




'''simple docstring'''


from manim import *

class     A					(	_a					):







							def      __lowerCAmelCase    (						self :						Tuple      )    ->							Dict:


														"""simple docstring"""


														_a			  =       Rectangle(height=0.5							,    width=0.5      )
														_a			  =       Rectangle(height=0.4_6							,    width=0.4_6      ).set_stroke(width=0      )

														_a			  =       [mem.copy() for i in range(6      )]
														_a			  =       [mem.copy() for i in range(6      )]
														_a			  =       VGroup(*lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0      )
														_a			  =       VGroup(*lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0      )
														_a			  =       VGroup(lowerCAmelCase_							,    lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0      )
														_a			  =       Text('''CPU'''							,    font_size=24      )
														_a			  =       Group(lowerCAmelCase_							,    lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0.5							,    aligned_edge=lowerCAmelCase_      )
														cpu.move_to([-2.5, -0.5, 0]      )
														self.add(lowerCAmelCase_      )

														_a			  =       [mem.copy() for i in range(4      )]
														_a			  =       VGroup(*lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0      )
														_a			  =       Text('''GPU'''							,    font_size=24      )
														_a			  =       Group(lowerCAmelCase_							,    lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0.5							,    aligned_edge=lowerCAmelCase_      )
														gpu.move_to([-1, -1, 0]      )
														self.add(lowerCAmelCase_      )

														_a			  =       [mem.copy() for i in range(6      )]
														_a			  =       VGroup(*lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0      )

														_a			  =       Text('''Model'''							,    font_size=24      )
														_a			  =       Group(lowerCAmelCase_							,    lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0.5							,    aligned_edge=lowerCAmelCase_      )
														model.move_to([3, -1.0, 0]      )
														self.add(lowerCAmelCase_      )

														_a			  =       []
														for i, rect in enumerate(lowerCAmelCase_      ):
																					rect.set_stroke(lowerCAmelCase_      )
																					# target = fill.copy().set_fill(YELLOW, opacity=0.7)
																					# target.move_to(rect)
																					# self.add(target)

																					_a			  =       Rectangle(height=0.4_6 / 4							,    width=0.4_6 / 3      ).set_stroke(width=0.0      ).set_fill(lowerCAmelCase_							,    opacity=0.7      )

																					if i == 0:
																												cpu_target.next_to(cpu_left_col_base[0].get_corner(DOWN + LEFT      )							,    buff=0.0_2							,    direction=lowerCAmelCase_      )
																												cpu_target.set_x(cpu_target.get_x() + 0.1      )
																					elif i == 3:
																												cpu_target.next_to(cpu_targs[0]							,    direction=lowerCAmelCase_							,    buff=0.0      )
																					else:
																												cpu_target.next_to(cpu_targs[i - 1]							,    direction=lowerCAmelCase_							,    buff=0.0      )
																					self.add(lowerCAmelCase_      )
																					cpu_targs.append(lowerCAmelCase_      )

														_a			  =       [mem.copy() for i in range(6      )]
														_a			  =       VGroup(*lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    buff=0      )

														_a			  =       Text('''Loaded Checkpoint'''							,    font_size=24      )
														_a			  =       Group(lowerCAmelCase_							,    lowerCAmelCase_      ).arrange(lowerCAmelCase_							,    aligned_edge=lowerCAmelCase_							,    buff=0.4      )
														checkpoint.move_to([3, 0.5, 0]      )

														_a			  =       Square(side_length=2.2      )
														key.move_to([-5, 2, 0]      )

														_a			  =       MarkupText(
														    F'<b>Key:</b>\n\n<span fgcolor=\'{YELLOW}\'>●</span> Empty Model'							,    font_size=18							,    )

														key_text.move_to([-5, 2.4, 0]      )

														self.add(lowerCAmelCase_							,    lowerCAmelCase_      )

