



from datetime import datetime

import matplotlib.pyplot as plt
import torch


def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


				for param in module.parameters():
								lowercase__					:   int													=					False


def  __lowerCamelCase (       ):

				"""simple docstring"""


				lowercase__					:   Union[str, Any]													=					"cuda" if torch.cuda.is_available() else "cpu"
				if torch.backends.mps.is_available() and torch.backends.mps.is_built():
								lowercase__					:   Union[str, Any]													=					"mps"
				if device == "mps":
								print(
								    "WARNING: MPS currently doesn't seem to work, and messes up backpropagation without any visible torch"
								    " errors. I recommend using CUDA on a colab notebook or CPU instead if you're facing inexplicable issues"
								    " with generations."						)
				return device


def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


				lowercase__					:   int													=					plt.imshow(lowerCamelCase__						)
				fig.axes.get_xaxis().set_visible(lowerCamelCase__						)
				fig.axes.get_yaxis().set_visible(lowerCamelCase__						)
				plt.show()


def  __lowerCamelCase (       ):

				"""simple docstring"""


				lowercase__					:   int													=					datetime.now()
				lowercase__					:   Tuple													=					current_time.strftime("%H:%M:%S"						)
				return timestamp









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 :     Optional[Any]				,       SCREAMING_SNAKE_CASE :     Collection[float] | None = None					):
									if components is None:
													lowercase__					:   List[Any]													=					[]
									lowercase__					:   str													=					list(SCREAMING_SNAKE_CASE					)







					def __len__(							self :     Tuple					):
									return len(self.__components					)







					def __str__(							self :     int					):
									return "(" + ",".join(map(SCREAMING_SNAKE_CASE				,       self.__components					)					) + ")"







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







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







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







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







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







					def 			snake_case					(							self :     Any					):
									return Vector(self.__components					)







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







					def 			snake_case					(							self :     Optional[int]				,       SCREAMING_SNAKE_CASE :     int				,       SCREAMING_SNAKE_CASE :     float					):
									assert -len(self.__components					) <= pos < len(self.__components					)
									lowercase__					:   int													=					value







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







					def 			snake_case					(							self :     Tuple				,       SCREAMING_SNAKE_CASE :     Vector				,       SCREAMING_SNAKE_CASE :     bool = False					):
									lowercase__					:   Optional[Any]													=					self * other
									lowercase__					:   Union[str, Any]													=					self.euclidean_length() * other.euclidean_length()
									if deg:
													return math.degrees(math.acos(num / den					)					)
									else:
													return math.acos(num / den					)






def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


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


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__						):

				"""simple docstring"""


				assert isinstance(lowerCamelCase__					,			lowerCamelCase__						) and (isinstance(lowerCamelCase__					,			lowerCamelCase__						))
				lowercase__					:   Tuple													=					[0] * dimension
				lowercase__					:   Union[str, Any]													=					1
				return Vector(lowerCamelCase__						)


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__						):

				"""simple docstring"""


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


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__						):

				"""simple docstring"""


				random.seed(lowerCamelCase__						)
				lowercase__					:   Optional[Any]													=					[random.randint(lowerCamelCase__					,			lowerCamelCase__						) for _ in range(lowerCamelCase__						)]
				return Vector(lowerCamelCase__						)

class 				snake_case__:

					"""simple docstring"""






					def __init__(							self :     Optional[Any]				,       SCREAMING_SNAKE_CASE :     list[list[float]]				,       SCREAMING_SNAKE_CASE :     int				,       SCREAMING_SNAKE_CASE :     int					):
									lowercase__					:   List[str]													=					matrix
									lowercase__					:   int													=					w
									lowercase__					:   str													=					h







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







					def __sub__(							self :     Dict				,       SCREAMING_SNAKE_CASE :     Matrix					):
									if self.__width == other.width() and self.__height == other.height():
													lowercase__					:   Dict													=					[]
													for i in range(self.__height					):
																	lowercase__					:   Optional[Any]													=					[
																	    self.__matrix[i][j] - other.component(SCREAMING_SNAKE_CASE				,       SCREAMING_SNAKE_CASE					)
																	    for j in range(self.__width					)
																	]
																	matrix.append(SCREAMING_SNAKE_CASE					)
													return Matrix(SCREAMING_SNAKE_CASE				,       self.__width				,       self.__height					)
									else:
													raise Exception("matrices must have the same dimension!"					)







					@overload
					def __mul__(							self :     Any				,       SCREAMING_SNAKE_CASE :     float					):
									...







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







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







					def 			snake_case					(							self :     Union[str, Any]					):
									return self.__height







					def 			snake_case					(							self :     Optional[Any]					):
									return self.__width







					def 			snake_case					(							self :     int				,       SCREAMING_SNAKE_CASE :     int				,       SCREAMING_SNAKE_CASE :     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 			snake_case					(							self :     Optional[Any]				,       SCREAMING_SNAKE_CASE :     int				,       SCREAMING_SNAKE_CASE :     int				,       SCREAMING_SNAKE_CASE :     float					):
									if 0 <= x < self.__height and 0 <= y < self.__width:
													lowercase__					:   Union[str, Any]													=					value
									else:
													raise Exception("change_component: indices out of bounds"					)







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







					def 			snake_case					(							self :     Dict				,       SCREAMING_SNAKE_CASE :     int				,       SCREAMING_SNAKE_CASE :     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(SCREAMING_SNAKE_CASE				,       SCREAMING_SNAKE_CASE					)
									else:
													raise Exception("Indices out of bounds"					)







					def 			snake_case					(							self :     List[str]					):
									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__					:   Dict													=					[
													    self.__matrix[0][y] * self.cofactor(0				,       SCREAMING_SNAKE_CASE					) for y in range(self.__width					)
													]
													return sum(SCREAMING_SNAKE_CASE					)






def  __lowerCamelCase (       lowerCamelCase__						):

				"""simple docstring"""


				lowercase__					:   list[list[float]]													=					[[0] * n for _ in range(lowerCamelCase__						)]
				return Matrix(lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__						)


def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__						):

				"""simple docstring"""


				random.seed(lowerCamelCase__						)
				lowercase__					:   list[list[float]]													=					[
				    [random.randint(lowerCamelCase__					,			lowerCamelCase__						) for _ in range(lowerCamelCase__						)] for _ in range(lowerCamelCase__						)
				]
				return Matrix(lowerCamelCase__					,			lowerCamelCase__					,			lowerCamelCase__						)




