




from datetime import datetime

import matplotlib.pyplot as plt
import torch



def       UpperCAmelCase       (     _snake_case							):
							for param in module.parameters():
														lowerCAmelCase   =		False



def       UpperCAmelCase       (     ):
							lowerCAmelCase   =		'''cuda''' if torch.cuda.is_available() else '''cpu'''
							if torch.backends.mps.is_available() and torch.backends.mps.is_built():
														lowerCAmelCase   =		'''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       UpperCAmelCase       (     _snake_case							):
							lowerCAmelCase   =		plt.imshow(_snake_case							)
							fig.axes.get_xaxis().set_visible(_snake_case							)
							fig.axes.get_yaxis().set_visible(_snake_case							)
							plt.show()



def       UpperCAmelCase       (     ):
							lowerCAmelCase   =		datetime.now()
							lowerCAmelCase   =		current_time.strftime('''%H:%M:%S'''							)
							return timestamp









from __future__ import annotations

from typing import Generic, TypeVar

UpperCAmelCase_						=TypeVar("""T""")


class 							__UpperCamelCase			( Generic[T]  ):





				'''simple docstring'''



				def __init__( self       , UpperCAmelCase_						):
											lowerCAmelCase   =		data
											lowerCAmelCase   =		self
											lowerCAmelCase   =		0




class 							__UpperCamelCase			( Generic[T]  ):





				'''simple docstring'''



				def __init__( self						):
											# map from node name to the node object
											lowerCAmelCase   =		{}



				def       __snake_case		( self       , UpperCAmelCase_						):
											# create a new set with x as its member
											lowerCAmelCase   =		DisjointSetTreeNode(UpperCAmelCase_						)



				def       __snake_case		( self       , UpperCAmelCase_						):
											# find the set x belongs to (with path-compression)
											lowerCAmelCase   =		self.map[data]
											if elem_ref != elem_ref.parent:
																		lowerCAmelCase   =		self.find_set(elem_ref.parent.data						)
											return elem_ref.parent



				def       __snake_case		( self       , UpperCAmelCase_       , UpperCAmelCase_						):
											# helper function for union operation
											if nodea.rank > nodea.rank:
																		lowerCAmelCase   =		nodea
											else:
																		lowerCAmelCase   =		nodea
																		if nodea.rank == nodea.rank:
																									nodea.rank += 1






				def       __snake_case		( self       , UpperCAmelCase_       , UpperCAmelCase_						):
											# merge 2 disjoint sets
											self.link(self.find_set(UpperCAmelCase_						)       , self.find_set(UpperCAmelCase_						)						)




class 							__UpperCamelCase			( Generic[T]  ):





				'''simple docstring'''



				def __init__( self						):
											# connections: map from the node to the neighbouring nodes (with weights)
											lowerCAmelCase   =		{}



				def       __snake_case		( self       , UpperCAmelCase_						):
											# add a node ONLY if its not present in the graph
											if node not in self.connections:
																		lowerCAmelCase   =		{}



				def       __snake_case		( self       , UpperCAmelCase_       , UpperCAmelCase_       , UpperCAmelCase_						):
											# add an edge with the given weight
											self.add_node(UpperCAmelCase_						)
											self.add_node(UpperCAmelCase_						)
											lowerCAmelCase   =		weight
											lowerCAmelCase   =		weight






				def       __snake_case		( self						):
											lowerCAmelCase   =		[]
											lowerCAmelCase   =		set()
											for start in self.connections:
																		for end in self.connections[start]:
																									if (start, end) not in seen:
																																seen.add((end, start)						)
																																edges.append((start, end, self.connections[start][end])						)
											edges.sort(key=lambda UpperCAmelCase_						: x[2]						)

											# creating the disjoint set
											lowerCAmelCase   =		DisjointSetTree[T]()
											for node in self.connections:
																		disjoint_set.make_set(UpperCAmelCase_						)

											# MST generation
											lowerCAmelCase   =		0
											lowerCAmelCase   =		0
											lowerCAmelCase   =		GraphUndirectedWeighted[T]()
											while num_edges < len(self.connections						) - 1:
																		lowerCAmelCase   ,     lowerCAmelCase   ,     lowerCAmelCase   =		edges[index]
																		index += 1
																		lowerCAmelCase   =		disjoint_set.find_set(UpperCAmelCase_						)
																		lowerCAmelCase   =		disjoint_set.find_set(UpperCAmelCase_						)
																		if parent_u != parent_v:
																									num_edges += 1
																									graph.add_edge(UpperCAmelCase_       , UpperCAmelCase_       , UpperCAmelCase_						)
																									disjoint_set.union(UpperCAmelCase_       , UpperCAmelCase_						)
											return graph



