




from __future__ import annotations

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




class     snake_case__							:
				"""simple docstring"""



				def __init__(      self				:     Dict					,      __lowerCamelCase				:     Collection[float] | None = None							)					->     None:
							if components is None:
										a    =			[]
							a    =			list(__lowerCamelCase							)





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





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





				def __add__(      self				:     Tuple					,      __lowerCamelCase				:     Vector							)					->     Vector:
							a    =			len(self							)
							if size == len(__lowerCamelCase							):
										a    =			[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				:     int					,      __lowerCamelCase				:     Vector							)					->     Vector:
							a    =			len(self							)
							if size == len(__lowerCamelCase							):
										a    =			[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				:     str					,      __lowerCamelCase				:     float							)					->     Vector:
							...





				@overload
				def __mul__(      self				:     Optional[int]					,      __lowerCamelCase				:     Vector							)					->     float:
							...





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





				def 							__UpperCAmelCase							(      self				:     Union[str, Any]							)					->     Vector:
							return Vector(self.__components							)





				def 							__UpperCAmelCase							(      self				:     List[Any]					,      __lowerCamelCase				:     int							)					->     float:
							if isinstance(__lowerCamelCase					,      __lowerCamelCase							) and -len(self.__components							) <= i < len(self.__components							):
										return self.__components[i]
							else:
										raise Exception("index out of range"							)





				def 							__UpperCAmelCase							(      self				:     Union[str, Any]					,      __lowerCamelCase				:     int					,      __lowerCamelCase				:     float							)					->     None:
							assert -len(self.__components							) <= pos < len(self.__components							)
							a    =			value





				def 							__UpperCAmelCase							(      self				:     Optional[int]							)					->     float:
							if len(self.__components							) == 0:
										raise Exception("Vector is empty"							)
							a    =			[c**2 for c in self.__components]
							return math.sqrt(sum(__lowerCamelCase							)							)





				def 							__UpperCAmelCase							(      self				:     Dict					,      __lowerCamelCase				:     Vector					,      __lowerCamelCase				:     bool = False							)					->     float:
							a    =			self * other
							a    =			self.euclidean_length() * other.euclidean_length()
							if deg:
										return math.degrees(math.acos(num / den							)							)
							else:
										return math.acos(num / den							)




def 			__magic_name__				( A		:					int   ):






			'''simple docstring'''







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




def 			__magic_name__				( A		:					int,  A		:					int   ):






			'''simple docstring'''







			assert isinstance(A,  A   ) and (isinstance(A,  A   ))
			a    =			[0] * dimension
			a    =			1
			return Vector(A   )




def 			__magic_name__				( A		:					float,  A		:					Vector,  A		:					Vector   ):






			'''simple docstring'''







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




def 			__magic_name__				( A		:					int,  A		:					int,  A		:					int   ):






			'''simple docstring'''







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




class     snake_case__							:
				"""simple docstring"""



				def __init__(      self				:     Tuple					,      __lowerCamelCase				:     list[list[float]]					,      __lowerCamelCase				:     int					,      __lowerCamelCase				:     int							)					->     None:
							a    =			matrix
							a    =			w
							a    =			h





				def __str__(      self				:     Optional[int]							)					->     str:
							a    =			""
							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					,      __lowerCamelCase				:     Matrix							)					->     Matrix:
							if self.__width == other.width() and self.__height == other.height():
										a    =			[]
										for i in range(self.__height							):
													a    =			[
													    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				:     int					,      __lowerCamelCase				:     Matrix							)					->     Matrix:
							if self.__width == other.width() and self.__height == other.height():
										a    =			[]
										for i in range(self.__height							):
													a    =			[
													    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				:     Optional[Any]					,      __lowerCamelCase				:     float							)					->     Matrix:
							...





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





				def __mul__(      self				:     Dict					,      __lowerCamelCase				:     float | Vector							)					->     Vector | Matrix:
							if isinstance(__lowerCamelCase					,      __lowerCamelCase							):  # matrix-vector
										if len(__lowerCamelCase							) == self.__width:
													a    =			zero_vector(self.__height							)
													for i in range(self.__height							):
																a    =			[
																    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
										a    =			[
										    [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 							__UpperCAmelCase							(      self				:     List[Any]							)					->     int:
							return self.__height





				def 							__UpperCAmelCase							(      self				:     Optional[int]							)					->     int:
							return self.__width





				def 							__UpperCAmelCase							(      self				:     List[str]					,      __lowerCamelCase				:     int					,      __lowerCamelCase				:     int							)					->     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 							__UpperCAmelCase							(      self				:     Dict					,      __lowerCamelCase				:     int					,      __lowerCamelCase				:     int					,      __lowerCamelCase				:     float							)					->     None:
							if 0 <= x < self.__height and 0 <= y < self.__width:
										a    =			value
							else:
										raise Exception("change_component: indices out of bounds"							)





