




"""simple docstring"""







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      =							logging.get_logger(__name__)

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

a      =							{
    '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      =							{
    '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      =							{
    '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      =							{
    'facebook/dpr-ctx_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-ctx_encoder-multiset-base': 5_1_2,
}
a      =							{
    'facebook/dpr-question_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-question_encoder-multiset-base': 5_1_2,
}
a      =							{
    'facebook/dpr-reader-single-nq-base': 5_1_2,
    'facebook/dpr-reader-multiset-base': 5_1_2,
}


a      =							{
    'facebook/dpr-ctx_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-ctx_encoder-multiset-base': {'do_lower_case': True},
}
a      =							{
    'facebook/dpr-question_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-question_encoder-multiset-base': {'do_lower_case': True},
}
a      =							{
    'facebook/dpr-reader-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-reader-multiset-base': {'do_lower_case': True},
}






class       SCREAMING_SNAKE_CASE__					(					_a					):
						_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       SCREAMING_SNAKE_CASE__					(					_a					):
						_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      =							collections.namedtuple(
    'DPRSpanPrediction', ['span_score', 'relevance_score', 'doc_id', 'start_index', 'end_index', 'text']
)

a      =							collections.namedtuple('DPRReaderOutput', ['start_logits', 'end_logits', 'relevance_logits'])


a      =							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(_a					)
class       SCREAMING_SNAKE_CASE__					:


						def __call__(							self				:			Tuple						,						lowerCAmelCase				:			List[str]						,						lowerCAmelCase				:			Optional[str] = None						,						lowerCAmelCase				:			Optional[str] = None						,						lowerCAmelCase				:			Union[bool, str] = False						,						lowerCAmelCase				:			Union[bool, str] = False						,						lowerCAmelCase				:			Optional[int] = None						,						lowerCAmelCase				:			Optional[Union[str, TensorType]] = None						,						lowerCAmelCase				:			Optional[bool] = None						,						**lowerCAmelCase				:			Union[str, Any]						,						):
										if titles is None and texts is None:
														return super().__call__(
														    lowerCAmelCase						,						padding=lowerCAmelCase						,						truncation=lowerCAmelCase						,						max_length=lowerCAmelCase						,						return_tensors=lowerCAmelCase						,						return_attention_mask=lowerCAmelCase						,						**lowerCAmelCase						,						)
										elif titles is None or texts is None:
														lowerCAmelCase  =				titles if texts is None else texts
														return super().__call__(
														    lowerCAmelCase						,						lowerCAmelCase						,						padding=lowerCAmelCase						,						truncation=lowerCAmelCase						,						max_length=lowerCAmelCase						,						return_tensors=lowerCAmelCase						,						return_attention_mask=lowerCAmelCase						,						**lowerCAmelCase						,						)
										lowerCAmelCase  =				titles if not isinstance(lowerCAmelCase						,						lowerCAmelCase					) else [titles]
										lowerCAmelCase  =				texts if not isinstance(lowerCAmelCase						,						lowerCAmelCase					) else [texts]
										lowerCAmelCase  =				len(lowerCAmelCase					)
										lowerCAmelCase  =				questions if not isinstance(lowerCAmelCase						,						lowerCAmelCase					) else [questions] * n_passages
										assert len(lowerCAmelCase					) == len(
										    lowerCAmelCase					), f'''There should be as many titles than texts but got {len(lowerCAmelCase					)} titles and {len(lowerCAmelCase					)} texts.'''
										lowerCAmelCase  =				super().__call__(lowerCAmelCase						,						lowerCAmelCase						,						padding=lowerCAmelCase						,						truncation=lowerCAmelCase					)["""input_ids"""]
										lowerCAmelCase  =				super().__call__(lowerCAmelCase						,						add_special_tokens=lowerCAmelCase						,						padding=lowerCAmelCase						,						truncation=lowerCAmelCase					)["""input_ids"""]
										lowerCAmelCase  =				{
										    """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(lowerCAmelCase						,						lowerCAmelCase					)
										    ]
										}
										if return_attention_mask is not False:
														lowerCAmelCase  =				[]
														for input_ids in encoded_inputs["input_ids"]:
																		attention_mask.append([int(input_id != self.pad_token_id					) for input_id in input_ids]					)
														lowerCAmelCase  =				attention_mask
										return self.pad(lowerCAmelCase						,						padding=lowerCAmelCase						,						max_length=lowerCAmelCase						,						return_tensors=lowerCAmelCase					)


