




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 __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload






class       SCREAMING_SNAKE_CASE__					:


						def __init__(							self				:			Dict						,						lowerCAmelCase				:			Collection[float] | None = None					):
										if components is None:
														lowerCAmelCase  =				[]
										lowerCAmelCase  =				list(lowerCAmelCase					)


						def __len__(							self				:			List[Any]					):
										return len(self.__components					)


						def __str__(							self				:			str					):
										return "(" + ",".join(map(lowerCAmelCase						,						self.__components					)					) + ")"


						def __add__(							self				:			Any						,						lowerCAmelCase				:			Vector					):
										lowerCAmelCase  =				len(self					)
										if size == len(lowerCAmelCase					):
														lowerCAmelCase  =				[self.__components[i] + other.component(lowerCAmelCase					) for i in range(lowerCAmelCase					)]
														return Vector(lowerCAmelCase					)
										else:
														raise Exception("""must have the same size"""					)


						def __sub__(							self				:			List[Any]						,						lowerCAmelCase				:			Vector					):
										lowerCAmelCase  =				len(self					)
										if size == len(lowerCAmelCase					):
														lowerCAmelCase  =				[self.__components[i] - other.component(lowerCAmelCase					) for i in range(lowerCAmelCase					)]
														return Vector(lowerCAmelCase					)
										else:  # error case
														raise Exception("""must have the same size"""					)


						@overload
						def __mul__(							self				:			Optional[int]						,						lowerCAmelCase				:			float					):
										...


						@overload
						def __mul__(							self				:			List[Any]						,						lowerCAmelCase				:			Vector					):
										...


						def __mul__(							self				:			Dict						,						lowerCAmelCase				:			float | Vector					):
										if isinstance(lowerCAmelCase						,						(float, int)					):
														lowerCAmelCase  =				[c * other for c in self.__components]
														return Vector(lowerCAmelCase					)
										elif isinstance(lowerCAmelCase						,						lowerCAmelCase					) and len(self					) == len(lowerCAmelCase					):
														lowerCAmelCase  =				len(self					)
														lowerCAmelCase  =				[self.__components[i] * other.component(lowerCAmelCase					) for i in range(lowerCAmelCase					)]
														return sum(lowerCAmelCase					)
										else:  # error case
														raise Exception("""invalid operand!"""					)


						def   __lowercase (							self				:			Tuple					):
										return Vector(self.__components					)


						def   __lowercase (							self				:			Dict						,						lowerCAmelCase				:			int					):
										if isinstance(lowerCAmelCase						,						lowerCAmelCase					) and -len(self.__components					) <= i < len(self.__components					):
														return self.__components[i]
										else:
														raise Exception("""index out of range"""					)


						def   __lowercase (							self				:			Any						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			float					):
										assert -len(self.__components					) <= pos < len(self.__components					)
										lowerCAmelCase  =				value


						def   __lowercase (							self				:			Optional[int]					):
										if len(self.__components					) == 0:
														raise Exception("""Vector is empty"""					)
										lowerCAmelCase  =				[c**2 for c in self.__components]
										return math.sqrt(sum(lowerCAmelCase					)					)




						def   __lowercase (							self				:			str						,						lowerCAmelCase				:			Vector						,						lowerCAmelCase				:			bool = False					):
										lowerCAmelCase  =				self * other
										lowerCAmelCase  =				self.euclidean_length() * other.euclidean_length()
										if deg:
														return math.degrees(math.acos(num / den					)					)
										else:
														return math.acos(num / den					)





def 							lowercase					(snake_case__   : int )     ->  Vector:


				'''simple docstring'''






				assert isinstance(snake_case__      ,       snake_case__ )
				return Vector([0] * dimension )





def 							lowercase					(snake_case__   : int      ,       snake_case__   : int )     ->  Vector:


				'''simple docstring'''






				assert isinstance(snake_case__      ,       snake_case__ ) and (isinstance(snake_case__      ,       snake_case__ ))
				lowerCAmelCase  =				[0] * dimension
				lowerCAmelCase  =				1
				return Vector(snake_case__ )





def 							lowercase					(snake_case__   : float      ,       snake_case__   : Vector      ,       snake_case__   : Vector )     ->  Vector:


				'''simple docstring'''






				assert (
				    isinstance(snake_case__      ,       snake_case__ )
				    and isinstance(snake_case__      ,       snake_case__ )
				    and (isinstance(snake_case__      ,       (int, float) ))
				)
				return x * scalar + y





def 							lowercase					(snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int )     ->  Vector:


				'''simple docstring'''






				random.seed(snake_case__ )
				lowerCAmelCase  =				[random.randint(snake_case__      ,       snake_case__ ) for _ in range(snake_case__ )]
				return Vector(snake_case__ )






class       SCREAMING_SNAKE_CASE__					:


						def __init__(							self				:			Any						,						lowerCAmelCase				:			list[list[float]]						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										lowerCAmelCase  =				matrix
										lowerCAmelCase  =				w
										lowerCAmelCase  =				h


						def __str__(							self				:			List[str]					):
										lowerCAmelCase  =				""""""
										for i in range(self.__height					):
														ans += "|"
														for j in range(self.__width					):
																		if j < self.__width - 1:
																						ans += str(self.__matrix[i][j]					) + ","
																		else:
																						ans += str(self.__matrix[i][j]					) + "|\n"
										return ans


