
from __future__ import annotations

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


class 			lowercase_		:


       def __init__(    self						,       __A = None				)						->    None:
              if components is None:
                     SCREAMING_SNAKE_CASE_							:				Dict		=[]
              SCREAMING_SNAKE_CASE_							:				List[Any]		=list(__A				)


       def __len__(    self				)						->    int:
              return len(self.__components				)


       def __str__(    self				)						->    str:
              return "(" + ",".join(map(__A						,       self.__components				)				) + ")"


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


       def __sub__(    self						,       __A				)						->    Vector:
              SCREAMING_SNAKE_CASE_							:				int		=len(self				)
              if size == len(__A				):
                     SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=[self.__components[i] - other.component(__A				) for i in range(__A				)]
                     return Vector(__A				)
              else:  # error case
                     raise Exception('''must have the same size'''				)


       @overload
       def __mul__(    self						,       __A				)						->    Vector:
              ...


       @overload
       def __mul__(    self						,       __A				)						->    float:
              ...


       def __mul__(    self						,       __A				)						->    float | Vector:
              if isinstance(__A						,       (float, int)				):
                     SCREAMING_SNAKE_CASE_							:				List[Any]		=[c * other for c in self.__components]
                     return Vector(__A				)
              elif isinstance(__A						,       __A				) and len(self				) == len(__A				):
                     SCREAMING_SNAKE_CASE_							:				int		=len(self				)
                     SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=[self.__components[i] * other.component(__A				) for i in range(__A				)]
                     return sum(__A				)
              else:  # error case
                     raise Exception('''invalid operand!'''				)


       def 	_snake_case				(    self				)						->    Vector:
              return Vector(self.__components				)


       def 	_snake_case				(    self						,       __A				)						->    float:
              if isinstance(__A						,       __A				) and -len(self.__components				) <= i < len(self.__components				):
                     return self.__components[i]
              else:
                     raise Exception('''index out of range'''				)


       def 	_snake_case				(    self						,       __A						,       __A				)						->    None:
              assert -len(self.__components				) <= pos < len(self.__components				)
              SCREAMING_SNAKE_CASE_							:				Optional[int]		=value


       def 	_snake_case				(    self				)						->    float:
              if len(self.__components				) == 0:
                     raise Exception('''Vector is empty'''				)
              SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=[c**2 for c in self.__components]
              return math.sqrt(sum(__A				)				)





       def 	_snake_case				(    self						,       __A						,       __A = False				)						->    float:
              SCREAMING_SNAKE_CASE_							:				str		=self * other
              SCREAMING_SNAKE_CASE_							:				Dict		=self.euclidean_length() * other.euclidean_length()
              if deg:
                     return math.degrees(math.acos(num / den				)				)
              else:
                     return math.acos(num / den				)






def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int				)			->						Vector:
       assert isinstance(UpperCAmelCase_			,							UpperCAmelCase_				)
       return Vector([0] * dimension				)
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int			,							UpperCAmelCase_	:     int				)			->						Vector:
       assert isinstance(UpperCAmelCase_			,							UpperCAmelCase_				) and (isinstance(UpperCAmelCase_			,							UpperCAmelCase_				))
       SCREAMING_SNAKE_CASE_							:				Dict		=[0] * dimension
       SCREAMING_SNAKE_CASE_							:				Dict		=1
       return Vector(UpperCAmelCase_				)
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     float			,							UpperCAmelCase_	:     Vector			,							UpperCAmelCase_	:     Vector				)			->						Vector:
       assert (
           isinstance(UpperCAmelCase_			,							UpperCAmelCase_				)
           and isinstance(UpperCAmelCase_			,							UpperCAmelCase_				)
           and (isinstance(UpperCAmelCase_			,							(int, float)				))
       )
       return x * scalar + y
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int			,							UpperCAmelCase_	:     int			,							UpperCAmelCase_	:     int				)			->						Vector:
       random.seed(UpperCAmelCase_				)
       SCREAMING_SNAKE_CASE_							:				Optional[Any]		=[random.randint(UpperCAmelCase_			,							UpperCAmelCase_				) for _ in range(UpperCAmelCase_				)]
       return Vector(UpperCAmelCase_				)


class 			lowercase_		:


       def __init__(    self						,       __A						,       __A						,       __A				)						->    None:
              SCREAMING_SNAKE_CASE_							:				Optional[Any]		=matrix
              SCREAMING_SNAKE_CASE_							:				Dict		=w
              SCREAMING_SNAKE_CASE_							:				Optional[int]		=h


