



from math import sqrt






def  lowerCamelCase_	(      lowerCAmelCase__	:	int				)       ->							bool:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (
							    number >= 0
							), "'number' must been an int and positive"

							A      						=    True

							# 0 and 1 are none primes.
							if number <= 1:
														A      						=    False

							for divisor in range(2			,	int(round(sqrt(lowerCAmelCase__				)				)				) + 1				):
														# if 'number' divisible by 'divisor' then sets 'status'
														# of false and break up the loop.
														if number % divisor == 0:
																					A      						=    False
																					break

    # precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'status' must been from type bool"

							return status






def  lowerCamelCase_	(      lowerCAmelCase__	:	Tuple				)       ->							str:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (n > 2), "'N' must been an int and > 2"

							# beginList: contains all natural numbers from 2 up to N
							A      						=    list(range(2			,	n + 1				)				)

							A      						=    []  # this list will be returns.

							# actual sieve of erathostenes
							for i in range(len(lowerCAmelCase__				)				):
														for j in range(i + 1			,	len(lowerCAmelCase__				)				):
																					if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
																												A      						=    0

    # filters actual prime numbers.
							A      						=    [x for x in begin_list if x != 0]

							# precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'ans' must been from type list"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	str				)       ->							Dict:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (n > 2), "'N' must been an int and > 2"

							A      						=    []

							# iterates over all numbers between 2 up to N+1
							# if a number is prime then appends to list 'ans'
							for number in range(2			,	n + 1				):
														if is_prime(lowerCAmelCase__				):
																					ans.append(lowerCAmelCase__				)

    # precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'ans' must been from type list"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	Optional[int]				)       ->							Dict:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and number >= 0, "'number' must been an int and >= 0"

							A      						=    []  # this list will be returns of the function.

							# potential prime number factors.

							A      						=    2

							A      						=    number

							if number == 0 or number == 1:
														ans.append(lowerCAmelCase__				)

							# if 'number' not prime then builds the prime factorization of 'number'
							elif not is_prime(lowerCAmelCase__				):
														while quotient != 1:
																					if is_prime(lowerCAmelCase__				) and (quotient % factor == 0):
																												ans.append(lowerCAmelCase__				)
																												quotient /= factor
																					else:
																												factor += 1

							else:
														ans.append(lowerCAmelCase__				)

							# precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'ans' must been from type list"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]				)       ->							Tuple:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (
							    number >= 0
							), "'number' bust been an int and >= 0"

							A      						=    0

							# prime factorization of 'number'
							A      						=    prime_factorization(lowerCAmelCase__				)

							A      						=    max(lowerCAmelCase__				)

							# precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'ans' must been from type int"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	int				)       ->							List[Any]:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (
							    number >= 0
							), "'number' bust been an int and >= 0"

							A      						=    0

							# prime factorization of 'number'
							A      						=    prime_factorization(lowerCAmelCase__				)

							A      						=    min(lowerCAmelCase__				)

							# precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'ans' must been from type int"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]				)       ->							Optional[int]:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'number' must been an int"
							assert isinstance(number % 2 == 0			,	lowerCAmelCase__				), "compare bust been from type bool"

							return number % 2 == 0






def  lowerCamelCase_	(      lowerCAmelCase__	:	Tuple				)       ->							Any:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				), "'number' must been an int"
							assert isinstance(number % 2 != 0			,	lowerCAmelCase__				), "compare bust been from type bool"

							return number % 2 != 0






def  lowerCamelCase_	(      lowerCAmelCase__	:	Optional[int]				)       ->							int:

							'''simple docstring'''






							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (number > 2) and is_even(lowerCAmelCase__				)
							), "'number' must been an int, even and > 2"

							A      						=    []  # this list will returned

							# creates a list of prime numbers between 2 up to 'number'
							A      						=    get_prime_numbers(lowerCAmelCase__				)
							A      						=    len(lowerCAmelCase__				)

							# run variable for while-loops.
							A      						=    0
							A      						=    None

							# exit variable. for break up the loops
							A      						=    True

							while i < len_pn and loop:
														A      						=    i + 1

														while j < len_pn and loop:
																					if prime_numbers[i] + prime_numbers[j] == number:
																												A      						=    False
																												ans.append(prime_numbers[i]				)
																												ans.append(prime_numbers[j]				)

																					j += 1

														i += 1

							# precondition
							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and (len(lowerCAmelCase__				) == 2)
							    and (ans[0] + ans[1] == number)
							    and is_prime(ans[0]				)
							    and is_prime(ans[1]				)
							), "'ans' must contains two primes. And sum of elements must been eq 'number'"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]			,	lowerCAmelCase__	:	Optional[int]				)       ->							List[Any]:

							'''simple docstring'''






							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and (numbera >= 0)
							    and (numbera >= 0)
							), "'number1' and 'number2' must been positive integer."

