0120lo",
				    "\u0120low",
				    "er",
				    "\u0120lowest",
				    "\u0120newer",
				    "\u0120wider",
				    "<unk>",
				]
				__lowerCAmelCase :    int				=			dict(zip(_SCREAMING_SNAKE_CASE			,     range(len(_SCREAMING_SNAKE_CASE))))
				__lowerCAmelCase :    int				=			["#version: 0.2", "\u0120 l", "\u0120l o", "\u0120lo w", "e r", ""]
				__lowerCAmelCase :    Any				=			{"unk_token": "<unk>"}

				__lowerCAmelCase :    Optional[int]				=			os.path.join(self.tmpdirname			,     "bart_tokenizer")
				os.makedirs(_SCREAMING_SNAKE_CASE			,     exist_ok=_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    List[str]				=			os.path.join(_SCREAMING_SNAKE_CASE			,     BART_VOCAB_FILES_NAMES["vocab_file"])
				__lowerCAmelCase :    Dict				=			os.path.join(_SCREAMING_SNAKE_CASE			,     BART_VOCAB_FILES_NAMES["merges_file"])
				with open(self.vocab_file			,     "w"			,     encoding="utf-8") as fp:
							fp.write(json.dumps(_SCREAMING_SNAKE_CASE) + "\n")
				with open(self.merges_file			,     "w"			,     encoding="utf-8") as fp:
							fp.write("\n".join(_SCREAMING_SNAKE_CASE))

	def 				_SCREAMING_SNAKE_CASE  (	self:						List[str])							->			DPRQuestionEncoderTokenizer:

				"""simple docstring"""

				return DPRQuestionEncoderTokenizer.from_pretrained(os.path.join(self.tmpdirname			,     "dpr_tokenizer"))

	def 				_SCREAMING_SNAKE_CASE  (	self:						Optional[Any])							->			DPRContextEncoderTokenizer:

				"""simple docstring"""

				return DPRContextEncoderTokenizer.from_pretrained(os.path.join(self.tmpdirname			,     "dpr_tokenizer"))

	def 				_SCREAMING_SNAKE_CASE  (	self:						Tuple)							->			BartTokenizer:

				"""simple docstring"""

				return BartTokenizer.from_pretrained(os.path.join(self.tmpdirname			,     "bart_tokenizer"))

	def 				_SCREAMING_SNAKE_CASE  (	self:						str)							->			str:

				"""simple docstring"""

				shutil.rmtree(self.tmpdirname)

	def 				_SCREAMING_SNAKE_CASE  (	self:						Any)							->			Optional[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    List[Any]				=			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 				_SCREAMING_SNAKE_CASE  (	self:						Optional[Any])							->			List[str]:

				"""simple docstring"""

				__lowerCAmelCase :    Optional[Any]				=			self.get_dummy_dataset()
				__lowerCAmelCase :    Any				=			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:
							__lowerCAmelCase :    List[str]				=			dataset
							__lowerCAmelCase :    Union[str, Any]				=			RagRetriever(
							    _SCREAMING_SNAKE_CASE			,     question_encoder_tokenizer=self.get_dpr_tokenizer()			,     generator_tokenizer=self.get_bart_tokenizer()			,     )
				return retriever

	def 				_SCREAMING_SNAKE_CASE  (	self:						Optional[int]			,     _SCREAMING_SNAKE_CASE:						bool)							->			List[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    str				=			self.get_dummy_dataset()
				__lowerCAmelCase :    Any				=			RagConfig(
				    retrieval_vector_size=self.retrieval_vector_size			,     question_encoder=DPRConfig().to_dict()			,     generator=BartConfig().to_dict()			,     index_name="custom"			,     )
				if from_disk:
							__lowerCAmelCase :    Optional[Any]				=			os.path.join(self.tmpdirname			,     "dataset")
							__lowerCAmelCase :    Dict				=			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
							__lowerCAmelCase :    Dict				=			RagRetriever(
							    _SCREAMING_SNAKE_CASE			,     question_encoder_tokenizer=self.get_dpr_tokenizer()			,     generator_tokenizer=self.get_bart_tokenizer()			,     )
				else:
							__lowerCAmelCase :    Any				=			RagRetriever(
							    _SCREAMING_SNAKE_CASE			,     question_encoder_tokenizer=self.get_dpr_tokenizer()			,     generator_tokenizer=self.get_bart_tokenizer()			,     index=CustomHFIndex(config.retrieval_vector_size			,     _SCREAMING_SNAKE_CASE)			,     )
				return retriever

