



'''simple docstring'''




from __future__ import annotations

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






class 		_UpperCamelCase    :


			'''simple docstring'''

			def __init__(				self	:					Any				,	lowerCAmelCase__	:					Collection[float] | None = None		):





					"""simple docstring"""






					if components is None:
							__SCREAMING_SNAKE_CASE			:						Dict       			=						[]
					__SCREAMING_SNAKE_CASE			:						Optional[Any]       			=						list(_lowercase		)

			def __len__(				self	:					str		):





					"""simple docstring"""






					return len(self.__components		)

			def __str__(				self	:					Dict		):





					"""simple docstring"""






					return "(" + ",".join(map(_lowercase				,	self.__components		)		) + ")"

			def __add__(				self	:					Any				,	lowerCAmelCase__	:					Vector		):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE			:						Tuple       			=						len(self		)
					if size == len(_lowercase		):
							__SCREAMING_SNAKE_CASE			:						Union[str, Any]       			=						[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	:					Union[str, Any]				,	lowerCAmelCase__	:					Vector		):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE			:						List[Any]       			=						len(self		)
					if size == len(_lowercase		):
							__SCREAMING_SNAKE_CASE			:						List[str]       			=						[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	:					List[Any]				,	lowerCAmelCase__	:					float		):





					"""simple docstring"""






					...

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





					"""simple docstring"""






					...

			def __mul__(				self	:					Union[str, Any]				,	lowerCAmelCase__	:					float | Vector		):





					"""simple docstring"""






					if isinstance(_lowercase				,	(float, int)		):
							__SCREAMING_SNAKE_CASE			:						Optional[Any]       			=						[c * other for c in self.__components]
							return Vector(_lowercase		)
					elif isinstance(_lowercase				,	_lowercase		) and len(self		) == len(_lowercase		):
							__SCREAMING_SNAKE_CASE			:						Tuple       			=						len(self		)
							__SCREAMING_SNAKE_CASE			:						str       			=						[self.__components[i] * other.component(_lowercase		) for i in range(_lowercase		)]
							return sum(_lowercase		)
					else:  # error case
							raise Exception("""invalid operand!"""		)

			def UpperCamelCase__   (				self	:					Dict		):





					"""simple docstring"""






					return Vector(self.__components		)

			def UpperCamelCase__   (				self	:					Any				,	lowerCAmelCase__	:					int		):





					"""simple docstring"""






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

			def UpperCamelCase__   (				self	:					List[Any]				,	lowerCAmelCase__	:					int				,	lowerCAmelCase__	:					float		):





					"""simple docstring"""






					assert -len(self.__components		) <= pos < len(self.__components		)
					__SCREAMING_SNAKE_CASE			:						Dict       			=						value

			def UpperCamelCase__   (				self	:					Optional[int]		):





					"""simple docstring"""






					if len(self.__components		) == 0:
							raise Exception("""Vector is empty"""		)
					__SCREAMING_SNAKE_CASE			:						str       			=						[c**2 for c in self.__components]
					return math.sqrt(sum(_lowercase		)		)



			def UpperCamelCase__   (				self	:					Union[str, Any]				,	lowerCAmelCase__	:					Vector				,	lowerCAmelCase__	:					bool = False		):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE			:						List[Any]       			=						self * other
					__SCREAMING_SNAKE_CASE			:						Tuple       			=						self.euclidean_length() * other.euclidean_length()
					if deg:
							return math.degrees(math.acos(num / den		)		)
					else:
							return math.acos(num / den		)


def 							lowerCAmelCase_  (      _lowerCamelCase:  int   ):
		assert isinstance(_lowerCamelCase			, _lowerCamelCase   )
		return Vector([0] * dimension   )


def 							lowerCAmelCase_  (      _lowerCamelCase:  int			, _lowerCamelCase:  int   ):
		assert isinstance(_lowerCamelCase			, _lowerCamelCase   ) and (isinstance(_lowerCamelCase			, _lowerCamelCase   ))
		__SCREAMING_SNAKE_CASE			:						Any       			=						[0] * dimension
		__SCREAMING_SNAKE_CASE			:						Tuple       			=						1
		return Vector(_lowerCamelCase   )


def 							lowerCAmelCase_  (      _lowerCamelCase:  float			, _lowerCamelCase:  Vector			, _lowerCamelCase:  Vector   ):
		assert (
		    isinstance(_lowerCamelCase			, _lowerCamelCase   )
		    and isinstance(_lowerCamelCase			, _lowerCamelCase   )
		    and (isinstance(_lowerCamelCase			, (int, float)   ))
		)
		return x * scalar + y


def 							lowerCAmelCase_  (      _lowerCamelCase:  int			, _lowerCamelCase:  int			, _lowerCamelCase:  int   ):
		random.seed(_lowerCamelCase   )
		__SCREAMING_SNAKE_CASE			:						Tuple       			=						[random.randint(_lowerCamelCase			, _lowerCamelCase   ) for _ in range(_lowerCamelCase   )]
		return Vector(_lowerCamelCase   )






class 		_UpperCamelCase    :