							A      						=    0

							while numbera != 0:
														A      						=    numbera % numbera
														A      						=    numbera
														A      						=    rest

							# precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (
							    numbera >= 0
							), "'number' must been from type int and positive"

							return numbera






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]			,	lowerCAmelCase__	:	List[Any]				)       ->							Union[str, Any]:

							'''simple docstring'''






							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and (numbera >= 1)
							    and (numbera >= 1)
							), "'number1' and 'number2' must been positive integer."

							A      						=    1  # actual answer that will be return.

							# for kgV (x,1)
							if numbera > 1 and numbera > 1:
														# builds the prime factorization of 'number1' and 'number2'
														A      						=    prime_factorization(lowerCAmelCase__				)
														A      						=    prime_factorization(lowerCAmelCase__				)

							elif numbera == 1 or numbera == 1:
														A      						=    []
														A      						=    []
														A      						=    max(lowerCAmelCase__			,	lowerCAmelCase__				)

							A      						=    0
							A      						=    0

							A      						=    []  # captured numbers int both 'primeFac1' and 'primeFac2'

							# iterates through primeFac1
							for n in prime_fac_a:
														if n not in done:
																					if n in prime_fac_a:
																												A      						=    prime_fac_a.count(lowerCAmelCase__				)
																												A      						=    prime_fac_a.count(lowerCAmelCase__				)

																												for _ in range(max(lowerCAmelCase__			,	lowerCAmelCase__				)				):
																																			ans *= n

																					else:
																												A      						=    prime_fac_a.count(lowerCAmelCase__				)

																												for _ in range(lowerCAmelCase__				):
																																			ans *= n

																					done.append(lowerCAmelCase__				)

    # iterates through primeFac2
							for n in prime_fac_a:
														if n not in done:
																					A      						=    prime_fac_a.count(lowerCAmelCase__				)

																					for _ in range(lowerCAmelCase__				):
																												ans *= n

																					done.append(lowerCAmelCase__				)

    # precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (
							    ans >= 0
							), "'ans' must been from type int and positive"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	Tuple				)       ->							Any:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (n >= 0), "'number' must been a positive int"

							A      						=    0
							A      						=    2  # this variable holds the answer

							while index < n:
														index += 1

														ans += 1  # counts to the next number

														# if ans not prime then
														# runs to the next prime number.
														while not is_prime(lowerCAmelCase__				):
																					ans += 1

    # precondition
							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and is_prime(
							    lowerCAmelCase__				), "'ans' must been a prime number and from type int"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]			,	lowerCAmelCase__	:	str				)       ->							Optional[int]:

							'''simple docstring'''






							assert (
							    is_prime(lowerCAmelCase__				) and is_prime(lowerCAmelCase__				) and (p_number_a < p_number_a)
							), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

							A      						=    p_number_a + 1  # jump to the next number

							A      						=    []  # this list will be returns.

							# if number is not prime then
							# fetch the next prime number.
							while not is_prime(lowerCAmelCase__				):
														number += 1

							while number < p_number_a:
														ans.append(lowerCAmelCase__				)

														number += 1

														# fetch the next prime number.
														while not is_prime(lowerCAmelCase__				):
																					number += 1

    # precondition
							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and ans[0] != p_number_a
							    and ans[len(lowerCAmelCase__				) - 1] != p_number_a
							), "'ans' must been a list without the arguments"

							# 'ans' contains not 'pNumber1' and 'pNumber2' !
							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[Any]				)       ->							List[str]:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (n >= 1), "'n' must been int and >= 1"

							A      						=    []  # will be returned.

							for divisor in range(1			,	n + 1				):
														if n % divisor == 0:
																					ans.append(lowerCAmelCase__				)

    # precondition
							assert ans[0] == 1 and ans[len(lowerCAmelCase__				) - 1] == n, "Error in function getDivisiors(...)"