						def   __lowercase (							self				:			Tuple						,						lowerCAmelCase				:			BatchEncoding						,						lowerCAmelCase				:			DPRReaderOutput						,						lowerCAmelCase				:			int = 16						,						lowerCAmelCase				:			int = 64						,						lowerCAmelCase				:			int = 4						,						):
										lowerCAmelCase  =				reader_input["""input_ids"""]
										lowerCAmelCase ,						lowerCAmelCase ,						lowerCAmelCase  =				reader_output[:3]
										lowerCAmelCase  =				len(lowerCAmelCase					)
										lowerCAmelCase  =				sorted(range(lowerCAmelCase					)						,						reverse=lowerCAmelCase						,						key=relevance_logits.__getitem__					)
										lowerCAmelCase  =				[]
										for doc_id in sorted_docs:
														lowerCAmelCase  =				list(input_ids[doc_id]					)
														# assuming question & title information is at the beginning of the sequence
														lowerCAmelCase  =				sequence_ids.index(self.sep_token_id						,						2					) + 1  # second sep id
														if sequence_ids[-1] == self.pad_token_id:
																		lowerCAmelCase  =				sequence_ids.index(self.pad_token_id					)
														else:
																		lowerCAmelCase  =				len(lowerCAmelCase					)

														lowerCAmelCase  =				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=lowerCAmelCase						,						top_spans=lowerCAmelCase						,						)
														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=lowerCAmelCase						,						start_index=lowerCAmelCase						,						end_index=lowerCAmelCase						,						text=self.decode(sequence_ids[start_index : end_index + 1]					)						,						)					)
														if len(lowerCAmelCase					) >= num_spans:
																		break
										return nbest_spans_predictions[:num_spans]




						def   __lowercase (							self				:			Optional[Any]						,						lowerCAmelCase				:			List[int]						,						lowerCAmelCase				:			List[int]						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int						,						):
										lowerCAmelCase  =				[]
										for start_index, start_score in enumerate(lowerCAmelCase					):
														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)					)
										lowerCAmelCase  =				sorted(lowerCAmelCase						,						key=lambda lowerCAmelCase					: x[1]						,						reverse=lowerCAmelCase					)
										lowerCAmelCase  =				[]
										for (start_index, end_index), score in scores:
														assert start_index <= end_index, f'''Wrong span indices: [{start_index}:{end_index}]'''
														lowerCAmelCase  =				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(lowerCAmelCase					) == top_spans:
																		break
										return chosen_span_intervals






@add_end_docstrings(_a					)
class       SCREAMING_SNAKE_CASE__					(					_a						,				_a					):
						_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











"""simple docstring"""







from collections import deque
from math import floor
from random import random
from time import time






class       SCREAMING_SNAKE_CASE__					:


						def __init__(							self				:			Union[str, Any]					):
										lowerCAmelCase  =				{}


						def   __lowercase (							self				:			Optional[int]						,						lowerCAmelCase				:			Union[str, Any]						,						lowerCAmelCase				:			Optional[Any]						,						lowerCAmelCase				:			Union[str, Any]=1					):
										if self.graph.get(lowerCAmelCase					):
														if self.graph[u].count([w, v]					) == 0:
																		self.graph[u].append([w, v]					)
										else:
														lowerCAmelCase  =				[[w, v]]
										if not self.graph.get(lowerCAmelCase					):
														lowerCAmelCase  =				[]


