





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 import BertTokenizer


_A					:				Tuple				=			logging.get_logger(__name__)

_A					:				Optional[Any]				=			{"""vocab_file""": """vocab.txt""", """tokenizer_file""": """tokenizer.json"""}

_A					:				List[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					:				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					:				str				=			{
    """facebook/dpr-ctx_encoder-single-nq-base""": 5_12,
    """facebook/dpr-ctx_encoder-multiset-base""": 5_12,
}
_A					:				int				=			{
    """facebook/dpr-question_encoder-single-nq-base""": 5_12,
    """facebook/dpr-question_encoder-multiset-base""": 5_12,
}
_A					:				Optional[int]				=			{
    """facebook/dpr-reader-single-nq-base""": 5_12,
    """facebook/dpr-reader-multiset-base""": 5_12,
}


_A					:				List[Any]				=			{
    """facebook/dpr-ctx_encoder-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-ctx_encoder-multiset-base""": {"""do_lower_case""": True},
}
_A					:				Optional[int]				=			{
    """facebook/dpr-question_encoder-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-question_encoder-multiset-base""": {"""do_lower_case""": True},
}
_A					:				List[str]				=			{
    """facebook/dpr-reader-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-reader-multiset-base""": {"""do_lower_case""": True},
}



class 					__snake_case	(  __SCREAMING_SNAKE_CASE    ):


    '''simple docstring'''







    lowerCamelCase__    :		Union[str, Any]				=	VOCAB_FILES_NAMES
    lowerCamelCase__    :		Any				=	CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
    lowerCamelCase__    :		List[Any]				=	CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    lowerCamelCase__    :		Optional[int]				=	CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION





class 					__snake_case	(  __SCREAMING_SNAKE_CASE    ):


    '''simple docstring'''







    lowerCamelCase__    :		List[str]				=	VOCAB_FILES_NAMES
    lowerCamelCase__    :		Dict				=	QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
    lowerCamelCase__    :		Dict				=	QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    lowerCamelCase__    :		Union[str, Any]				=	QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION





_A					:				Optional[Any]				=			collections.namedtuple(
    """DPRSpanPrediction""", ["""span_score""", """relevance_score""", """doc_id""", """start_index""", """end_index""", """text"""]
)

_A					:				Any				=			collections.namedtuple("""DPRReaderOutput""", ["""start_logits""", """end_logits""", """relevance_logits"""])


_A					:				Optional[Any]				=			r"""
    Return a dictionary with the token ids of the input strings and other information to give to `.decode_best_spans`.
    It converts the strings of a question and different passages (title and text) in a sequence of IDs (integers),
    using the tokenizer and vocabulary. The resulting `input_ids` is a matrix of size `(n_passages, sequence_length)`
    with the format:

    ```
    [CLS] <question token ids> [SEP] <titles ids> [SEP] <texts ids>
    ```

    Args:
        questions (`str` or `List[str]`):
            The questions to be encoded. You can specify one question for many passages. In this case, the question
            will be duplicated like `[questions] * n_passages`. Otherwise you have to specify as many questions as in
            `titles` or `texts`.
        titles (`str` or `List[str]`):
            The passages titles to be encoded. This can be a string or a list of strings if there are several passages.
        texts (`str` or `List[str]`):
            The passages texts to be encoded. This can be a string or a list of strings if there are several passages.
        padding (`bool`, `str` or [`~utils.PaddingStrategy`], *optional*, defaults to `False`):
            Activates and controls padding. Accepts the following values:

            - `True` or `'longest'`: Pad to the longest sequence in the batch (or no padding if only a single sequence
              if provided).
            - `'max_length'`: Pad to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided.
            - `False` or `'do_not_pad'` (default): No padding (i.e., can output a batch with sequences of different
              lengths).
        truncation (`bool`, `str` or [`~tokenization_utils_base.TruncationStrategy`], *optional*, defaults to `False`):
            Activates and controls truncation. Accepts the following values:

            - `True` or `'longest_first'`: Truncate to a maximum length specified with the argument `max_length` or to
              the maximum acceptable input length for the model if that argument is not provided. This will truncate
              token by token, removing a token from the longest sequence in the pair if a pair of sequences (or a batch
              of pairs) is provided.
            - `'only_first'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the first
              sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `'only_second'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the
              second sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `False` or `'do_not_truncate'` (default): No truncation (i.e., can output batch with sequence lengths
              greater than the model maximum admissible input size).
        max_length (`int`, *optional*):
                Controls the maximum length to use by one of the truncation/padding parameters.