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	Optional[int]				)       ->							Optional[Any]:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (
							    number > 1
							), "'number' must been an int and >= 1"

							A      						=    get_divisors(lowerCAmelCase__				)

							# precondition
							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and (divisors[0] == 1)
							    and (divisors[len(lowerCAmelCase__				) - 1] == number)
							), "Error in help-function getDivisiors(...)"

							# summed all divisors up to 'number' (exclusive), hence [:-1]
							return sum(divisors[:-1]				) == number






def  lowerCamelCase_	(      lowerCAmelCase__	:	Any			,	lowerCAmelCase__	:	Union[str, Any]				)       ->							str:

							'''simple docstring'''






							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and (denominator != 0)
							), "The arguments must been from type int and 'denominator' != 0"

							# build the greatest common divisor of numerator and denominator.
							A      						=    gcd(abs(lowerCAmelCase__				)			,	abs(lowerCAmelCase__				)				)

							# precondition
							assert (
							    isinstance(lowerCAmelCase__			,	lowerCAmelCase__				)
							    and (numerator % gcd_of_fraction == 0)
							    and (denominator % gcd_of_fraction == 0)
							), "Error in function gcd(...,...)"

							return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)






def  lowerCamelCase_	(      lowerCAmelCase__	:	Dict				)       ->							int:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (n >= 0), "'n' must been a int and >= 0"

							A      						=    1  # this will be return.

							for factor in range(1			,	n + 1				):
														ans *= factor

							return ans






def  lowerCamelCase_	(      lowerCAmelCase__	:	List[str]				)       ->							Union[str, Any]:

							'''simple docstring'''






							assert isinstance(lowerCAmelCase__			,	lowerCAmelCase__				) and (n >= 0), "'n' must been an int and >= 0"

							A      						=    0
							A      						=    1
							A      						=    1  # this will be return

							for _ in range(n - 1				):
														A      						=    ans
														ans += fiba
														A      						=    tmp

							return ans



import collections
from typing import List, Optional, Union

from ...tokenization_utils_base import BatchEncoding
from ...utils import TensorType, add_end_docstrings, add_start_docstrings, logging
from ..bert.tokenization_bert_fast import BertTokenizerFast
from .tokenization_dpr import DPRContextEncoderTokenizer, DPRQuestionEncoderTokenizer, DPRReaderTokenizer


A			:						Optional[Any]        =  logging.get_logger(__name__)

A			:						str        =  {'vocab_file': 'vocab.txt', 'tokenizer_file': 'tokenizer.json'}

A			:						Any        =  {
    'vocab_file': {
        'facebook/dpr-ctx_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/vocab.txt'
        ),
        'facebook/dpr-ctx_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/vocab.txt'
        ),
    },
    'tokenizer_file': {
        'facebook/dpr-ctx_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/tokenizer.json'
        ),
        'facebook/dpr-ctx_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/tokenizer.json'
        ),
    },
}
A			:						Dict        =  {
    'vocab_file': {
        'facebook/dpr-question_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/vocab.txt'
        ),
        'facebook/dpr-question_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/vocab.txt'
        ),
    },
    'tokenizer_file': {
        'facebook/dpr-question_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/tokenizer.json'
        ),
        'facebook/dpr-question_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/tokenizer.json'
        ),
    },
}
A			:						Optional[int]        =  {
    'vocab_file': {
        'facebook/dpr-reader-single-nq-base': (
            'https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/vocab.txt'
        ),
        'facebook/dpr-reader-multiset-base': (
            'https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/vocab.txt'
        ),
    },
    'tokenizer_file': {
        'facebook/dpr-reader-single-nq-base': (
            'https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/tokenizer.json'
        ),
        'facebook/dpr-reader-multiset-base': (
            'https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/tokenizer.json'
        ),
    },
}

A			:						int        =  {
    'facebook/dpr-ctx_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-ctx_encoder-multiset-base': 5_1_2,
}
A			:						Optional[Any]        =  {
    'facebook/dpr-question_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-question_encoder-multiset-base': 5_1_2,
}
A			:						Any        =  {
    'facebook/dpr-reader-single-nq-base': 5_1_2,
    'facebook/dpr-reader-multiset-base': 5_1_2,
}