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





				def 							__UpperCAmelCase							(      self				:     Dict					,      __lowerCamelCase				:     int					,      __lowerCamelCase				:     int							)					->     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(__lowerCamelCase					,      __lowerCamelCase							)
							else:
										raise Exception("Indices out of bounds"							)





				def 							__UpperCAmelCase							(      self				:     Optional[int]							)					->     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:
										a    =			[
										    self.__matrix[0][y] * self.cofactor(0					,      __lowerCamelCase							) for y in range(self.__width							)
										]
										return sum(__lowerCamelCase							)




def 			__magic_name__				( A		:					int   ):






			'''simple docstring'''







			a    =			[[0] * n for _ in range(A   )]
			return Matrix(A,  A,  A   )






def 			__magic_name__				( A		:					int,  A		:					int,  A		:					int,  A		:					int   ):






			'''simple docstring'''







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












from . import __version__

# Backward compatibility imports, to make sure all those objects can be found in file_utils
from .utils import (
    CLOUDFRONT_DISTRIB_PREFIX,
    CONFIG_NAME,
    DISABLE_TELEMETRY,
    DUMMY_INPUTS,
    DUMMY_MASK,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    FEATURE_EXTRACTOR_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_PREFIX,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    MODEL_CARD_NAME,
    MULTIPLE_CHOICE_DUMMY_INPUTS,
    PYTORCH_PRETRAINED_BERT_CACHE,
    PYTORCH_TRANSFORMERS_CACHE,
    S3_BUCKET_PREFIX,
    SENTENCEPIECE_UNDERLINE,
    SPIECE_UNDERLINE,
    TF2_WEIGHTS_NAME,
    TF_WEIGHTS_NAME,
    TORCH_FX_REQUIRED_VERSION,
    TRANSFORMERS_CACHE,
    TRANSFORMERS_DYNAMIC_MODULE_NAME,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
    ContextManagers,
    DummyObject,
    EntryNotFoundError,
    ExplicitEnum,
    ModelOutput,
    PaddingStrategy,
    PushToHubMixin,
    RepositoryNotFoundError,
    RevisionNotFoundError,
    TensorType,
    _LazyModule,
    add_code_sample_docstrings,
    add_end_docstrings,
    add_start_docstrings,
    add_start_docstrings_to_model_forward,
    cached_property,
    copy_func,
    default_cache_path,
    define_sagemaker_information,
    get_cached_models,
    get_file_from_repo,
    get_full_repo_name,
    get_torch_version,
    has_file,
    http_user_agent,
    is_apex_available,
    is_bsa_available,
    is_coloredlogs_available,
    is_datasets_available,
    is_detectrona_available,
    is_faiss_available,
    is_flax_available,
    is_ftfy_available,
    is_in_notebook,
    is_ipex_available,
    is_librosa_available,
    is_offline_mode,
    is_onnx_available,
    is_pandas_available,
    is_phonemizer_available,
    is_protobuf_available,
    is_psutil_available,
    is_pyanvml_available,
    is_pyctcdecode_available,
    is_pytesseract_available,
    is_pytorch_quantization_available,
    is_rjieba_available,
    is_sagemaker_dp_enabled,
    is_sagemaker_mp_enabled,
    is_scipy_available,
    is_sentencepiece_available,
    is_seqio_available,
    is_sklearn_available,
    is_soundfile_availble,
    is_spacy_available,
    is_speech_available,
    is_tensor,
    is_tensorflow_probability_available,
    is_tfaonnx_available,
    is_tf_available,
    is_timm_available,
    is_tokenizers_available,
    is_torch_available,
    is_torch_bfaa_available,
    is_torch_cuda_available,
    is_torch_fx_available,
    is_torch_fx_proxy,
    is_torch_mps_available,
    is_torch_tfaa_available,
    is_torch_tpu_available,
    is_torchaudio_available,
    is_training_run_on_sagemaker,
    is_vision_available,
    replace_return_docstrings,
    requires_backends,
    to_numpy,
    to_py_obj,
    torch_only_method,
)






