'''simple docstring'''





from __future__ import annotations

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




class 		SCREAMING_SNAKE_CASE     :







				'''simple docstring'''





				def __init__(						self					:						Union[str, Any]       ,		lowercase__					:						Collection[float] | None = None					)							->None:


										'''simple docstring'''




										if components is None:
																_UpperCamelCase			:			Optional[Any]   			=						[]
										_UpperCamelCase			:			Tuple   			=						list(lowercase__					)





				def __len__(						self					:						Dict					)							->int:


										'''simple docstring'''




										return len(self.__components					)





				def __str__(						self					:						List[str]					)							->str:


										'''simple docstring'''




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





				def __add__(						self					:						Dict       ,		lowercase__					:						Vector					)							->Vector:


										'''simple docstring'''




										_UpperCamelCase			:			Optional[int]   			=						len(self					)
										if size == len(lowercase__					):
																_UpperCamelCase			:			int   			=						[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					:						List[Any]       ,		lowercase__					:						Vector					)							->Vector:


										'''simple docstring'''




										_UpperCamelCase			:			int   			=						len(self					)
										if size == len(lowercase__					):
																_UpperCamelCase			:			Union[str, Any]   			=						[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					:						str       ,		lowercase__					:						float					)							->Vector:


										'''simple docstring'''




										...





				@overload
				def __mul__(						self					:						Optional[Any]       ,		lowercase__					:						Vector					)							->float:


										'''simple docstring'''




										...





				def __mul__(						self					:						str       ,		lowercase__					:						float | Vector					)							->float | Vector:


										'''simple docstring'''




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





				def  snake_case__				(						self					:						int					)							->Vector:


										'''simple docstring'''




										return Vector(self.__components					)





				def  snake_case__				(						self					:						Any       ,		lowercase__					:						int					)							->float:


										'''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  snake_case__				(						self					:						Dict       ,		lowercase__					:						int       ,		lowercase__					:						float					)							->None:


										'''simple docstring'''




										assert -len(self.__components					) <= pos < len(self.__components					)
										_UpperCamelCase			:			int   			=						value





				def  snake_case__				(						self					:						Optional[Any]					)							->float:


										'''simple docstring'''




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







				def  snake_case__				(						self					:						Optional[int]       ,		lowercase__					:						Vector       ,		lowercase__					:						bool = False					)							->float:


										'''simple docstring'''




										_UpperCamelCase			:			Any   			=						self * other
										_UpperCamelCase			:			int   			=						self.euclidean_length() * other.euclidean_length()
										if deg:
																return math.degrees(math.acos(num / den					)					)
										else:
																return math.acos(num / den					)





def 						__A							(     UpperCAmelCase					)     ->			Vector:




						'''simple docstring'''
						assert isinstance(UpperCAmelCase     ,UpperCAmelCase					)
						return Vector([0] * dimension					)
def 						__A							(     UpperCAmelCase     ,UpperCAmelCase					)     ->			Vector:




						'''simple docstring'''
						assert isinstance(UpperCAmelCase     ,UpperCAmelCase					) and (isinstance(UpperCAmelCase     ,UpperCAmelCase					))
						_UpperCamelCase			:			Union[str, Any]   			=						[0] * dimension
						_UpperCamelCase			:			Dict   			=						1
						return Vector(UpperCAmelCase					)
def 						__A							(     UpperCAmelCase     ,UpperCAmelCase     ,UpperCAmelCase					)     ->			Vector:




						'''simple docstring'''
						assert (
						    isinstance(UpperCAmelCase     ,UpperCAmelCase					)
						    and isinstance(UpperCAmelCase     ,UpperCAmelCase					)
						    and (isinstance(UpperCAmelCase     ,(int, float)					))
						)
						return x * scalar + y
def 						__A							(     UpperCAmelCase     ,UpperCAmelCase     ,UpperCAmelCase					)     ->			Vector:




						'''simple docstring'''
						random.seed(UpperCAmelCase					)
						_UpperCamelCase			:			str   			=						[random.randint(UpperCAmelCase     ,UpperCAmelCase					) for _ in range(UpperCAmelCase					)]
						return Vector(UpperCAmelCase					)




class 		SCREAMING_SNAKE_CASE     :







				'''simple docstring'''





				def __init__(						self					:						List[Any]       ,		lowercase__					:						list[list[float]]       ,		lowercase__					:						int       ,		lowercase__					:						int					)							->None:


										'''simple docstring'''




										_UpperCamelCase			:			str   			=						matrix
										_UpperCamelCase			:			Optional[Any]   			=						w
										_UpperCamelCase			:			Tuple   			=						h





				def __str__(						self					:						Dict					)							->str:


										'''simple docstring'''




										_UpperCamelCase			:			str   			=						""
										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					:						Optional[Any]       ,		lowercase__					:						Matrix					)							->Matrix:


										'''simple docstring'''




										if self.__width == other.width() and self.__height == other.height():
																_UpperCamelCase			:			Any   			=						[]
																for i in range(self.__height					):
																						_UpperCamelCase			:			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]       ,		lowercase__					:						Matrix					)							->Matrix:


										'''simple docstring'''




										if self.__width == other.width() and self.__height == other.height():
																_UpperCamelCase			:			Optional[int]   			=						[]
																for i in range(self.__height					):
																						_UpperCamelCase			:			Optional[int]   			=						[
																						    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					:						Optional[int]       ,		lowercase__					:						float					)							->Matrix:


										'''simple docstring'''




										...