														_a			  =       MarkupText(
														    F'<span fgcolor=\'{BLUE}\'>●</span> Checkpoint'							,    font_size=18							,    )

														blue_text.next_to(lowerCAmelCase_							,    DOWN * 2.4							,    aligned_edge=key_text.get_left()      )

														_a			  =       MarkupText(
														    F'Next, a <i><span fgcolor="{BLUE}">second</span></i> model is loaded into memory,\nwith the weights of a <span fgcolor="{BLUE}">single shard</span>.'							,    font_size=24							,    )
														step_a.move_to([2, 2, 0]      )
														self.play(Write(lowerCAmelCase_      )							,    Write(lowerCAmelCase_      )      )

														self.play(Write(lowerCAmelCase_							,    run_time=1      )							,    Create(lowerCAmelCase_							,    run_time=1      )      )

														_a			  =       []
														_a			  =       []
														for i, rect in enumerate(lowerCAmelCase_      ):
																					_a			  =       fill.copy().set_fill(lowerCAmelCase_							,    opacity=0.7      )
																					target.move_to(lowerCAmelCase_      )
																					first_animations.append(GrowFromCenter(lowerCAmelCase_							,    run_time=1      )      )

																					_a			  =       target.copy()
																					cpu_target.generate_target()
																					if i < 5:
																												cpu_target.target.move_to(cpu_left_col_base[i + 1]      )
																					else:
																												cpu_target.target.move_to(cpu_right_col_base[i - 5]      )
																					second_animations.append(MoveToTarget(lowerCAmelCase_							,    run_time=1.5      )      )

														self.play(*lowerCAmelCase_      )
														self.play(*lowerCAmelCase_      )
														self.wait()







'''simple docstring'''


import sys
from collections import defaultdict

class     A					:







							def __init__(						self :						Optional[Any]      )    ->							Union[str, Any]:


														"""simple docstring"""


														_a			  =       []







							def      __lowerCAmelCase    (						self :						Union[str, Any]							,    lowerCAmelCase_ :						List[Any]      )    ->							int:


														"""simple docstring"""


														return self.node_position[vertex]







							def      __lowerCAmelCase    (						self :						List[Any]							,    lowerCAmelCase_ :						Optional[Any]							,    lowerCAmelCase_ :						Optional[Any]      )    ->							Tuple:


														"""simple docstring"""


														_a			  =       pos







							def      __lowerCAmelCase    (						self :						Dict							,    lowerCAmelCase_ :						str							,    lowerCAmelCase_ :						Any							,    lowerCAmelCase_ :						Dict							,    lowerCAmelCase_ :						int      )    ->							Any:


														"""simple docstring"""


														if start > size // 2 - 1:
																					return
														else:
																					if 2 * start + 2 >= size:
																												_a			  =       2 * start + 1
																					else:
																												if heap[2 * start + 1] < heap[2 * start + 2]:
																																			_a			  =       2 * start + 1
																												else:
																																			_a			  =       2 * start + 2
																					if heap[smallest_child] < heap[start]:
																												_a  ,							_a			  =       heap[smallest_child], positions[smallest_child]
																												_a  ,							_a			  =       (
																												    heap[start],
																												    positions[start],
																												)
																												_a  ,							_a			  =       temp, tempa

																												_a			  =       self.get_position(positions[smallest_child]      )
																												self.set_position(
																												    positions[smallest_child]							,    self.get_position(positions[start]      )      )
																												self.set_position(positions[start]							,    lowerCAmelCase_      )

																												self.top_to_bottom(lowerCAmelCase_							,    lowerCAmelCase_							,    lowerCAmelCase_							,    lowerCAmelCase_      )







							def      __lowerCAmelCase    (						self :						Optional[int]							,    lowerCAmelCase_ :						List[str]							,    lowerCAmelCase_ :						List[Any]							,    lowerCAmelCase_ :						Any							,    lowerCAmelCase_ :						Dict      )    ->							Any:


														"""simple docstring"""


