




"""simple docstring"""




from __future__ import annotations

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

class   UpperCAmelCase_    :
		def __init__(						self				,						UpperCamelCase_ = None       )						->       None:
					if components is None:
								__lowercase			:  Optional[int]								=       []
					__lowercase			:  List[Any]								=       list(UpperCamelCase_       )
		def __len__(						self       )						->       int:
					return len(self.__components       )
		def __str__(						self       )						->       str:
					return "(" + ",".join(map(UpperCamelCase_				,						self.__components       )       ) + ")"
		def __add__(						self				,						UpperCamelCase_       )						->       Vector:
					__lowercase			:  Any								=       len(self       )
					if size == len(UpperCamelCase_       ):
								__lowercase			:  List[str]								=       [self.__components[i] + other.component(UpperCamelCase_       ) for i in range(UpperCamelCase_       )]
								return Vector(UpperCamelCase_       )
					else:
								raise Exception('''must have the same size'''       )
		def __sub__(						self				,						UpperCamelCase_       )						->       Vector:
					__lowercase			:  Dict								=       len(self       )
					if size == len(UpperCamelCase_       ):
								__lowercase			:  str								=       [self.__components[i] - other.component(UpperCamelCase_       ) for i in range(UpperCamelCase_       )]
								return Vector(UpperCamelCase_       )
					else:  # error case
								raise Exception('''must have the same size'''       )
		@overload
		def __mul__(						self				,						UpperCamelCase_       )						->       Vector:
					...
		@overload
		def __mul__(						self				,						UpperCamelCase_       )						->       float:
					...
		def __mul__(						self				,						UpperCamelCase_       )						->       float | Vector:
					if isinstance(UpperCamelCase_				,						(float, int)       ):
								__lowercase			:  List[str]								=       [c * other for c in self.__components]
								return Vector(UpperCamelCase_       )
					elif isinstance(UpperCamelCase_				,						UpperCamelCase_       ) and len(self       ) == len(UpperCamelCase_       ):
								__lowercase			:  Optional[Any]								=       len(self       )
								__lowercase			:  str								=       [self.__components[i] * other.component(UpperCamelCase_       ) for i in range(UpperCamelCase_       )]
								return sum(UpperCamelCase_       )
					else:  # error case
								raise Exception('''invalid operand!'''       )
		def 	_lowerCamelCase							(						self       )						->       Vector:
					return Vector(self.__components       )
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_       )						->       float:
					if isinstance(UpperCamelCase_				,						UpperCamelCase_       ) and -len(self.__components       ) <= i < len(self.__components       ):
								return self.__components[i]
					else:
								raise Exception('''index out of range'''       )
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_				,						UpperCamelCase_       )						->       None:
					assert -len(self.__components       ) <= pos < len(self.__components       )
					__lowercase			:  List[str]								=       value
		def 	_lowerCamelCase							(						self       )						->       float:
					if len(self.__components       ) == 0:
								raise Exception('''Vector is empty'''       )
					__lowercase			:  List[Any]								=       [c**2 for c in self.__components]
					return math.sqrt(sum(UpperCamelCase_       )       )
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_				,						UpperCamelCase_ = False       )						->       float:
					__lowercase			:  List[str]								=       self * other
					__lowercase			:  int								=       self.euclidean_length() * other.euclidean_length()
					if deg:
								return math.degrees(math.acos(num / den       )       )
					else:
								return math.acos(num / den       )







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







def      __UpperCAmelCase     ( __UpperCamelCase	,				__UpperCamelCase	):
			assert isinstance(__UpperCamelCase	,				__UpperCamelCase	) and (isinstance(__UpperCamelCase	,				__UpperCamelCase	))
			__lowercase			:  List[Any]								=       [0] * dimension
			__lowercase			:  List[Any]								=       1
			return Vector(__UpperCamelCase	)







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







def      __UpperCAmelCase     ( __UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	):
			random.seed(__UpperCamelCase	)
			__lowercase			:  Any								=       [random.randint(__UpperCamelCase	,				__UpperCamelCase	) for _ in range(__UpperCamelCase	)]
			return Vector(__UpperCamelCase	)

