






'''simple docstring'''

import sys
from collections import defaultdict




class      A     :






 """simple docstring"""





 def __init__(				self			):
       UpperCamelCase_					: Dict            =				[]
 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase			):
       return self.node_position[vertex]
 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase			):
       UpperCamelCase_					: Tuple            =				pos
 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase			):
       if start > size // 2 - 1:
             return
       else:
             if 2 * start + 2 >= size:
                   UpperCamelCase_					: Tuple            =				2 * start + 1
             else:
                   if heap[2 * start + 1] < heap[2 * start + 2]:
                         UpperCamelCase_					: Union[str, Any]            =				2 * start + 1
                   else:
                         UpperCamelCase_					: Dict            =				2 * start + 2
             if heap[smallest_child] < heap[start]:
                   UpperCamelCase_     ,      UpperCamelCase_					: int            =				heap[smallest_child], positions[smallest_child]
                   UpperCamelCase_     ,      UpperCamelCase_					: str            =				(
                       heap[start],
                       positions[start],
                   )
                   UpperCamelCase_     ,      UpperCamelCase_					: int            =				temp, tempa

                   UpperCamelCase_					: int            =				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 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase			):
       UpperCamelCase_					: Union[str, Any]            =				position[index]

       while index != 0:
             UpperCamelCase_					: Optional[int]            =				int((index - 2) / 2			) if index % 2 == 0 else int((index - 1) / 2			)

             if val < heap[parent]:
                   UpperCamelCase_					: Dict            =				heap[parent]
                   UpperCamelCase_					: Union[str, Any]            =				position[parent]
                   self.set_position(position[parent]      ,  __lowerCAmelCase			)
             else:
                   UpperCamelCase_					: int            =				val
                   UpperCamelCase_					: Optional[int]            =				temp
                   self.set_position(__lowerCAmelCase      ,  __lowerCAmelCase			)
                   break
             UpperCamelCase_					: Optional[Any]            =				parent
       else:
             UpperCamelCase_					: List[Any]            =				val
             UpperCamelCase_					: List[Any]            =				temp
             self.set_position(__lowerCAmelCase      ,  0			)
 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase			):
       UpperCamelCase_					: int            =				len(__lowerCAmelCase			) // 2 - 1
       for i in range(__lowerCAmelCase      ,  -1      ,  -1			):
             self.top_to_bottom(__lowerCAmelCase      ,  __lowerCAmelCase      ,  len(__lowerCAmelCase			)      ,  __lowerCAmelCase			)





 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase			):
       UpperCamelCase_					: Any            =				positions[0]
       UpperCamelCase_					: Dict            =				sys.maxsize
       self.top_to_bottom(__lowerCAmelCase      ,  0      ,  len(__lowerCAmelCase			)      ,  __lowerCAmelCase			)
       return temp






def 				snake_case       (  a_				:			Union[str, Any]						)							->					List[str]:





      """simple docstring"""

      UpperCamelCase_					: List[Any]            =				Heap()

      UpperCamelCase_					: Optional[int]            =				[0] * len(a_						)
      UpperCamelCase_					: Optional[Any]            =				[-1] * len(a_						)  # Neighboring Tree Vertex of selected vertex
      # Minimum Distance of explored vertex with neighboring vertex of partial tree
      # formed in graph
      UpperCamelCase_					: Union[str, Any]            =				[]  # Heap of Distance of vertices from their neighboring vertex
      UpperCamelCase_					: str            =				[]

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

      UpperCamelCase_					: Any            =				[]
      UpperCamelCase_					: List[Any]            =				1
      UpperCamelCase_					: List[str]            =				sys.maxsize
      for neighbor, distance in adjacency_list[0]:
            UpperCamelCase_					: List[str]            =				0
            UpperCamelCase_					: Tuple            =				distance
      heap.heapify(a_     , a_						)

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


if __name__ == "__main__":  # pragma: no cover
      # < --------- Prims Algorithm --------- >
      UpperCamelCase      					=int(input("Enter number of edges: ").strip())
      UpperCamelCase      					=defaultdict(list)
      for _ in range(edges_number):
            UpperCamelCase      					=[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))














'''simple docstring'''

from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import ScoreSdeVeScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput




class      A     (   SCREAMING_SNAKE_CASE__    ):






 """simple docstring"""





 __a      :    UNetaDModel
 __a      :    ScoreSdeVeScheduler
 def __init__(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase			):
       super().__init__()
       self.register_modules(unet=__lowerCAmelCase      ,  scheduler=__lowerCAmelCase			)





 @torch.no_grad()
 def __call__(				self      ,  __lowerCAmelCase = 1      ,  __lowerCAmelCase = 20_00      ,  __lowerCAmelCase = None      ,  __lowerCAmelCase = "pil"      ,  __lowerCAmelCase = True      ,  **__lowerCAmelCase      ,  ):
       UpperCamelCase_					: str            =				self.unet.config.sample_size
       UpperCamelCase_					: int            =				(batch_size, 3, img_size, img_size)

       UpperCamelCase_					: List[Any]            =				self.unet

       UpperCamelCase_					: Union[str, Any]            =				randn_tensor(__lowerCAmelCase      ,  generator=__lowerCAmelCase			) * self.scheduler.init_noise_sigma
       UpperCamelCase_					: Union[str, Any]            =				sample.to(self.device			)

       self.scheduler.set_timesteps(__lowerCAmelCase			)
       self.scheduler.set_sigmas(__lowerCAmelCase			)

       for i, t in enumerate(self.progress_bar(self.scheduler.timesteps			)			):
             UpperCamelCase_					: Union[str, Any]            =				self.scheduler.sigmas[i] * torch.ones(shape[0]      ,  device=self.device			)

             # correction step
             for _ in range(self.scheduler.config.correct_steps			):
                   UpperCamelCase_					: List[str]            =				self.unet(__lowerCAmelCase      ,  __lowerCAmelCase			).sample
                   UpperCamelCase_					: List[str]            =				self.scheduler.step_correct(__lowerCAmelCase      ,  __lowerCAmelCase      ,  generator=__lowerCAmelCase			).prev_sample

             # prediction step
             UpperCamelCase_					: List[Any]            =				model(__lowerCAmelCase      ,  __lowerCAmelCase			).sample
             UpperCamelCase_					: Tuple            =				self.scheduler.step_pred(__lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  generator=__lowerCAmelCase			)

             UpperCamelCase_     ,      UpperCamelCase_					: List[Any]            =				output.prev_sample, output.prev_sample_mean

       UpperCamelCase_					: Tuple            =				sample_mean.clamp(0      ,  1			)
       UpperCamelCase_					: str            =				sample.cpu().permute(0      ,  2      ,  3      ,  1			).numpy()
       if output_type == "pil":
             UpperCamelCase_					: Dict            =				self.numpy_to_pil(__lowerCAmelCase			)

       if not return_dict:
             return (sample,)

       return ImagePipelineOutput(images=__lowerCAmelCase			)