                If left unset or set to `None`, this will use the predefined model maximum length if a maximum length
                is required by one of the truncation/padding parameters. If the model has no specific maximum input
                length (like XLNet) truncation/padding to a maximum length will be deactivated.
        return_tensors (`str` or [`~utils.TensorType`], *optional*):
                If set, will return tensors instead of list of python integers. Acceptable values are:

                - `'tf'`: Return TensorFlow `tf.constant` objects.
                - `'pt'`: Return PyTorch `torch.Tensor` objects.
                - `'np'`: Return Numpy `np.ndarray` objects.
        return_attention_mask (`bool`, *optional*):
            Whether or not to return the attention mask. If not set, will return the attention mask according to the
            specific tokenizer's default, defined by the `return_outputs` attribute.

            [What are attention masks?](../glossary#attention-mask)

    Returns:
        `Dict[str, List[List[int]]]`: A dictionary with the following keys:

        - `input_ids`: List of token ids to be fed to a model.
        - `attention_mask`: List of indices specifying which tokens should be attended to by the model.
    """



@add_start_docstrings(__SCREAMING_SNAKE_CASE    )
class 					__snake_case	:


    '''simple docstring'''







    def __call__(       self   ,				A_   ,				A_ = None   ,				A_ = None   ,				A_ = False   ,				A_ = False   ,				A_ = None   ,				A_ = None   ,				A_ = None   ,				**A_   ,				):





        '''simple docstring'''

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



    def  lowercase_					(       self   ,				A_   ,				A_   ,				A_ = 16   ,				A_ = 64   ,				A_ = 4   ,				):





        '''simple docstring'''

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

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




    def  lowercase_					(       self   ,				A_   ,				A_   ,				A_   ,				A_   ,				):





        '''simple docstring'''

        SCREAMING_SNAKE_CASE__											=			[]
        for start_index, start_score in enumerate(A_     ):
            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)     )
        SCREAMING_SNAKE_CASE__											=			sorted(A_   ,				key=lambda A_     : x[1]   ,				reverse=A_     )
        SCREAMING_SNAKE_CASE__											=			[]
        for (start_index, end_index), score in scores:
            if start_index > end_index:
                raise ValueError(f'''Wrong span indices: [{start_index}:{end_index}]'''     )
            SCREAMING_SNAKE_CASE__											=			end_index - start_index + 1
            if length > max_answer_length:
                raise ValueError(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(A_     ) == top_spans:
                break
        return chosen_span_intervals





@add_end_docstrings(__SCREAMING_SNAKE_CASE    )
class 					__snake_case	(  __SCREAMING_SNAKE_CASE			,     __SCREAMING_SNAKE_CASE    ):


    '''simple docstring'''







    lowerCamelCase__    :		Any				=	VOCAB_FILES_NAMES
    lowerCamelCase__    :		Dict				=	READER_PRETRAINED_VOCAB_FILES_MAP
    lowerCamelCase__    :		Any				=	READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    lowerCamelCase__    :		Optional[Any]				=	READER_PRETRAINED_INIT_CONFIGURATION
    lowerCamelCase__    :		str				=	["""input_ids""", """attention_mask"""]

'''simple docstring'''

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


class     __UpperCAmelCase       :





  def __init__(	self ):
     lowerCAmelCase_			=      {}





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase=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 						UpperCAmelCase_	(	self ):
     return list(self.graph )





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase ):
     if self.graph.get(_lowerCamelCase ):
        for _ in self.graph[u]:
           if _[1] == v:
              self.graph[u].remove(_lowerCamelCase )





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-2    ,     _lowerCamelCase=-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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase ):
     lowerCAmelCase_			=      0
     for x in self.graph:
        for y in self.graph[x]:
           if y[1] == u:
              count += 1
     return count





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase ):
     return len(self.graph[u] )





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-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 						UpperCAmelCase_	(	self ):
     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 						UpperCAmelCase_	(	self ):
     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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-2    ,     _lowerCamelCase=-1 ):
     lowerCAmelCase_			=      time()
     self.dfs(_lowerCamelCase    ,     _lowerCamelCase )
     lowerCAmelCase_			=      time()
     return end - begin







  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-2 ):
     lowerCAmelCase_			=      time()
     self.bfs(_lowerCamelCase )
     lowerCAmelCase_			=      time()
     return end - begin






class     __UpperCAmelCase       :





  def __init__(	self ):
     lowerCAmelCase_			=      {}





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase=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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase ):
     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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-2    ,     _lowerCamelCase=-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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-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 						UpperCAmelCase_	(	self    ,     _lowerCamelCase ):
     return len(self.graph[u] )





  def 						UpperCAmelCase_	(	self ):
     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 						UpperCAmelCase_	(	self ):
     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 						UpperCAmelCase_	(	self ):
     return list(self.graph )





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-2    ,     _lowerCamelCase=-1 ):
     lowerCAmelCase_			=      time()
     self.dfs(_lowerCamelCase    ,     _lowerCamelCase )
     lowerCAmelCase_			=      time()
     return end - begin







  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase=-2 ):
     lowerCAmelCase_			=      time()
     self.bfs(_lowerCamelCase )
     lowerCAmelCase_			=      time()
     return end - begin