class   UpperCAmelCase_    :
		def __init__(						self				,						UpperCamelCase_				,						UpperCamelCase_				,						UpperCamelCase_       )						->       None:
					__lowercase			:  List[Any]								=       matrix
					__lowercase			:  Optional[int]								=       w
					__lowercase			:  Union[str, Any]								=       h
		def __str__(						self       )						->       str:
					__lowercase			:  List[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				,						UpperCamelCase_       )						->       Matrix:
					if self.__width == other.width() and self.__height == other.height():
								__lowercase			:  Any								=       []
								for i in range(self.__height       ):
											__lowercase			:  Tuple								=       [
											    self.__matrix[i][j] + other.component(UpperCamelCase_				,						UpperCamelCase_       )
											    for j in range(self.__width       )
											]
											matrix.append(UpperCamelCase_       )
								return Matrix(UpperCamelCase_				,						self.__width				,						self.__height       )
					else:
								raise Exception('''matrix must have the same dimension!'''       )
		def __sub__(						self				,						UpperCamelCase_       )						->       Matrix:
					if self.__width == other.width() and self.__height == other.height():
								__lowercase			:  Dict								=       []
								for i in range(self.__height       ):
											__lowercase			:  str								=       [
											    self.__matrix[i][j] - other.component(UpperCamelCase_				,						UpperCamelCase_       )
											    for j in range(self.__width       )
											]
											matrix.append(UpperCamelCase_       )
								return Matrix(UpperCamelCase_				,						self.__width				,						self.__height       )
					else:
								raise Exception('''matrices must have the same dimension!'''       )
		@overload
		def __mul__(						self				,						UpperCamelCase_       )						->       Matrix:
					...
		@overload
		def __mul__(						self				,						UpperCamelCase_       )						->       Vector:
					...
		def __mul__(						self				,						UpperCamelCase_       )						->       Vector | Matrix:
					if isinstance(UpperCamelCase_				,						UpperCamelCase_       ):  # matrix-vector
								if len(UpperCamelCase_       ) == self.__width:
											__lowercase			:  str								=       zero_vector(self.__height       )
											for i in range(self.__height       ):
														__lowercase			:  List[Any]								=       [
														    self.__matrix[i][j] * other.component(UpperCamelCase_       )
														    for j in range(self.__width       )
														]
														ans.change_component(UpperCamelCase_				,						sum(UpperCamelCase_       )       )
											return ans
								else:
											raise Exception(
											    '''vector must have the same size as the '''
											    '''number of columns of the matrix!'''       )
					elif isinstance(UpperCamelCase_				,						(int, float)       ):  # matrix-scalar
								__lowercase			:  Any								=       [
								    [self.__matrix[i][j] * other for j in range(self.__width       )]
								    for i in range(self.__height       )
								]
								return Matrix(UpperCamelCase_				,						self.__width				,						self.__height       )
					return None
		def 	_lowerCamelCase							(						self       )						->       int:
					return self.__height
		def 	_lowerCamelCase							(						self       )						->       int:
					return self.__width
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_				,						UpperCamelCase_       )						->       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 	_lowerCamelCase							(						self				,						UpperCamelCase_				,						UpperCamelCase_				,						UpperCamelCase_       )						->       None:
					if 0 <= x < self.__height and 0 <= y < self.__width:
								__lowercase			:  int								=       value
					else:
								raise Exception('''change_component: indices out of bounds'''       )
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_				,						UpperCamelCase_       )						->       float:
					if self.__height != self.__width:
								raise Exception('''Matrix is not square'''       )
					__lowercase			:  Any								=       self.__matrix[:x] + self.__matrix[x + 1 :]
					for i in range(len(UpperCamelCase_       )       ):
								__lowercase			:  List[str]								=       minor[i][:y] + minor[i][y + 1 :]
					return Matrix(UpperCamelCase_				,						self.__width - 1				,						self.__height - 1       ).determinant()
		def 	_lowerCamelCase							(						self				,						UpperCamelCase_				,						UpperCamelCase_       )						->       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(UpperCamelCase_				,						UpperCamelCase_       )
					else:
								raise Exception('''Indices out of bounds'''       )
		def 	_lowerCamelCase							(						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:
								__lowercase			:  str								=       [
								    self.__matrix[0][y] * self.cofactor(0				,						UpperCamelCase_       ) for y in range(self.__width       )
								]
								return sum(UpperCamelCase_       )







def      __UpperCAmelCase     ( __UpperCamelCase	):
			__lowercase			:  list[list[float]]								=       [[0] * n for _ in range(__UpperCamelCase	)]
			return Matrix(__UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	)







def      __UpperCAmelCase     ( __UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	):
			random.seed(__UpperCamelCase	)
			__lowercase			:  list[list[float]]								=       [
			    [random.randint(__UpperCamelCase	,				__UpperCamelCase	) for _ in range(__UpperCamelCase	)] for _ in range(__UpperCamelCase	)
			]
			return Matrix(__UpperCamelCase	,				__UpperCamelCase	,				__UpperCamelCase	)




"""simple docstring"""


from transformers import BertTokenizerFast

from .custom_tokenization import CustomTokenizer


class 							a					(		lowerCAmelCase_ ):
    _snake_case  :	Dict  				=				CustomTokenizer
    pass