				@overload
				def __mul__(						self					:						int       ,		lowercase__					:						Vector					)							->Vector:


										'''simple docstring'''




										...





				def __mul__(						self					:						Any       ,		lowercase__					:						float | Vector					)							->Vector | Matrix:


										'''simple docstring'''




										if isinstance(lowercase__       ,		lowercase__					):  # matrix-vector
																if len(lowercase__					) == self.__width:
																						_UpperCamelCase			:			Optional[Any]   			=						zero_vector(self.__height					)
																						for i in range(self.__height					):
																												_UpperCamelCase			:			List[str]   			=						[
																												    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
																_UpperCamelCase			:			str   			=						[
																    [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  snake_case__				(						self					:						Any					)							->int:


										'''simple docstring'''




										return self.__height





				def  snake_case__				(						self					:						Optional[Any]					)							->int:


										'''simple docstring'''




										return self.__width





				def  snake_case__				(						self					:						str       ,		lowercase__					:						int       ,		lowercase__					:						int					)							->float:


										'''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  snake_case__				(						self					:						str       ,		lowercase__					:						int       ,		lowercase__					:						int       ,		lowercase__					:						float					)							->None:


										'''simple docstring'''




										if 0 <= x < self.__height and 0 <= y < self.__width:
																_UpperCamelCase			:			List[Any]   			=						value
										else:
																raise Exception("change_component: indices out of bounds"					)





				def  snake_case__				(						self					:						Optional[int]       ,		lowercase__					:						int       ,		lowercase__					:						int					)							->float:


										'''simple docstring'''




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





				def  snake_case__				(						self					:						Tuple       ,		lowercase__					:						int       ,		lowercase__					:						int					)							->float:


										'''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  snake_case__				(						self					:						Any					)							->float:


										'''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:
																_UpperCamelCase			:			Any   			=						[
																    self.__matrix[0][y] * self.cofactor(0       ,		lowercase__					) for y in range(self.__width					)
																]
																return sum(lowercase__					)





def 						__A							(     UpperCAmelCase					)     ->			Matrix:




						'''simple docstring'''
						_UpperCamelCase			:			list[list[float]]   			=						[[0] * n for _ in range(UpperCAmelCase					)]
						return Matrix(UpperCAmelCase     ,UpperCAmelCase     ,UpperCAmelCase					)






def 						__A							(     UpperCAmelCase     ,UpperCAmelCase     ,UpperCAmelCase     ,UpperCAmelCase					)     ->			Matrix:




						'''simple docstring'''
						random.seed(UpperCAmelCase					)
						_UpperCamelCase			:			list[list[float]]   			=						[
						    [random.randint(UpperCAmelCase     ,UpperCAmelCase					) for _ in range(UpperCAmelCase					)] for _ in range(UpperCAmelCase					)
						]
						return Matrix(UpperCAmelCase     ,UpperCAmelCase     ,UpperCAmelCase					)



'''simple docstring'''





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCAmelCase_	:		Union[str, Any]			=     {"""configuration_opt""": ["""OPT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """OPTConfig"""]}

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			lowerCAmelCase_	:		Tuple			=     [
			    """OPT_PRETRAINED_MODEL_ARCHIVE_LIST""",
			    """OPTForCausalLM""",
			    """OPTModel""",
			    """OPTPreTrainedModel""",
			    """OPTForSequenceClassification""",
			    """OPTForQuestionAnswering""",
			]

try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			lowerCAmelCase_	:		str			=     ["""TFOPTForCausalLM""", """TFOPTModel""", """TFOPTPreTrainedModel"""]

try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			lowerCAmelCase_	:		List[Any]			=     [
			    """FlaxOPTForCausalLM""",
			    """FlaxOPTModel""",
			    """FlaxOPTPreTrainedModel""",
			]


if TYPE_CHECKING:
			from .configuration_opt import OPT_PRETRAINED_CONFIG_ARCHIVE_MAP, OPTConfig

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_opt import (
						    OPT_PRETRAINED_MODEL_ARCHIVE_LIST,
						    OPTForCausalLM,
						    OPTForQuestionAnswering,
						    OPTForSequenceClassification,
						    OPTModel,
						    OPTPreTrainedModel,
						)

			try:
						if not is_tf_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_tf_opt import TFOPTForCausalLM, TFOPTModel, TFOPTPreTrainedModel

			try:
						if not is_flax_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_flax_opt import FlaxOPTForCausalLM, FlaxOPTModel, FlaxOPTPreTrainedModel

else:
			import sys

			lowerCAmelCase_	:		Any			=     _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)