       def __str__(    self				)						->    str:
              SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=''''''
              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						,       __A				)						->    Matrix:
              if self.__width == other.width() and self.__height == other.height():
                     SCREAMING_SNAKE_CASE_							:				int		=[]
                     for i in range(self.__height				):
                            SCREAMING_SNAKE_CASE_							:				str		=[
                                self.__matrix[i][j] + other.component(__A						,       __A				)
                                for j in range(self.__width				)
                            ]
                            matrix.append(__A				)
                     return Matrix(__A						,       self.__width						,       self.__height				)
              else:
                     raise Exception('''matrix must have the same dimension!'''				)


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


       @overload
       def __mul__(    self						,       __A				)						->    Matrix:
              ...


       @overload
       def __mul__(    self						,       __A				)						->    Vector:
              ...


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


       def 	_snake_case				(    self				)						->    int:
              return self.__height


       def 	_snake_case				(    self				)						->    int:
              return self.__width


       def 	_snake_case				(    self						,       __A						,       __A				)						->    float:
              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 	_snake_case				(    self						,       __A						,       __A						,       __A				)						->    None:
              if 0 <= x < self.__height and 0 <= y < self.__width:
                     SCREAMING_SNAKE_CASE_							:				Any		=value
              else:
                     raise Exception('''change_component: indices out of bounds'''				)


       def 	_snake_case				(    self						,       __A						,       __A				)						->    float:
              if self.__height != self.__width:
                     raise Exception('''Matrix is not square'''				)
              SCREAMING_SNAKE_CASE_							:				int		=self.__matrix[:x] + self.__matrix[x + 1 :]
              for i in range(len(__A				)				):
                     SCREAMING_SNAKE_CASE_							:				int		=minor[i][:y] + minor[i][y + 1 :]
              return Matrix(__A						,       self.__width - 1						,       self.__height - 1				).determinant()


       def 	_snake_case				(    self						,       __A						,       __A				)						->    float:
              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(__A						,       __A				)
              else:
                     raise Exception('''Indices out of bounds'''				)





       def 	_snake_case				(    self				)						->    float:
              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:
                     SCREAMING_SNAKE_CASE_							:				Tuple		=[
                         self.__matrix[0][y] * self.cofactor(0						,       __A				) for y in range(self.__width				)
                     ]
                     return sum(__A				)






def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int				)			->						Matrix:
       SCREAMING_SNAKE_CASE_							:				list[list[float]]		=[[0] * n for _ in range(UpperCAmelCase_				)]
       return Matrix(UpperCAmelCase_			,							UpperCAmelCase_			,							UpperCAmelCase_				)

def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int			,							UpperCAmelCase_	:     int			,							UpperCAmelCase_	:     int			,							UpperCAmelCase_	:     int				)			->						Matrix:
       random.seed(UpperCAmelCase_				)
       SCREAMING_SNAKE_CASE_							:				list[list[float]]		=[
           [random.randint(UpperCAmelCase_			,							UpperCAmelCase_				) for _ in range(UpperCAmelCase_				)] for _ in range(UpperCAmelCase_				)
       ]
       return Matrix(UpperCAmelCase_			,							UpperCAmelCase_			,							UpperCAmelCase_				)


import absl  # noqa: F401 # Here to have a nice missing dependency error message early on
import nltk  # noqa: F401 # Here to have a nice missing dependency error message early on
import numpy  # noqa: F401 # Here to have a nice missing dependency error message early on
import six  # noqa: F401 # Here to have a nice missing dependency error message early on
from rouge_score import rouge_scorer, scoring

import datasets


_lowercase											=    """\
@inproceedings{lin-2004-rouge,
    title = \"{ROUGE}: A Package for Automatic Evaluation of Summaries\",
    author = \"Lin, Chin-Yew\",
    booktitle = \"Text Summarization Branches Out\",
    month = jul,
    year = \"2004\",
    address = \"Barcelona, Spain\",
    publisher = \"Association for Computational Linguistics\",
    url = \"https://www.aclweb.org/anthology/W04-1013\",
    pages = \"74--81\",
}
"""

_lowercase											=    """\
ROUGE, or Recall-Oriented Understudy for Gisting Evaluation, is a set of metrics and a software package used for
evaluating automatic summarization and machine translation software in natural language processing.
The metrics compare an automatically produced summary or translation against a reference or a set of references (human-produced) summary or translation.

