






"""simple docstring"""





from typing import List, Optional, Union

import numpy as np
import PIL
import torch
from PIL import Image

from ...models import UNetaDConditionModel, VQModel
from ...pipelines import DiffusionPipeline
from ...pipelines.pipeline_utils import ImagePipelineOutput
from ...schedulers import DDPMScheduler
from ...utils import (
    is_accelerate_available,
    is_accelerate_version,
    logging,
    randn_tensor,
    replace_example_docstring,
)


A__					: Tuple=	logging.get_logger(__name__)  # pylint: disable=invalid-name

A__					: List[str]=	"""
    Examples:
        ```py
        >>> from diffusers import KandinskyV22Img2ImgPipeline, KandinskyV22PriorPipeline
        >>> from diffusers.utils import load_image
        >>> import torch

        >>> pipe_prior = KandinskyV22PriorPipeline.from_pretrained(
        ...     \"kandinsky-community/kandinsky-2-2-prior\", torch_dtype=torch.float16
        ... )
        >>> pipe_prior.to(\"cuda\")

        >>> prompt = \"A red cartoon frog, 4k\"
        >>> image_emb, zero_image_emb = pipe_prior(prompt, return_dict=False)

        >>> pipe = KandinskyV22Img2ImgPipeline.from_pretrained(
        ...     \"kandinsky-community/kandinsky-2-2-decoder\", torch_dtype=torch.float16
        ... )
        >>> pipe.to(\"cuda\")

        >>> init_image = load_image(
        ...     \"https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main\"
        ...     \"/kandinsky/frog.png\"
        ... )

        >>> image = pipe(
        ...     image=init_image,
        ...     image_embeds=image_emb,
        ...     negative_image_embeds=zero_image_emb,
        ...     height=768,
        ...     width=768,
        ...     num_inference_steps=100,
        ...     strength=0.2,
        ... ).images

        >>> image[0].save(\"red_frog.png\")
        ```
"""







def 	lowerCAmelCase_( SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE=8					)					->	Optional[int]:
    """simple docstring"""

    UpperCamelCase__         =    height // scale_factor**2
    if height % scale_factor**2 != 0:
        new_height += 1
    UpperCamelCase__         =    width // scale_factor**2
    if width % scale_factor**2 != 0:
        new_width += 1
    return new_height * scale_factor, new_width * scale_factor







def 	lowerCAmelCase_( SCREAMING_SNAKE_CASE ,	SCREAMING_SNAKE_CASE=5_12 ,	SCREAMING_SNAKE_CASE=5_12					)					->	Tuple:
    """simple docstring"""

    UpperCamelCase__         =    pil_image.resize((w, h) ,	resample=Image.BICUBIC ,	reducing_gap=1					)
    UpperCamelCase__         =    np.array(pil_image.convert('RGB'					)					)
    UpperCamelCase__         =    arr.astype(np.floataa					) / 127.5 - 1
    UpperCamelCase__         =    np.transpose(SCREAMING_SNAKE_CASE ,	[2, 0, 1]					)
    UpperCamelCase__         =    torch.from_numpy(SCREAMING_SNAKE_CASE					).unsqueeze(0					)
    return image





class    __lowerCamelCase    (  _a  ):

   def __init__(					self ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				)		->       Union[str, Any]:
       super().__init__()

       self.register_modules(
           unet=snake_case_ ,				scheduler=snake_case_ ,				movq=snake_case_ ,				)
       UpperCamelCase__         =    2 ** (len(self.movq.config.block_out_channels      ) - 1)

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_ ,				snake_case_      )		->       Union[str, Any]:
       # get the original timestep using init_timestep
       UpperCamelCase__         =    min(int(num_inference_steps * strength      ) ,				snake_case_      )

       UpperCamelCase__         =    max(num_inference_steps - init_timestep ,				0      )
       UpperCamelCase__         =    self.scheduler.timesteps[t_start:]

       return timesteps, num_inference_steps - t_start

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_=None      )		->       str:
       if not isinstance(snake_case_ ,				(torch.Tensor, PIL.Image.Image, list)      ):
           raise ValueError(
               F'`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(snake_case_      )}'      )

       UpperCamelCase__         =    image.to(device=snake_case_ ,				dtype=snake_case_      )

       UpperCamelCase__         =    batch_size * num_images_per_prompt

       if image.shape[1] == 4:
           UpperCamelCase__         =    image

       else:
           if isinstance(snake_case_ ,				snake_case_      ) and len(snake_case_      ) != batch_size:
               raise ValueError(
                   F'You have passed a list of generators of length {len(snake_case_      )}, but requested an effective batch'
                   F' size of {batch_size}. Make sure the batch size matches the length of the generators.'      )

           elif isinstance(snake_case_ ,				snake_case_      ):
               UpperCamelCase__         =    [
                   self.movq.encode(image[i : i + 1]      ).latent_dist.sample(generator[i]      ) for i in range(snake_case_      )
               ]
               UpperCamelCase__         =    torch.cat(snake_case_ ,				dim=0      )
           else:
               UpperCamelCase__         =    self.movq.encode(snake_case_      ).latent_dist.sample(snake_case_      )

