




'''simple docstring'''

from __future__ import annotations

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






class 		a							:


				def __init__(						self       :   int			,							lowercase_       :   Collection[float] | None = None   ):
									if components is None:
														snake_case_		     =							[]
									snake_case_		     =							list(lowercase_   )


				def __len__(						self       :   Optional[int]   ):
									return len(self.__components   )


				def __str__(						self       :   Union[str, Any]   ):
									return "(" + ",".join(map(lowercase_			,							self.__components   )   ) + ")"


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


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


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


				@overload
				def __mul__(						self       :   Dict			,							lowercase_       :   Vector   ):
									...


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


				def     A_					(						self       :   List[Any]   ):
									return Vector(self.__components   )


				def     A_					(						self       :   Any			,							lowercase_       :   int   ):
									if isinstance(lowercase_			,							lowercase_   ) and -len(self.__components   ) <= i < len(self.__components   ):
														return self.__components[i]
									else:
														raise Exception('''index out of range'''   )


				def     A_					(						self       :   Union[str, Any]			,							lowercase_       :   int			,							lowercase_       :   float   ):
									assert -len(self.__components   ) <= pos < len(self.__components   )
									snake_case_		     =							value


				def     A_					(						self       :   Dict   ):
									if len(self.__components   ) == 0:
														raise Exception('''Vector is empty'''   )
									snake_case_		     =							[c**2 for c in self.__components]
									return math.sqrt(sum(lowercase_   )   )


				def     A_					(						self       :   Any			,							lowercase_       :   Vector			,							lowercase_       :   bool = False   ):
									snake_case_		     =							self * other
									snake_case_		     =							self.euclidean_length() * other.euclidean_length()
									if deg:
														return math.degrees(math.acos(num / den   )   )
									else:
														return math.acos(num / den   )







def 						__magic_name__       (      __UpperCAmelCase      )						->   Vector:

					'''simple docstring'''

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


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   Vector:

					'''simple docstring'''

					assert isinstance(__UpperCAmelCase, __UpperCAmelCase      ) and (isinstance(__UpperCAmelCase, __UpperCAmelCase      ))
					snake_case_		     =							[0] * dimension
					snake_case_		     =							1
					return Vector(__UpperCAmelCase      )


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )						->   Vector:

					'''simple docstring'''

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


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )						->   Vector:

					'''simple docstring'''

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






class 		a							:


				def __init__(						self       :   Optional[int]			,							lowercase_       :   list[list[float]]			,							lowercase_       :   int			,							lowercase_       :   int   ):
									snake_case_		     =							matrix
									snake_case_		     =							w
									snake_case_		     =							h


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


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


				@overload
				def __mul__(						self       :   int			,							lowercase_       :   float   ):
									...


				@overload
				def __mul__(						self       :   Tuple			,							lowercase_       :   Vector   ):
									...


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


				def     A_					(						self       :   Tuple   ):
									return self.__height


				def     A_					(						self       :   Dict   ):
									return self.__width


				def     A_					(						self       :   Tuple			,							lowercase_       :   int			,							lowercase_       :   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     A_					(						self       :   Optional[Any]			,							lowercase_       :   int			,							lowercase_       :   int			,							lowercase_       :   float   ):
									if 0 <= x < self.__height and 0 <= y < self.__width:
														snake_case_		     =							value
									else:
														raise Exception('''change_component: indices out of bounds'''   )


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


				def     A_					(						self       :   Union[str, Any]			,							lowercase_       :   int			,							lowercase_       :   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(lowercase_			,							lowercase_   )
									else:
														raise Exception('''Indices out of bounds'''   )


				def     A_					(						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:
														snake_case_		     =							[
														    self.__matrix[0][y] * self.cofactor(0			,							lowercase_   ) for y in range(self.__width   )
														]
														return sum(lowercase_   )







def 						__magic_name__       (      __UpperCAmelCase      )						->   Matrix:

					'''simple docstring'''

					snake_case_		     =							[[0] * n for _ in range(__UpperCAmelCase      )]
					return Matrix(__UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase, __UpperCAmelCase      )						->   Matrix:

					'''simple docstring'''

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







'''simple docstring'''

import argparse
from collections import defaultdict

import yaml


a    :							List[Any]										=    'docs/source/en/_toctree.yml'


def 						__magic_name__       (      __UpperCAmelCase      )						->   str:

					'''simple docstring'''

					snake_case_		     =							defaultdict(__UpperCAmelCase      )
					for doc in model_doc:
										counts[doc["local"]] += 1
					snake_case_		     =							[key for key, value in counts.items() if value > 1]

					snake_case_		     =							[]
					for duplicate_key in duplicates:
										snake_case_		     =							list({doc['''title'''] for doc in model_doc if doc['''local'''] == duplicate_key}      )
										if len(__UpperCAmelCase      ) > 1:
															raise ValueError(
															    F"{duplicate_key} is present several times in the documentation table of content at "
															    '''`docs/source/en/_toctree.yml` with different *Title* values. Choose one of those and remove the '''
															    '''others.'''      )
										# Only add this once
										new_doc.append({'''local''': duplicate_key, '''title''': titles[0]}      )

					# Add none duplicate-keys
					new_doc.extend([doc for doc in model_doc if counts[doc['''local''']] == 1]      )

					# Sort
					return sorted(__UpperCAmelCase, key=lambda __UpperCAmelCase      : s["title"].lower()      )


def 						__magic_name__       (      __UpperCAmelCase=False      )						->   List[Any]:

					'''simple docstring'''

					with open(__UpperCAmelCase, encoding='''utf-8'''      ) as f:
										snake_case_		     =							yaml.safe_load(f.read()      )

					# Get to the API doc
					snake_case_		     =							0
					while content[api_idx]["title"] != "API":
										api_idx += 1
					snake_case_		     =							content[api_idx]['''sections''']

					# Then to the model doc
					snake_case_		     =							0
					while api_doc[model_idx]["title"] != "Models":
										model_idx += 1

					snake_case_		     =							api_doc[model_idx]['''sections''']

					snake_case_		     =							[(idx, section) for idx, section in enumerate(__UpperCAmelCase      ) if '''sections''' in section]
					snake_case_		     =							False
					for idx, modality_doc in modalities_docs:
										snake_case_		     =							modality_doc['''sections''']
										snake_case_		     =							clean_model_doc_toc(__UpperCAmelCase      )

										if old_modality_doc != new_modality_doc:
															snake_case_		     =							True
															if overwrite:
																				snake_case_		     =							new_modality_doc

					if diff:
										if overwrite:
															snake_case_		     =							model_doc
															snake_case_		     =							api_doc
															with open(__UpperCAmelCase, '''w''', encoding='''utf-8'''      ) as f:
																				f.write(yaml.dump(__UpperCAmelCase, allow_unicode=__UpperCAmelCase      )      )
										else:
															raise ValueError(
															    '''The model doc part of the table of content is not properly sorted, run `make style` to fix this.'''      )


if __name__ == "__main__":
							a    :							Dict										=    argparse.ArgumentParser()
							parser.add_argument('--fix_and_overwrite', action='store_true', help='Whether to fix inconsistencies.')
							a    :							Union[str, Any]										=    parser.parse_args()

							check_model_doc(args.fix_and_overwrite)