A			:						Union[str, Any]        =  {
    'facebook/dpr-ctx_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-ctx_encoder-multiset-base': {'do_lower_case': True},
}
A			:						Tuple        =  {
    'facebook/dpr-question_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-question_encoder-multiset-base': {'do_lower_case': True},
}
A			:						Any        =  {
    'facebook/dpr-reader-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-reader-multiset-base': {'do_lower_case': True},
}



class 				A       (			UpperCAmelCase__				):
					'''simple docstring'''






					A__     =					VOCAB_FILES_NAMES
					A__     =					CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
					A__     =					CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
					A__     =					CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION
					A__     =					DPRContextEncoderTokenizer






class 				A       (			UpperCAmelCase__				):
					'''simple docstring'''






					A__     =					VOCAB_FILES_NAMES
					A__     =					QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
					A__     =					QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
					A__     =					QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION
					A__     =					DPRQuestionEncoderTokenizer






A			:						Any        =  collections.namedtuple(
    'DPRSpanPrediction', ['span_score', 'relevance_score', 'doc_id', 'start_index', 'end_index', 'text']
)

A			:						Optional[Any]        =  collections.namedtuple('DPRReaderOutput', ['start_logits', 'end_logits', 'relevance_logits'])


A			:						int        =  r'\n    Return a dictionary with the token ids of the input strings and other information to give to `.decode_best_spans`.\n    It converts the strings of a question and different passages (title and text) in a sequence of IDs (integers),\n    using the tokenizer and vocabulary. The resulting `input_ids` is a matrix of size `(n_passages, sequence_length)`\n    with the format:\n\n    [CLS] <question token ids> [SEP] <titles ids> [SEP] <texts ids>\n\n    Args:\n        questions (`str` or `List[str]`):\n            The questions to be encoded. You can specify one question for many passages. In this case, the question\n            will be duplicated like `[questions] * n_passages`. Otherwise you have to specify as many questions as in\n            `titles` or `texts`.\n        titles (`str` or `List[str]`):\n            The passages titles to be encoded. This can be a string or a list of strings if there are several passages.\n        texts (`str` or `List[str]`):\n            The passages texts to be encoded. This can be a string or a list of strings if there are several passages.\n        padding (`bool`, `str` or [`~utils.PaddingStrategy`], *optional*, defaults to `False`):\n            Activates and controls padding. Accepts the following values:\n\n            - `True` or `\'longest\'`: Pad to the longest sequence in the batch (or no padding if only a single sequence\n              if provided).\n            - `\'max_length\'`: Pad to a maximum length specified with the argument `max_length` or to the maximum\n              acceptable input length for the model if that argument is not provided.\n            - `False` or `\'do_not_pad\'` (default): No padding (i.e., can output a batch with sequences of different\n              lengths).\n        truncation (`bool`, `str` or [`~tokenization_utils_base.TruncationStrategy`], *optional*, defaults to `False`):\n            Activates and controls truncation. Accepts the following values:\n\n            - `True` or `\'longest_first\'`: Truncate to a maximum length specified with the argument `max_length` or to\n              the maximum acceptable input length for the model if that argument is not provided. This will truncate\n              token by token, removing a token from the longest sequence in the pair if a pair of sequences (or a batch\n              of pairs) is provided.\n            - `\'only_first\'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum\n              acceptable input length for the model if that argument is not provided. This will only truncate the first\n              sequence of a pair if a pair of sequences (or a batch of pairs) is provided.\n            - `\'only_second\'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum\n              acceptable input length for the model if that argument is not provided. This will only truncate the\n              second sequence of a pair if a pair of sequences (or a batch of pairs) is provided.\n            - `False` or `\'do_not_truncate\'` (default): No truncation (i.e., can output batch with sequence lengths\n              greater than the model maximum admissible input size).\n        max_length (`int`, *optional*):\n                Controls the maximum length to use by one of the truncation/padding parameters.\n\n                If left unset or set to `None`, this will use the predefined model maximum length if a maximum length\n                is required by one of the truncation/padding parameters. If the model has no specific maximum input\n                length (like XLNet) truncation/padding to a maximum length will be deactivated.\n        return_tensors (`str` or [`~utils.TensorType`], *optional*):\n                If set, will return tensors instead of list of python integers. Acceptable values are:\n\n                - `\'tf\'`: Return TensorFlow `tf.constant` objects.\n                - `\'pt\'`: Return PyTorch `torch.Tensor` objects.\n                - `\'np\'`: Return Numpy `np.ndarray` objects.\n        return_attention_mask (`bool`, *optional*):\n            Whether or not to return the attention mask. If not set, will return the attention mask according to the\n            specific tokenizer\'s default, defined by the `return_outputs` attribute.\n\n            [What are attention masks?](../glossary#attention-mask)\n\n    Return:\n        `Dict[str, List[List[int]]]`: A dictionary with the following keys:\n\n        - `input_ids`: List of token ids to be fed to a model.\n        - `attention_mask`: List of indices specifying which tokens should be attended to by the model.\n    '