						def   __lowercase (							self				:			Optional[int]					):
										return list(self.graph					)


						def   __lowercase (							self				:			Optional[Any]						,						lowerCAmelCase				:			Optional[Any]						,						lowerCAmelCase				:			Dict					):
										if self.graph.get(lowerCAmelCase					):
														for _ in self.graph[u]:
																		if _[1] == v:
																						self.graph[u].remove(lowerCAmelCase					)


						def   __lowercase (							self				:			List[str]						,						lowerCAmelCase				:			Tuple=-2						,						lowerCAmelCase				:			List[Any]=-1					):
										if s == d:
														return []
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				[]
										if s == -2:
														lowerCAmelCase  =				list(self.graph					)[0]
										stack.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										lowerCAmelCase  =				s

										while True:
														# check if there is any non isolated nodes
														if len(self.graph[s]					) != 0:
																		lowerCAmelCase  =				s
																		for node in self.graph[s]:
																						if visited.count(node[1]					) < 1:
																										if node[1] == d:
																														visited.append(lowerCAmelCase					)
																														return visited
																										else:
																														stack.append(node[1]					)
																														visited.append(node[1]					)
																														lowerCAmelCase  =				node[1]
																														break

            # check if all the children are visited
														if s == ss:
																		stack.pop()
																		if len(lowerCAmelCase					) != 0:
																						lowerCAmelCase  =				stack[len(lowerCAmelCase					) - 1]
														else:
																		lowerCAmelCase  =				ss

														# check if se have reached the starting point
														if len(lowerCAmelCase					) == 0:
																		return visited


						def   __lowercase (							self				:			Tuple						,						lowerCAmelCase				:			Any=-1					):
										if c == -1:
														lowerCAmelCase  =				floor(random() * 1_0000					) + 10
										for i in range(lowerCAmelCase					):
														# every vertex has max 100 edges
														for _ in range(floor(random() * 102					) + 1					):
																		lowerCAmelCase  =				floor(random() * c					) + 1
																		if n != i:
																						self.add_pair(lowerCAmelCase						,						lowerCAmelCase						,						1					)


						def   __lowercase (							self				:			Optional[int]						,						lowerCAmelCase				:			List[str]=-2					):
										lowerCAmelCase  =				deque()
										lowerCAmelCase  =				[]
										if s == -2:
														lowerCAmelCase  =				list(self.graph					)[0]
										d.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										while d:
														lowerCAmelCase  =				d.popleft()
														if len(self.graph[s]					) != 0:
																		for node in self.graph[s]:
																						if visited.count(node[1]					) < 1:
																										d.append(node[1]					)
																										visited.append(node[1]					)
										return visited


						def   __lowercase (							self				:			List[Any]						,						lowerCAmelCase				:			Union[str, Any]					):
										lowerCAmelCase  =				0
										for x in self.graph:
														for y in self.graph[x]:
																		if y[1] == u:
																						count += 1
										return count


						def   __lowercase (							self				:			int						,						lowerCAmelCase				:			Tuple					):
										return len(self.graph[u]					)


						def   __lowercase (							self				:			Optional[int]						,						lowerCAmelCase				:			Optional[Any]=-2					):
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				[]
										if s == -2:
														lowerCAmelCase  =				list(self.graph					)[0]
										stack.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										lowerCAmelCase  =				s
										lowerCAmelCase  =				[]

										while True:
														# check if there is any non isolated nodes
														if len(self.graph[s]					) != 0:
																		lowerCAmelCase  =				s
																		for node in self.graph[s]:
																						if visited.count(node[1]					) < 1:
																										stack.append(node[1]					)
																										visited.append(node[1]					)
																										lowerCAmelCase  =				node[1]
																										break

            # check if all the children are visited
														if s == ss:
																		sorted_nodes.append(stack.pop()					)
																		if len(lowerCAmelCase					) != 0:
																						lowerCAmelCase  =				stack[len(lowerCAmelCase					) - 1]
														else:
																		lowerCAmelCase  =				ss