	def 				_SCREAMING_SNAKE_CASE  (	self:						Union[str, Any])							->			Optional[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    List[str]				=			Dataset.from_dict(
				    {
				        "id": ["0", "1"],
				        "text": ["foo", "bar"],
				        "title": ["Foo", "Bar"],
				        "embeddings": [np.ones(self.retrieval_vector_size + 1), 2 * np.ones(self.retrieval_vector_size + 1)],
				    })
				dataset.add_faiss_index("embeddings"			,     string_factory="Flat"			,     metric_type=faiss.METRIC_INNER_PRODUCT)

				__lowerCAmelCase :    Any				=			os.path.join(self.tmpdirname			,     "hf_bert_base.hnswSQ8_correct_phi_128.c_index")
				dataset.save_faiss_index("embeddings"			,     index_file_name + ".index.dpr")
				pickle.dump(dataset["id"]			,     open(index_file_name + ".index_meta.dpr"			,     "wb"))

				__lowerCAmelCase :    str				=			os.path.join(self.tmpdirname			,     "psgs_w100.tsv.pkl")
				__lowerCAmelCase :    Optional[int]				=			{sample["id"]: [sample["text"], sample["title"]] for sample in dataset}
				pickle.dump(_SCREAMING_SNAKE_CASE			,     open(_SCREAMING_SNAKE_CASE			,     "wb"))

				__lowerCAmelCase :    int				=			RagConfig(
				    retrieval_vector_size=self.retrieval_vector_size			,     question_encoder=DPRConfig().to_dict()			,     generator=BartConfig().to_dict()			,     index_name="legacy"			,     index_path=self.tmpdirname			,     )
				__lowerCAmelCase :    Union[str, Any]				=			RagRetriever(
				    _SCREAMING_SNAKE_CASE			,     question_encoder_tokenizer=self.get_dpr_tokenizer()			,     generator_tokenizer=self.get_bart_tokenizer())
				return retriever

	def 				_SCREAMING_SNAKE_CASE  (	self:						List[str])							->			str:

				"""simple docstring"""

				__lowerCAmelCase :    Optional[Any]				=			1
				__lowerCAmelCase :    str				=			self.get_dummy_canonical_hf_index_retriever()
				__lowerCAmelCase :    str				=			np.array(
				    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
				__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    str				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=_SCREAMING_SNAKE_CASE)
				self.assertEqual(retrieved_doc_embeds.shape			,     (2, n_docs, self.retrieval_vector_size))
				self.assertEqual(len(_SCREAMING_SNAKE_CASE)			,     2)
				self.assertEqual(sorted(doc_dicts[0])			,     ["embeddings", "id", "text", "title"])
				self.assertEqual(len(doc_dicts[0]["id"])			,     _SCREAMING_SNAKE_CASE)
				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 				_SCREAMING_SNAKE_CASE  (	self:						int)							->			List[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    Tuple				=			self.get_dummy_canonical_hf_index_retriever()
				with tempfile.TemporaryDirectory() as tmp_dirname:
							with patch("transformers.models.rag.retrieval_rag.load_dataset") as mock_load_dataset:
										__lowerCAmelCase :    Union[str, Any]				=			self.get_dummy_dataset()
										retriever.save_pretrained(_SCREAMING_SNAKE_CASE)
										__lowerCAmelCase :    Optional[int]				=			RagRetriever.from_pretrained(_SCREAMING_SNAKE_CASE)
										self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)
										__lowerCAmelCase :    Union[str, Any]				=			np.array(
										    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
										__lowerCAmelCase :    Any				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=1)
										self.assertTrue(out is not None)

	def 				_SCREAMING_SNAKE_CASE  (	self:						List[str])							->			str:

				"""simple docstring"""