@add_start_docstrings(UpperCAmelCase__				)
class 				A       :
					'''simple docstring'''






					def __call__(self       :		str ,   _UpperCAmelCase       :		str ,   _UpperCAmelCase       :		Optional[str] = None ,   _UpperCAmelCase       :		Optional[str] = None ,   _UpperCAmelCase       :		Union[bool, str] = False ,   _UpperCAmelCase       :		Union[bool, str] = False ,   _UpperCAmelCase       :		Optional[int] = None ,   _UpperCAmelCase       :		Optional[Union[str, TensorType]] = None ,   _UpperCAmelCase       :		Optional[bool] = None ,   **_UpperCAmelCase       :		Any ,   )		->  BatchEncoding:




							"""simple docstring"""


							if titles is None and texts is None:
									return super().__call__(
									    _UpperCAmelCase ,   padding=_UpperCAmelCase ,   truncation=_UpperCAmelCase ,   max_length=_UpperCAmelCase ,   return_tensors=_UpperCAmelCase ,   return_attention_mask=_UpperCAmelCase ,   **_UpperCAmelCase ,   )
							elif titles is None or texts is None:
									lowercase__	     =						titles if texts is None else texts
									return super().__call__(
									    _UpperCAmelCase ,   _UpperCAmelCase ,   padding=_UpperCAmelCase ,   truncation=_UpperCAmelCase ,   max_length=_UpperCAmelCase ,   return_tensors=_UpperCAmelCase ,   return_attention_mask=_UpperCAmelCase ,   **_UpperCAmelCase ,   )
							lowercase__	     =						titles if not isinstance(_UpperCAmelCase ,   _UpperCAmelCase						) else [titles]
							lowercase__	     =						texts if not isinstance(_UpperCAmelCase ,   _UpperCAmelCase						) else [texts]
							lowercase__	     =						len(_UpperCAmelCase						)
							lowercase__	     =						questions if not isinstance(_UpperCAmelCase ,   _UpperCAmelCase						) else [questions] * n_passages
							assert len(_UpperCAmelCase						) == len(
							    _UpperCAmelCase						), f'''There should be as many titles than texts but got {len(_UpperCAmelCase						)} titles and {len(_UpperCAmelCase						)} texts.'''
							lowercase__	     =						super().__call__(_UpperCAmelCase ,   _UpperCAmelCase ,   padding=_UpperCAmelCase ,   truncation=_UpperCAmelCase						)["""input_ids"""]
							lowercase__	     =						super().__call__(_UpperCAmelCase ,   add_special_tokens=_UpperCAmelCase ,   padding=_UpperCAmelCase ,   truncation=_UpperCAmelCase						)["""input_ids"""]
							lowercase__	     =						{
							    """input_ids""": [
							        (encoded_question_and_title + encoded_text)[:max_length]
							        if max_length is not None and truncation
							        else encoded_question_and_title + encoded_text
							        for encoded_question_and_title, encoded_text in zip(_UpperCAmelCase ,   _UpperCAmelCase						)
							    ]
							}
							if return_attention_mask is not False:
									lowercase__	     =						[]
									for input_ids in encoded_inputs["input_ids"]:
											attention_mask.append([int(input_id != self.pad_token_id						) for input_id in input_ids]						)
									lowercase__	     =						attention_mask
							return self.pad(_UpperCAmelCase ,   padding=_UpperCAmelCase ,   max_length=_UpperCAmelCase ,   return_tensors=_UpperCAmelCase						)

					def     lowerCamelCase__	(self       :		List[str] ,   _UpperCAmelCase       :		BatchEncoding ,   _UpperCAmelCase       :		DPRReaderOutput ,   _UpperCAmelCase       :		int = 16 ,   _UpperCAmelCase       :		int = 64 ,   _UpperCAmelCase       :		int = 4 ,   )		->  List[DPRSpanPrediction]:




							"""simple docstring"""


							lowercase__	     =						reader_input["""input_ids"""]
							lowercase__     ,      lowercase__     ,      lowercase__	     =						reader_output[:3]
							lowercase__	     =						len(_UpperCAmelCase						)
							lowercase__	     =						sorted(range(_UpperCAmelCase						) ,   reverse=_UpperCAmelCase ,   key=relevance_logits.__getitem__						)
							lowercase__	     =						[]
							for doc_id in sorted_docs:
									lowercase__	     =						list(input_ids[doc_id]						)
									# assuming question & title information is at the beginning of the sequence
									lowercase__	     =						sequence_ids.index(self.sep_token_id ,   2						) + 1  # second sep id
									if sequence_ids[-1] == self.pad_token_id:
											lowercase__	     =						sequence_ids.index(self.pad_token_id						)
									else:
											lowercase__	     =						len(_UpperCAmelCase						)

									lowercase__	     =						self._get_best_spans(
									    start_logits=start_logits[doc_id][passage_offset:sequence_len] ,   end_logits=end_logits[doc_id][passage_offset:sequence_len] ,   max_answer_length=_UpperCAmelCase ,   top_spans=_UpperCAmelCase ,   )
									for start_index, end_index in best_spans:
											start_index += passage_offset
											end_index += passage_offset
											nbest_spans_predictions.append(
											    DPRSpanPrediction(
											        span_score=start_logits[doc_id][start_index] + end_logits[doc_id][end_index] ,   relevance_score=relevance_logits[doc_id] ,   doc_id=_UpperCAmelCase ,   start_index=_UpperCAmelCase ,   end_index=_UpperCAmelCase ,   text=self.decode(sequence_ids[start_index : end_index + 1]						) ,   )						)
									if len(_UpperCAmelCase						) >= num_spans:
											break
							return nbest_spans_predictions[:num_spans]


					def     lowerCamelCase__	(self       :		Optional[int] ,   _UpperCAmelCase       :		List[int] ,   _UpperCAmelCase       :		List[int] ,   _UpperCAmelCase       :		int ,   _UpperCAmelCase       :		int ,   )		->  List[DPRSpanPrediction]:




							"""simple docstring"""


							lowercase__	     =						[]
							for start_index, start_score in enumerate(_UpperCAmelCase						):
									for answer_length, end_score in enumerate(end_logits[start_index : start_index + max_answer_length]						):
											scores.append(((start_index, start_index + answer_length), start_score + end_score)						)
							lowercase__	     =						sorted(_UpperCAmelCase ,   key=lambda _UpperCAmelCase						: x[1] ,   reverse=_UpperCAmelCase						)
							lowercase__	     =						[]
							for (start_index, end_index), score in scores:
									assert start_index <= end_index, f'''Wrong span indices: [{start_index}:{end_index}]'''
									lowercase__	     =						end_index - start_index + 1
									assert length <= max_answer_length, f'''Span is too long: {length} > {max_answer_length}'''
									if any(
									    start_index <= prev_start_index <= prev_end_index <= end_index
									    or prev_start_index <= start_index <= end_index <= prev_end_index
									    for (prev_start_index, prev_end_index) in chosen_span_intervals						):
											continue
									chosen_span_intervals.append((start_index, end_index)						)

									if len(_UpperCAmelCase						) == top_spans:
											break
							return chosen_span_intervals






@add_end_docstrings(UpperCAmelCase__				)
class 				A       (			UpperCAmelCase__					,    UpperCAmelCase__				):
					'''simple docstring'''






					A__     =					VOCAB_FILES_NAMES
					A__     =					READER_PRETRAINED_VOCAB_FILES_MAP
					A__     =					READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
					A__     =					READER_PRETRAINED_INIT_CONFIGURATION
					A__     =					['''input_ids''', '''attention_mask''']
					A__     =					DPRReaderTokenizer