						def __add__(							self				:			Optional[Any]						,						lowerCAmelCase				:			Matrix					):
										if self.__width == other.width() and self.__height == other.height():
														lowerCAmelCase  =				[]
														for i in range(self.__height					):
																		lowerCAmelCase  =				[
																		    self.__matrix[i][j] + other.component(lowerCAmelCase						,						lowerCAmelCase					)
																		    for j in range(self.__width					)
																		]
																		matrix.append(lowerCAmelCase					)
														return Matrix(lowerCAmelCase						,						self.__width						,						self.__height					)
										else:
														raise Exception("""matrix must have the same dimension!"""					)


						def __sub__(							self				:			Union[str, Any]						,						lowerCAmelCase				:			Matrix					):
										if self.__width == other.width() and self.__height == other.height():
														lowerCAmelCase  =				[]
														for i in range(self.__height					):
																		lowerCAmelCase  =				[
																		    self.__matrix[i][j] - other.component(lowerCAmelCase						,						lowerCAmelCase					)
																		    for j in range(self.__width					)
																		]
																		matrix.append(lowerCAmelCase					)
														return Matrix(lowerCAmelCase						,						self.__width						,						self.__height					)
										else:
														raise Exception("""matrices must have the same dimension!"""					)


						@overload
						def __mul__(							self				:			Any						,						lowerCAmelCase				:			float					):
										...


						@overload
						def __mul__(							self				:			Optional[int]						,						lowerCAmelCase				:			Vector					):
										...


						def __mul__(							self				:			Dict						,						lowerCAmelCase				:			float | Vector					):
										if isinstance(lowerCAmelCase						,						lowerCAmelCase					):  # matrix-vector
														if len(lowerCAmelCase					) == self.__width:
																		lowerCAmelCase  =				zero_vector(self.__height					)
																		for i in range(self.__height					):
																						lowerCAmelCase  =				[
																						    self.__matrix[i][j] * other.component(lowerCAmelCase					)
																						    for j in range(self.__width					)
																						]
																						ans.change_component(lowerCAmelCase						,						sum(lowerCAmelCase					)					)
																		return ans
														else:
																		raise Exception(
																		    """vector must have the same size as the """
																		    """number of columns of the matrix!"""					)
										elif isinstance(lowerCAmelCase						,						(int, float)					):  # matrix-scalar
														lowerCAmelCase  =				[
														    [self.__matrix[i][j] * other for j in range(self.__width					)]
														    for i in range(self.__height					)
														]
														return Matrix(lowerCAmelCase						,						self.__width						,						self.__height					)
										return None


						def   __lowercase (							self				:			Any					):
										return self.__height


						def   __lowercase (							self				:			int					):
										return self.__width


						def   __lowercase (							self				:			Optional[Any]						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										if 0 <= x < self.__height and 0 <= y < self.__width:
														return self.__matrix[x][y]
										else:
														raise Exception("""change_component: indices out of bounds"""					)


						def   __lowercase (							self				:			int						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			float					):
										if 0 <= x < self.__height and 0 <= y < self.__width:
														lowerCAmelCase  =				value
										else:
														raise Exception("""change_component: indices out of bounds"""					)


						def   __lowercase (							self				:			int						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										if self.__height != self.__width:
														raise Exception("""Matrix is not square"""					)
										lowerCAmelCase  =				self.__matrix[:x] + self.__matrix[x + 1 :]
										for i in range(len(lowerCAmelCase					)					):
														lowerCAmelCase  =				minor[i][:y] + minor[i][y + 1 :]
										return Matrix(lowerCAmelCase						,						self.__width - 1						,						self.__height - 1					).determinant()


						def   __lowercase (							self				:			Optional[Any]						,						lowerCAmelCase				:			int						,						lowerCAmelCase				:			int					):
										if self.__height != self.__width:
														raise Exception("""Matrix is not square"""					)
										if 0 <= x < self.__height and 0 <= y < self.__width:
														return (-1) ** (x + y) * self.minor(lowerCAmelCase						,						lowerCAmelCase					)
										else:
														raise Exception("""Indices out of bounds"""					)




						def   __lowercase (							self				:			List[Any]					):
										if self.__height != self.__width:
														raise Exception("""Matrix is not square"""					)
										if self.__height < 1:
														raise Exception("""Matrix has no element"""					)
										elif self.__height == 1:
														return self.__matrix[0][0]
										elif self.__height == 2:
														return (
														    self.__matrix[0][0] * self.__matrix[1][1]
														    - self.__matrix[0][1] * self.__matrix[1][0]
														)
										else:
														lowerCAmelCase  =				[
														    self.__matrix[0][y] * self.cofactor(0						,						lowerCAmelCase					) for y in range(self.__width					)
														]
														return sum(lowerCAmelCase					)





def 							lowercase					(snake_case__   : int )     ->  Matrix:


				'''simple docstring'''






				lowerCAmelCase  =				[[0] * n for _ in range(snake_case__ )]
				return Matrix(snake_case__      ,       snake_case__      ,       snake_case__ )






def 							lowercase					(snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int      ,       snake_case__   : int )     ->  Matrix:


				'''simple docstring'''






				random.seed(snake_case__ )
				lowerCAmelCase  =				[
				    [random.randint(snake_case__      ,       snake_case__ ) for _ in range(snake_case__ )] for _ in range(snake_case__ )
				]
				return Matrix(snake_case__      ,       snake_case__      ,       snake_case__ )