														# check if se have reached the starting point
														if len(lowerCAmelCase					) == 0:
																		return sorted_nodes


						def   __lowercase (							self				:			Any					):
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				list(self.graph					)[0]
										stack.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										lowerCAmelCase  =				-2
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				s
										lowerCAmelCase  =				False
										lowerCAmelCase  =				set()

										while True:
														# check if there is any non isolated nodes
														if len(self.graph[s]					) != 0:
																		lowerCAmelCase  =				s
																		for node in self.graph[s]:
																						if (
																						    visited.count(node[1]					) > 0
																						    and node[1] != parent
																						    and indirect_parents.count(node[1]					) > 0
																						    and not on_the_way_back
																						):
																										lowerCAmelCase  =				len(lowerCAmelCase					) - 1
																										while len_stack >= 0:
																														if stack[len_stack] == node[1]:
																																		anticipating_nodes.add(node[1]					)
																																		break
																														else:
																																		anticipating_nodes.add(stack[len_stack]					)
																																		len_stack -= 1
																						if visited.count(node[1]					) < 1:
																										stack.append(node[1]					)
																										visited.append(node[1]					)
																										lowerCAmelCase  =				node[1]
																										break

            # check if all the children are visited
														if s == ss:
																		stack.pop()
																		lowerCAmelCase  =				True
																		if len(lowerCAmelCase					) != 0:
																						lowerCAmelCase  =				stack[len(lowerCAmelCase					) - 1]
														else:
																		lowerCAmelCase  =				False
																		indirect_parents.append(lowerCAmelCase					)
																		lowerCAmelCase  =				s
																		lowerCAmelCase  =				ss

														# check if se have reached the starting point
														if len(lowerCAmelCase					) == 0:
																		return list(lowerCAmelCase					)


						def   __lowercase (							self				:			Tuple					):
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				list(self.graph					)[0]
										stack.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										lowerCAmelCase  =				-2
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				s
										lowerCAmelCase  =				False
										lowerCAmelCase  =				set()

										while True:
														# check if there is any non isolated nodes
														if len(self.graph[s]					) != 0:
																		lowerCAmelCase  =				s
																		for node in self.graph[s]:
																						if (
																						    visited.count(node[1]					) > 0
																						    and node[1] != parent
																						    and indirect_parents.count(node[1]					) > 0
																						    and not on_the_way_back
																						):
																										lowerCAmelCase  =				len(lowerCAmelCase					) - 1
																										while len_stack_minus_one >= 0:
																														if stack[len_stack_minus_one] == node[1]:
																																		anticipating_nodes.add(node[1]					)
																																		break
																														else:
																																		return True
																						if visited.count(node[1]					) < 1:
																										stack.append(node[1]					)
																										visited.append(node[1]					)
																										lowerCAmelCase  =				node[1]
																										break

            # check if all the children are visited
														if s == ss:
																		stack.pop()
																		lowerCAmelCase  =				True
																		if len(lowerCAmelCase					) != 0:
																						lowerCAmelCase  =				stack[len(lowerCAmelCase					) - 1]
														else:
																		lowerCAmelCase  =				False
																		indirect_parents.append(lowerCAmelCase					)
																		lowerCAmelCase  =				s
																		lowerCAmelCase  =				ss

														# check if se have reached the starting point
														if len(lowerCAmelCase					) == 0:
																		return False


						def   __lowercase (							self				:			List[Any]						,						lowerCAmelCase				:			Any=-2						,						lowerCAmelCase				:			Tuple=-1					):
										lowerCAmelCase  =				time()
										self.dfs(lowerCAmelCase						,						lowerCAmelCase					)
										lowerCAmelCase  =				time()
										return end - begin




						def   __lowercase (							self				:			int						,						lowerCAmelCase				:			str=-2					):
										lowerCAmelCase  =				time()
										self.bfs(lowerCAmelCase					)
										lowerCAmelCase  =				time()
										return end - begin