Note that ROUGE is case insensitive, meaning that upper case letters are treated the same way as lower case letters.

This metrics is a wrapper around Google Research reimplementation of ROUGE:
https://github.com/google-research/google-research/tree/master/rouge
"""

_lowercase											=    """
Calculates average rouge scores for a list of hypotheses and references
Args:
    predictions: list of predictions to score. Each prediction
        should be a string with tokens separated by spaces.
    references: list of reference for each prediction. Each
        reference should be a string with tokens separated by spaces.
    rouge_types: A list of rouge types to calculate.
        Valid names:
        `\"rouge{n}\"` (e.g. `\"rouge1\"`, `\"rouge2\"`) where: {n} is the n-gram based scoring,
        `\"rougeL\"`: Longest common subsequence based scoring.
        `\"rougeLSum\"`: rougeLsum splits text using `\"\n\"`.
        See details in https://github.com/huggingface/datasets/issues/617
    use_stemmer: Bool indicating whether Porter stemmer should be used to strip word suffixes.
    use_aggregator: Return aggregates if this is set to True
Returns:
    rouge1: rouge_1 (precision, recall, f1),
    rouge2: rouge_2 (precision, recall, f1),
    rougeL: rouge_l (precision, recall, f1),
    rougeLsum: rouge_lsum (precision, recall, f1)
Examples:

    >>> rouge = datasets.load_metric('rouge')
    >>> predictions = [\"hello there\", \"general kenobi\"]
    >>> references = [\"hello there\", \"general kenobi\"]
    >>> results = rouge.compute(predictions=predictions, references=references)
    >>> print(list(results.keys()))
    ['rouge1', 'rouge2', 'rougeL', 'rougeLsum']
    >>> print(results[\"rouge1\"])
    AggregateScore(low=Score(precision=1.0, recall=1.0, fmeasure=1.0), mid=Score(precision=1.0, recall=1.0, fmeasure=1.0), high=Score(precision=1.0, recall=1.0, fmeasure=1.0))
    >>> print(results[\"rouge1\"].mid.fmeasure)
    1.0
"""


@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION  ,      _KWARGS_DESCRIPTION       )
class 			lowercase_		(      datasets.Metric       ):


       def 	_snake_case				(    self				)						->    Union[str, Any]:
              return datasets.MetricInfo(
                  description=_DESCRIPTION						,       citation=_CITATION						,       inputs_description=_KWARGS_DESCRIPTION						,       features=datasets.Features(
                      {
                          '''predictions''': datasets.Value('''string'''						,       id='''sequence'''				),
                          '''references''': datasets.Value('''string'''						,       id='''sequence'''				),
                      }				)						,       codebase_urls=['''https://github.com/google-research/google-research/tree/master/rouge''']						,       reference_urls=[
                      '''https://en.wikipedia.org/wiki/ROUGE_(metric)''',
                      '''https://github.com/google-research/google-research/tree/master/rouge''',
                  ]						,       )





       def 	_snake_case				(    self						,       __A						,       __A						,       __A=None						,       __A=True						,       __A=False				)						->    List[str]:
              if rouge_types is None:
                     SCREAMING_SNAKE_CASE_							:				Union[str, Any]		=['''rouge1''', '''rouge2''', '''rougeL''', '''rougeLsum''']

              SCREAMING_SNAKE_CASE_							:				Tuple		=rouge_scorer.RougeScorer(rouge_types=__A						,       use_stemmer=__A				)
              if use_aggregator:
                     SCREAMING_SNAKE_CASE_							:				List[str]		=scoring.BootstrapAggregator()
              else:
                     SCREAMING_SNAKE_CASE_							:				Tuple		=[]

              for ref, pred in zip(__A						,       __A				):
                     SCREAMING_SNAKE_CASE_							:				int		=scorer.score(__A						,       __A				)
                     if use_aggregator:
                            aggregator.add_scores(__A				)
                     else:
                            scores.append(__A				)

              if use_aggregator:
                     SCREAMING_SNAKE_CASE_							:				Tuple		=aggregator.aggregate()
              else:
                     SCREAMING_SNAKE_CASE_							:				Optional[int]		={}
                     for key in scores[0]:
                            SCREAMING_SNAKE_CASE_							:				Tuple		=[score[key] for score in scores]

              return result