														_a			  =       position[index]

														while index != 0:
																					_a			  =       int((index - 2) / 2      ) if index % 2 == 0 else int((index - 1) / 2      )

																					if val < heap[parent]:
																												_a			  =       heap[parent]
																												_a			  =       position[parent]
																												self.set_position(position[parent]							,    lowerCAmelCase_      )
																					else:
																												_a			  =       val
																												_a			  =       temp
																												self.set_position(lowerCAmelCase_							,    lowerCAmelCase_      )
																												break
																					_a			  =       parent
														else:
																					_a			  =       val
																					_a			  =       temp
																					self.set_position(lowerCAmelCase_							,    0      )







							def      __lowerCAmelCase    (						self :						Any							,    lowerCAmelCase_ :						List[Any]							,    lowerCAmelCase_ :						Optional[Any]      )    ->							Optional[int]:


														"""simple docstring"""


														_a			  =       len(lowerCAmelCase_      ) // 2 - 1
														for i in range(lowerCAmelCase_							,    -1							,    -1      ):
																					self.top_to_bottom(lowerCAmelCase_							,    lowerCAmelCase_							,    len(lowerCAmelCase_      )							,    lowerCAmelCase_      )







							def      __lowerCAmelCase    (						self :						str							,    lowerCAmelCase_ :						str							,    lowerCAmelCase_ :						int      )    ->							List[Any]:


														"""simple docstring"""


														_a			  =       positions[0]
														_a			  =       sys.maxsize
														self.top_to_bottom(lowerCAmelCase_							,    0							,    len(lowerCAmelCase_      )							,    lowerCAmelCase_      )
														return temp



def 	snake_case_					(UpperCamelCase :						Any   ):





							'''simple docstring'''


							_a			  =       Heap()

							_a			  =       [0] * len(UpperCamelCase   )
							_a			  =       [-1] * len(UpperCamelCase   )  # Neighboring Tree Vertex of selected vertex
							# Minimum Distance of explored vertex with neighboring vertex of partial tree
							# formed in graph
							_a			  =       []  # Heap of Distance of vertices from their neighboring vertex
							_a			  =       []

							for vertex in range(len(UpperCamelCase   )   ):
														distance_tv.append(sys.maxsize   )
														positions.append(UpperCamelCase   )
														heap.node_position.append(UpperCamelCase   )

							_a			  =       []
							_a			  =       1
							_a			  =       sys.maxsize
							for neighbor, distance in adjacency_list[0]:
														_a			  =       0
														_a			  =       distance
							heap.heapify(UpperCamelCase				,		UpperCamelCase   )

							for _ in range(1				,		len(UpperCamelCase   )   ):
														_a			  =       heap.delete_minimum(UpperCamelCase				,		UpperCamelCase   )
														if visited[vertex] == 0:
																					tree_edges.append((nbr_tv[vertex], vertex)   )
																					_a			  =       1
																					for neighbor, distance in adjacency_list[vertex]:
																												if (
																												    visited[neighbor] == 0
																												    and distance < distance_tv[heap.get_position(UpperCamelCase   )]
																												):
																																			_a			  =       distance
																																			heap.bottom_to_top(
																																			    UpperCamelCase				,		heap.get_position(UpperCamelCase   )				,		UpperCamelCase				,		UpperCamelCase   )
																																			_a			  =       vertex
							return tree_edges


if __name__ == "__main__":  # pragma: no cover
				# < --------- Prims Algorithm --------- >
				_snake_case   :   List[str]     							=	int(input('Enter number of edges: ').strip())
				_snake_case   :   Union[str, Any]     							=	defaultdict(list)
				for _ in range(edges_number):
								_snake_case   :   Tuple     							=	[int(x) for x in input().strip().split()]
								adjacency_list[edge[0]].append([edge[1], edge[2]])
								adjacency_list[edge[1]].append([edge[0], edge[2]])
				print(prisms_algorithm(adjacency_list))