class       SCREAMING_SNAKE_CASE__					:


						def __init__(							self				:			int					):
										lowerCAmelCase  =				{}


						def   __lowercase (							self				:			Optional[Any]						,						lowerCAmelCase				:			Tuple						,						lowerCAmelCase				:			str						,						lowerCAmelCase				:			str=1					):
										# check if the u exists
										if self.graph.get(lowerCAmelCase					):
														# if there already is a edge
														if self.graph[u].count([w, v]					) == 0:
																		self.graph[u].append([w, v]					)
										else:
														# if u does not exist
														lowerCAmelCase  =				[[w, v]]
										# add the other way
										if self.graph.get(lowerCAmelCase					):
														# if there already is a edge
														if self.graph[v].count([w, u]					) == 0:
																		self.graph[v].append([w, u]					)
										else:
														# if u does not exist
														lowerCAmelCase  =				[[w, u]]


						def   __lowercase (							self				:			Dict						,						lowerCAmelCase				:			Any						,						lowerCAmelCase				:			int					):
										if self.graph.get(lowerCAmelCase					):
														for _ in self.graph[u]:
																		if _[1] == v:
																						self.graph[u].remove(lowerCAmelCase					)
        # the other way round
										if self.graph.get(lowerCAmelCase					):
														for _ in self.graph[v]:
																		if _[1] == u:
																						self.graph[v].remove(lowerCAmelCase					)


						def   __lowercase (							self				:			Dict						,						lowerCAmelCase				:			Optional[int]=-2						,						lowerCAmelCase				:			Optional[Any]=-1					):
										if s == d:
														return []
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				[]
										if s == -2:
														lowerCAmelCase  =				list(self.graph					)[0]
										stack.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										lowerCAmelCase  =				s

										while True:
														# check if there is any non isolated nodes
														if len(self.graph[s]					) != 0:
																		lowerCAmelCase  =				s
																		for node in self.graph[s]:
																						if visited.count(node[1]					) < 1:
																										if node[1] == d:
																														visited.append(lowerCAmelCase					)
																														return visited
																										else:
																														stack.append(node[1]					)
																														visited.append(node[1]					)
																														lowerCAmelCase  =				node[1]
																														break

            # check if all the children are visited
														if s == ss:
																		stack.pop()
																		if len(lowerCAmelCase					) != 0:
																						lowerCAmelCase  =				stack[len(lowerCAmelCase					) - 1]
														else:
																		lowerCAmelCase  =				ss

														# check if se have reached the starting point
														if len(lowerCAmelCase					) == 0:
																		return visited


						def   __lowercase (							self				:			Any						,						lowerCAmelCase				:			Dict=-1					):
										if c == -1:
														lowerCAmelCase  =				floor(random() * 1_0000					) + 10
										for i in range(lowerCAmelCase					):
														# every vertex has max 100 edges
														for _ in range(floor(random() * 102					) + 1					):
																		lowerCAmelCase  =				floor(random() * c					) + 1
																		if n != i:
																						self.add_pair(lowerCAmelCase						,						lowerCAmelCase						,						1					)


						def   __lowercase (							self				:			int						,						lowerCAmelCase				:			Tuple=-2					):
										lowerCAmelCase  =				deque()
										lowerCAmelCase  =				[]
										if s == -2:
														lowerCAmelCase  =				list(self.graph					)[0]
										d.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										while d:
														lowerCAmelCase  =				d.popleft()
														if len(self.graph[s]					) != 0:
																		for node in self.graph[s]:
																						if visited.count(node[1]					) < 1:
																										d.append(node[1]					)
																										visited.append(node[1]					)
										return visited


						def   __lowercase (							self				:			List[str]						,						lowerCAmelCase				:			str					):
										return len(self.graph[u]					)


						def   __lowercase (							self				:			Optional[Any]					):
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				list(self.graph					)[0]
										stack.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										lowerCAmelCase  =				-2
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				s
										lowerCAmelCase  =				False
										lowerCAmelCase  =				set()