				__lowerCAmelCase :    str				=			1
				__lowerCAmelCase :    Any				=			self.get_dummy_custom_hf_index_retriever(from_disk=_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    str				=			np.array(
				    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
				__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    List[Any]				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=_SCREAMING_SNAKE_CASE)
				self.assertEqual(retrieved_doc_embeds.shape			,     (2, n_docs, self.retrieval_vector_size))
				self.assertEqual(len(_SCREAMING_SNAKE_CASE)			,     2)
				self.assertEqual(sorted(doc_dicts[0])			,     ["embeddings", "id", "text", "title"])
				self.assertEqual(len(doc_dicts[0]["id"])			,     _SCREAMING_SNAKE_CASE)
				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 				_SCREAMING_SNAKE_CASE  (	self:						Union[str, Any])							->			List[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    Any				=			self.get_dummy_custom_hf_index_retriever(from_disk=_SCREAMING_SNAKE_CASE)
				with tempfile.TemporaryDirectory() as tmp_dirname:
							retriever.save_pretrained(_SCREAMING_SNAKE_CASE)
							__lowerCAmelCase :    Optional[int]				=			RagRetriever.from_pretrained(_SCREAMING_SNAKE_CASE)
							self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)
							__lowerCAmelCase :    Optional[int]				=			np.array(
							    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
							__lowerCAmelCase :    Optional[int]				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=1)
							self.assertTrue(out is not None)

	def 				_SCREAMING_SNAKE_CASE  (	self:						Optional[int])							->			int:

				"""simple docstring"""

				__lowerCAmelCase :    Any				=			1
				__lowerCAmelCase :    List[str]				=			self.get_dummy_custom_hf_index_retriever(from_disk=_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    Optional[int]				=			np.array(
				    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
				__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    Union[str, Any]				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=_SCREAMING_SNAKE_CASE)
				self.assertEqual(retrieved_doc_embeds.shape			,     (2, n_docs, self.retrieval_vector_size))
				self.assertEqual(len(_SCREAMING_SNAKE_CASE)			,     2)
				self.assertEqual(sorted(doc_dicts[0])			,     ["embeddings", "id", "text", "title"])
				self.assertEqual(len(doc_dicts[0]["id"])			,     _SCREAMING_SNAKE_CASE)
				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 				_SCREAMING_SNAKE_CASE  (	self:						str)							->			List[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    Any				=			self.get_dummy_custom_hf_index_retriever(from_disk=_SCREAMING_SNAKE_CASE)
				with tempfile.TemporaryDirectory() as tmp_dirname:
							retriever.save_pretrained(_SCREAMING_SNAKE_CASE)
							__lowerCAmelCase :    Any				=			RagRetriever.from_pretrained(_SCREAMING_SNAKE_CASE)
							self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)
							__lowerCAmelCase :    Union[str, Any]				=			np.array(
							    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
							__lowerCAmelCase :    List[str]				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=1)
							self.assertTrue(out is not None)

	def 				_SCREAMING_SNAKE_CASE  (	self:						Tuple)							->			List[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    str				=			1
				__lowerCAmelCase :    Union[str, Any]				=			self.get_dummy_legacy_index_retriever()
				__lowerCAmelCase :    List[Any]				=			np.array(
				    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
				__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    Optional[Any]				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=_SCREAMING_SNAKE_CASE)
				self.assertEqual(retrieved_doc_embeds.shape			,     (2, n_docs, self.retrieval_vector_size))
				self.assertEqual(len(_SCREAMING_SNAKE_CASE)			,     2)
				self.assertEqual(sorted(doc_dicts[0])			,     ["text", "title"])
				self.assertEqual(len(doc_dicts[0]["text"])			,     _SCREAMING_SNAKE_CASE)
				self.assertEqual(doc_dicts[0]["text"][0]			,     "bar")  # max inner product is reached with second doc
				self.assertEqual(doc_dicts[1]["text"][0]			,     "foo")  # max inner product is reached with first doc
				self.assertListEqual(doc_ids.tolist()			,     [[1], [0]])

	def 				_SCREAMING_SNAKE_CASE  (	self:						int)							->			int:

				"""simple docstring"""

				__lowerCAmelCase :    Dict				=			self.get_dummy_legacy_index_retriever()
				with tempfile.TemporaryDirectory() as tmp_dirname:
							retriever.save_pretrained(_SCREAMING_SNAKE_CASE)
							__lowerCAmelCase :    Any				=			RagRetriever.from_pretrained(_SCREAMING_SNAKE_CASE)
							self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)
							__lowerCAmelCase :    Any				=			np.array(
							    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
							__lowerCAmelCase :    List[str]				=			retriever.retrieve(_SCREAMING_SNAKE_CASE			,     n_docs=1)
							self.assertTrue(out is not None)

