



"""simple docstring"""

import math





def       __magic_name__    (   _lowerCamelCase				: int = 1_0_0					):
							__a		:		str									=       sum(i * i for i in range(1  ,       n + 1					)					)
							__a		:		Tuple									=       int(math.pow(sum(range(1  ,       n + 1					)					)  ,       2					)					)
							return square_of_sum - sum_of_squares


if __name__ == "__main__":
	print(f'{solution() = }')










"""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


lowercase__			   =  logging.get_logger(__name__)

lowercase__			   =  {"vocab_file": "vocab.txt", "tokenizer_file": "tokenizer.json"}

lowercase__			   =  {
    "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"
        ),
    },
}
lowercase__			   =  {
    "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"
        ),
    },
}
lowercase__			   =  {
    "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"
        ),
    },
}

lowercase__			   =  {
    "facebook/dpr-ctx_encoder-single-nq-base": 512,
    "facebook/dpr-ctx_encoder-multiset-base": 512,
}
lowercase__			   =  {
    "facebook/dpr-question_encoder-single-nq-base": 512,
    "facebook/dpr-question_encoder-multiset-base": 512,
}
lowercase__			   =  {
    "facebook/dpr-reader-single-nq-base": 512,
    "facebook/dpr-reader-multiset-base": 512,
}


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




class SCREAMING_SNAKE_CASE__					(		__snake_case      ):
						_lowerCAmelCase							=					VOCAB_FILES_NAMES
						_lowerCAmelCase							=					CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
						_lowerCAmelCase							=					CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
						_lowerCAmelCase							=					CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION
						_lowerCAmelCase							=					DPRContextEncoderTokenizer







class SCREAMING_SNAKE_CASE__					(		__snake_case      ):
						_lowerCAmelCase							=					VOCAB_FILES_NAMES
						_lowerCAmelCase							=					QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
						_lowerCAmelCase							=					QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
						_lowerCAmelCase							=					QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION
						_lowerCAmelCase							=					DPRQuestionEncoderTokenizer







lowercase__			   =  collections.namedtuple(
    "DPRSpanPrediction", ["span_score", "relevance_score", "doc_id", "start_index", "end_index", "text"]
)

lowercase__			   =  collections.namedtuple("DPRReaderOutput", ["start_logits", "end_logits", "relevance_logits"])


lowercase__			   =  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(__snake_case      )
class SCREAMING_SNAKE_CASE__					:



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





													'''simple docstring'''

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



						def     lowerCAmelCase__(self						,     _lowercase						,     _lowercase						,     _lowercase = 16						,     _lowercase = 64						,     _lowercase = 4						,     ):





													'''simple docstring'''

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

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





						def     lowerCAmelCase__(self						,     _lowercase						,     _lowercase						,     _lowercase						,     _lowercase						,     ):





													'''simple docstring'''

													__a		:		Tuple									=       []
													for start_index, start_score in enumerate(_lowercase							):
																				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)							)
													__a		:		str									=       sorted(_lowercase						,     key=lambda _lowercase							: x[1]						,     reverse=_lowercase							)
													__a		:		Union[str, Any]									=       []
													for (start_index, end_index), score in scores:
																				assert start_index <= end_index, F'''Wrong span indices: [{start_index}:{end_index}]'''
																				__a		:		List[str]									=       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(_lowercase							) == top_spans:
																											break
													return chosen_span_intervals







@add_end_docstrings(__snake_case      )
class SCREAMING_SNAKE_CASE__					(		__snake_case     ,					__snake_case      ):
						_lowerCAmelCase							=					VOCAB_FILES_NAMES
						_lowerCAmelCase							=					READER_PRETRAINED_VOCAB_FILES_MAP
						_lowerCAmelCase							=					READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
						_lowerCAmelCase							=					READER_PRETRAINED_INIT_CONFIGURATION
						_lowerCAmelCase							=					["input_ids", "attention_mask"]
						_lowerCAmelCase							=					DPRReaderTokenizer