										while True:
														# check if there is any non isolated nodes
														if len(self.graph[s]					) != 0:
																		lowerCAmelCase  =				s
																		for node in self.graph[s]:
																						if (
																						    visited.count(node[1]					) > 0
																						    and node[1] != parent
																						    and indirect_parents.count(node[1]					) > 0
																						    and not on_the_way_back
																						):
																										lowerCAmelCase  =				len(lowerCAmelCase					) - 1
																										while len_stack >= 0:
																														if stack[len_stack] == node[1]:
																																		anticipating_nodes.add(node[1]					)
																																		break
																														else:
																																		anticipating_nodes.add(stack[len_stack]					)
																																		len_stack -= 1
																						if visited.count(node[1]					) < 1:
																										stack.append(node[1]					)
																										visited.append(node[1]					)
																										lowerCAmelCase  =				node[1]
																										break

            # check if all the children are visited
														if s == ss:
																		stack.pop()
																		lowerCAmelCase  =				True
																		if len(lowerCAmelCase					) != 0:
																						lowerCAmelCase  =				stack[len(lowerCAmelCase					) - 1]
														else:
																		lowerCAmelCase  =				False
																		indirect_parents.append(lowerCAmelCase					)
																		lowerCAmelCase  =				s
																		lowerCAmelCase  =				ss

														# check if se have reached the starting point
														if len(lowerCAmelCase					) == 0:
																		return list(lowerCAmelCase					)


						def   __lowercase (							self				:			int					):
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				list(self.graph					)[0]
										stack.append(lowerCAmelCase					)
										visited.append(lowerCAmelCase					)
										lowerCAmelCase  =				-2
										lowerCAmelCase  =				[]
										lowerCAmelCase  =				s
										lowerCAmelCase  =				False
										lowerCAmelCase  =				set()

										while True:
														# check if there is any non isolated nodes
														if len(self.graph[s]					) != 0:
																		lowerCAmelCase  =				s
																		for node in self.graph[s]:
																						if (
																						    visited.count(node[1]					) > 0
																						    and node[1] != parent
																						    and indirect_parents.count(node[1]					) > 0
																						    and not on_the_way_back
																						):
																										lowerCAmelCase  =				len(lowerCAmelCase					) - 1
																										while len_stack_minus_one >= 0:
																														if stack[len_stack_minus_one] == node[1]:
																																		anticipating_nodes.add(node[1]					)
																																		break
																														else:
																																		return True
																						if visited.count(node[1]					) < 1:
																										stack.append(node[1]					)
																										visited.append(node[1]					)
																										lowerCAmelCase  =				node[1]
																										break

            # check if all the children are visited
														if s == ss:
																		stack.pop()
																		lowerCAmelCase  =				True
																		if len(lowerCAmelCase					) != 0:
																						lowerCAmelCase  =				stack[len(lowerCAmelCase					) - 1]
														else:
																		lowerCAmelCase  =				False
																		indirect_parents.append(lowerCAmelCase					)
																		lowerCAmelCase  =				s
																		lowerCAmelCase  =				ss

														# check if se have reached the starting point
														if len(lowerCAmelCase					) == 0:
																		return False


						def   __lowercase (							self				:			str					):
										return list(self.graph					)


						def   __lowercase (							self				:			Dict						,						lowerCAmelCase				:			Dict=-2						,						lowerCAmelCase				:			List[str]=-1					):
										lowerCAmelCase  =				time()
										self.dfs(lowerCAmelCase						,						lowerCAmelCase					)
										lowerCAmelCase  =				time()
										return end - begin




						def   __lowercase (							self				:			str						,						lowerCAmelCase				:			Union[str, Any]=-2					):
										lowerCAmelCase  =				time()
										self.bfs(lowerCAmelCase					)
										lowerCAmelCase  =				time()
										return end - begin