	@require_torch
	@require_tokenizers
	@require_sentencepiece
	def 				_SCREAMING_SNAKE_CASE  (	self:						Tuple)							->			Any:

				"""simple docstring"""

				import torch

				__lowerCAmelCase :    Dict				=			1
				__lowerCAmelCase :    List[Any]				=			self.get_dummy_canonical_hf_index_retriever()
				__lowerCAmelCase :    Tuple				=			[[5, 7], [10, 11]]
				__lowerCAmelCase :    List[str]				=			np.array(
				    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
				__lowerCAmelCase :    List[str]				=			retriever(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE			,     prefix=retriever.config.generator.prefix			,     n_docs=_SCREAMING_SNAKE_CASE)
				__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    List[Any]				=			(
				    out["context_input_ids"],
				    out["context_attention_mask"],
				    out["retrieved_doc_embeds"],
				)
				self.assertEqual(retrieved_doc_embeds.shape			,     (2, n_docs, self.retrieval_vector_size))
				self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)
				self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE)
				self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     np.ndarray)

				__lowerCAmelCase :    Dict				=			retriever(
				    _SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE			,     prefix=retriever.config.generator.prefix			,     n_docs=_SCREAMING_SNAKE_CASE			,     return_tensors="pt"			,     )
				__lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase		,      __lowerCAmelCase :    Optional[int]				=			(  # noqa: F841
				    out["context_input_ids"],
				    out["context_attention_mask"],
				    out["retrieved_doc_embeds"],
				    out["doc_ids"],
				)
				self.assertEqual(retrieved_doc_embeds.shape			,     (2, n_docs, self.retrieval_vector_size))
				self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     torch.Tensor)
				self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     torch.Tensor)
				self.assertIsInstance(_SCREAMING_SNAKE_CASE			,     torch.Tensor)







	@require_torch
	@require_tokenizers
	@require_sentencepiece
	def 				_SCREAMING_SNAKE_CASE  (	self:						Union[str, Any])							->			Optional[Any]:

				"""simple docstring"""

				__lowerCAmelCase :    Union[str, Any]				=			self.get_dpr_ctx_encoder_tokenizer()
				__lowerCAmelCase :    int				=			1
				__lowerCAmelCase :    Union[str, Any]				=			self.get_dummy_custom_hf_index_retriever(from_disk=_SCREAMING_SNAKE_CASE)
				retriever.set_ctx_encoder_tokenizer(_SCREAMING_SNAKE_CASE)

				__lowerCAmelCase :    List[str]				=			[[5, 7], [10, 11]]
				__lowerCAmelCase :    List[str]				=			np.array(
				    [np.ones(self.retrieval_vector_size), -np.ones(self.retrieval_vector_size)]			,     dtype=np.floataa)
				__lowerCAmelCase :    List[Any]				=			retriever(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE			,     prefix=retriever.config.generator.prefix			,     n_docs=_SCREAMING_SNAKE_CASE)

				self.assertEqual(
				    len(_SCREAMING_SNAKE_CASE)			,     6)  # check whether the retriever output consist of 6 attributes including tokenized docs
				self.assertEqual(
				    all(k in out for k in ("tokenized_doc_ids", "tokenized_doc_attention_mask"))			,     _SCREAMING_SNAKE_CASE)  # check for doc token related keys in dictionary.




"""simple docstring"""






from math import factorial



class      A__  :




	'''simple docstring'''





	def __init__(	self:						str			,     _SCREAMING_SNAKE_CASE:						Tuple			,     _SCREAMING_SNAKE_CASE:						Any)							->			str:

				"""simple docstring"""

				__lowerCAmelCase :    str				=			real
				if isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    Optional[int]				=			[1] * rank
				else:
							__lowerCAmelCase :    Optional[Any]				=			rank

	def __repr__(	self:						Optional[int])							->			List[str]:

				"""simple docstring"""

				return (
				    F"""{self.real}+"""
				    F"""{'+'.join(str(_SCREAMING_SNAKE_CASE)+'E'+str(n+1)for n,dual in enumerate(self.duals))}"""
				)

	def 				_SCREAMING_SNAKE_CASE  (	self:						List[str])							->			Union[str, Any]:

				"""simple docstring"""