			'''simple docstring'''

			def __init__(				self	:					List[str]				,	lowerCAmelCase__	:					list[list[float]]				,	lowerCAmelCase__	:					int				,	lowerCAmelCase__	:					int		):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE			:						List[str]       			=						matrix
					__SCREAMING_SNAKE_CASE			:						int       			=						w
					__SCREAMING_SNAKE_CASE			:						Optional[int]       			=						h

			def __str__(				self	:					List[str]		):





					"""simple docstring"""






					__SCREAMING_SNAKE_CASE			:						Tuple       			=						''''''
					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	:					List[str]				,	lowerCAmelCase__	:					Matrix		):





					"""simple docstring"""






					if self.__width == other.width() and self.__height == other.height():
							__SCREAMING_SNAKE_CASE			:						str       			=						[]
							for i in range(self.__height		):
									__SCREAMING_SNAKE_CASE			:						Tuple       			=						[
									    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	:					Optional[int]				,	lowerCAmelCase__	:					Matrix		):





					"""simple docstring"""






					if self.__width == other.width() and self.__height == other.height():
							__SCREAMING_SNAKE_CASE			:						List[str]       			=						[]
							for i in range(self.__height		):
									__SCREAMING_SNAKE_CASE			:						List[str]       			=						[
									    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	:					Any				,	lowerCAmelCase__	:					float		):





					"""simple docstring"""






					...

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





					"""simple docstring"""






					...

			def __mul__(				self	:					Any				,	lowerCAmelCase__	:					float | Vector		):





					"""simple docstring"""






					if isinstance(_lowercase				,	_lowercase		):  # matrix-vector
							if len(_lowercase		) == self.__width:
									__SCREAMING_SNAKE_CASE			:						int       			=						zero_vector(self.__height		)
									for i in range(self.__height		):
											__SCREAMING_SNAKE_CASE			:						int       			=						[
											    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
							__SCREAMING_SNAKE_CASE			:						Union[str, Any]       			=						[
							    [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 UpperCamelCase__   (				self	:					Dict		):





					"""simple docstring"""






					return self.__height

			def UpperCamelCase__   (				self	:					Dict		):





					"""simple docstring"""






					return self.__width

			def UpperCamelCase__   (				self	:					int				,	lowerCAmelCase__	:					int				,	lowerCAmelCase__	:					int		):





					"""simple docstring"""






					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		):





					"""simple docstring"""






					if 0 <= x < self.__height and 0 <= y < self.__width:
							__SCREAMING_SNAKE_CASE			:						Tuple       			=						value
					else:
							raise Exception("""change_component: indices out of bounds"""		)

			def UpperCamelCase__   (				self	:					Optional[Any]				,	lowerCAmelCase__	:					int				,	lowerCAmelCase__	:					int		):





					"""simple docstring"""






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

			def UpperCamelCase__   (				self	:					Optional[Any]				,	lowerCAmelCase__	:					int				,	lowerCAmelCase__	:					int		):





					"""simple docstring"""






					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 UpperCamelCase__   (				self	:					Union[str, Any]		):





					"""simple docstring"""






					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			:						Dict       			=						[
							    self.__matrix[0][y] * self.cofactor(0				,	_lowercase		) for y in range(self.__width		)
							]
							return sum(_lowercase		)


def 							lowerCAmelCase_  (      _lowerCamelCase:  int   ):
		__SCREAMING_SNAKE_CASE			:						list[list[float]]       			=						[[0] * n for _ in range(_lowerCamelCase   )]
		return Matrix(_lowerCamelCase			, _lowerCamelCase			, _lowerCamelCase   )


def 							lowerCAmelCase_  (      _lowerCamelCase:  int			, _lowerCamelCase:  int			, _lowerCamelCase:  int			, _lowerCamelCase:  int   ):
		random.seed(_lowerCamelCase   )
		__SCREAMING_SNAKE_CASE			:						list[list[float]]       			=						[
		    [random.randint(_lowerCamelCase			, _lowerCamelCase   ) for _ in range(_lowerCamelCase   )] for _ in range(_lowerCamelCase   )
		]
		return Matrix(_lowerCamelCase			, _lowerCamelCase			, _lowerCamelCase   )
UpperCAmelCase_           =				'''
# Transformers installation
! pip install transformers datasets
# To install from source instead of the last release, comment the command above and uncomment the following one.
# ! pip install git+https://github.com/huggingface/transformers.git
'''

UpperCAmelCase_           =				[{'''type''': '''code''', '''content''': INSTALL_CONTENT}]
UpperCAmelCase_           =				{
    '''{processor_class}''': '''FakeProcessorClass''',
    '''{model_class}''': '''FakeModelClass''',
    '''{object_class}''': '''FakeObjectClass''',
}