				__lowerCAmelCase :    List[str]				=			self.duals.copy()
				while cur[-1] == 0:
							cur.pop(-1)
				return Dual(self.real			,     _SCREAMING_SNAKE_CASE)

	def __add__(	self:						Optional[int]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			Union[str, Any]:

				"""simple docstring"""

				if not isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							return Dual(self.real + other			,     self.duals)
				__lowerCAmelCase :    int				=			self.duals.copy()
				__lowerCAmelCase :    List[Any]				=			other.duals.copy()
				if len(_SCREAMING_SNAKE_CASE) > len(_SCREAMING_SNAKE_CASE):
							o_dual.extend([1] * (len(_SCREAMING_SNAKE_CASE) - len(_SCREAMING_SNAKE_CASE)))
				elif len(_SCREAMING_SNAKE_CASE) < len(_SCREAMING_SNAKE_CASE):
							s_dual.extend([1] * (len(_SCREAMING_SNAKE_CASE) - len(_SCREAMING_SNAKE_CASE)))
				__lowerCAmelCase :    Tuple				=			[]
				for i in range(len(_SCREAMING_SNAKE_CASE)):
							new_duals.append(s_dual[i] + o_dual[i])
				return Dual(self.real + other.real			,     _SCREAMING_SNAKE_CASE)

	SCREAMING_SNAKE_CASE        =      __add__

	def __sub__(	self:						Dict			,     _SCREAMING_SNAKE_CASE:						str)							->			Optional[Any]:

				"""simple docstring"""

				return self + other * -1

	def __mul__(	self:						str			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			Optional[int]:

				"""simple docstring"""

				if not isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    List[Any]				=			[]
							for i in self.duals:
										new_duals.append(i * other)
							return Dual(self.real * other			,     _SCREAMING_SNAKE_CASE)
				__lowerCAmelCase :    List[str]				=			[0] * (len(self.duals) + len(other.duals) + 1)
				for i, item in enumerate(self.duals):
							for j, jtem in enumerate(other.duals):
										new_duals[i + j + 1] += item * jtem
				for k in range(len(self.duals)):
							new_duals[k] += self.duals[k] * other.real
				for index in range(len(other.duals)):
							new_duals[index] += other.duals[index] * self.real
				return Dual(self.real * other.real			,     _SCREAMING_SNAKE_CASE)

	SCREAMING_SNAKE_CASE        =      __mul__

	def __truediv__(	self:						Any			,     _SCREAMING_SNAKE_CASE:						str)							->			Dict:

				"""simple docstring"""

				if not isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    List[str]				=			[]
							for i in self.duals:
										new_duals.append(i / other)
							return Dual(self.real / other			,     _SCREAMING_SNAKE_CASE)
				raise ValueError

	def __floordiv__(	self:						List[Any]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			str:

				"""simple docstring"""

				if not isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							__lowerCAmelCase :    str				=			[]
							for i in self.duals:
										new_duals.append(i // other)
							return Dual(self.real // other			,     _SCREAMING_SNAKE_CASE)
				raise ValueError







	def __pow__(	self:						Optional[Any]			,     _SCREAMING_SNAKE_CASE:						Tuple)							->			List[Any]:

				"""simple docstring"""

				if n < 0 or isinstance(_SCREAMING_SNAKE_CASE			,     _SCREAMING_SNAKE_CASE):
							raise ValueError("power must be a positive integer")
				if n == 0:
							return 1
				if n == 1:
							return self
				__lowerCAmelCase :    List[Any]				=			self
				for _ in range(n - 1):
							x *= self
				return x






def      _lowercase							(    __snake_case   ,__snake_case   ,__snake_case      )		->  Any:
			if not callable(__snake_case      ):
						raise ValueError("differentiate() requires a function as input for func"      )
			if not isinstance(__snake_case   ,(float, int)      ):
						raise ValueError("differentiate() requires a float as input for position"      )
			if not isinstance(__snake_case   ,__snake_case      ):
						raise ValueError("differentiate() requires an int as input for order"      )
			__lowerCAmelCase :    Any				=			Dual(__snake_case   ,1      )
			__lowerCAmelCase :    Tuple				=			func(__snake_case      )
			if order == 0:
						return result.real
			return result.duals[order - 1] * factorial(__snake_case      )


if __name__ == "__main__":
	import doctest

	doctest.testmod()


	def      _lowercase							(    __snake_case      )		->  Tuple:
				return y**2 * y**4





	print(differentiate(f, 9, 2))