           UpperCamelCase__         =    self.movq.config.scaling_factor * init_latents

       UpperCamelCase__         =    torch.cat([init_latents] ,				dim=0      )

       UpperCamelCase__         =    init_latents.shape
       UpperCamelCase__         =    randn_tensor(snake_case_ ,				generator=snake_case_ ,				device=snake_case_ ,				dtype=snake_case_      )

       # get latents
       UpperCamelCase__         =    self.scheduler.add_noise(snake_case_ ,				snake_case_ ,				snake_case_      )

       UpperCamelCase__         =    init_latents

       return latents

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_=0      )		->       Tuple:
       if is_accelerate_available():
           from accelerate import cpu_offload
       else:
           raise ImportError('Please install accelerate via `pip install accelerate`'      )

       UpperCamelCase__         =    torch.device(F'cuda:{gpu_id}'      )

       UpperCamelCase__         =    [
           self.unet,
           self.movq,
       ]
       for cpu_offloaded_model in models:
           if cpu_offloaded_model is not None:
               cpu_offload(snake_case_ ,				snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_=0      )		->       List[str]:
       if is_accelerate_available() and is_accelerate_version('>=' ,				'0.17.0.dev0'      ):
           from accelerate import cpu_offload_with_hook
       else:
           raise ImportError('`enable_model_cpu_offload` requires `accelerate v0.17.0` or higher.'      )

       UpperCamelCase__         =    torch.device(F'cuda:{gpu_id}'      )

       if self.device.type != "cpu":
           self.to('cpu' ,				silence_dtype_warnings=snake_case_      )
           torch.cuda.empty_cache()  # otherwise we don't see the memory savings (but they probably exist)

       UpperCamelCase__         =    None
       for cpu_offloaded_model in [self.unet, self.movq]:
           UpperCamelCase__       ,						UpperCamelCase__         =    cpu_offload_with_hook(snake_case_ ,				snake_case_ ,				prev_module_hook=snake_case_      )

       # We'll offload the last model manually.
       UpperCamelCase__         =    hook

   @property
   # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[int]:
       if not hasattr(self.unet ,				'_hf_hook'      ):
           return self.device
       for module in self.unet.modules():
           if (
               hasattr(snake_case_ ,				'_hf_hook'      )
               and hasattr(module._hf_hook ,				'execution_device'      )
               and module._hf_hook.execution_device is not None
           ):
               return torch.device(module._hf_hook.execution_device      )
       return self.device







   @torch.no_grad()
   @replace_example_docstring(snake_case_      )
   def __call__(					self ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_ = 512 ,				snake_case_ = 512 ,				snake_case_ = 100 ,				snake_case_ = 4.0 ,				snake_case_ = 0.3 ,				snake_case_ = 1 ,				snake_case_ = None ,				snake_case_ = "pil" ,				snake_case_ = True ,				)		->       List[str]:
       UpperCamelCase__         =    self._execution_device

       UpperCamelCase__         =    guidance_scale > 1.0

       if isinstance(snake_case_ ,				snake_case_      ):
           UpperCamelCase__         =    torch.cat(snake_case_ ,				dim=0      )
       UpperCamelCase__         =    image_embeds.shape[0]
       if isinstance(snake_case_ ,				snake_case_      ):
           UpperCamelCase__         =    torch.cat(snake_case_ ,				dim=0      )

       if do_classifier_free_guidance:
           UpperCamelCase__         =    image_embeds.repeat_interleave(snake_case_ ,				dim=0      )
           UpperCamelCase__         =    negative_image_embeds.repeat_interleave(snake_case_ ,				dim=0      )

       UpperCamelCase__         =    torch.cat([negative_image_embeds, image_embeds] ,				dim=0      ).to(dtype=self.unet.dtype ,				device=snake_case_      )

       if not isinstance(snake_case_ ,				snake_case_      ):
           UpperCamelCase__         =    [image]
       if not all(isinstance(snake_case_ ,				(PIL.Image.Image, torch.Tensor)      ) for i in image      ):
           raise ValueError(
               F'Input is in incorrect format: {[type(snake_case_      ) for i in image]}. Currently, we only support  PIL image and pytorch tensor'      )

       UpperCamelCase__         =    torch.cat([prepare_image(snake_case_ ,				snake_case_ ,				snake_case_      ) for i in image] ,				dim=0      )
       UpperCamelCase__         =    image.to(dtype=image_embeds.dtype ,				device=snake_case_      )

       UpperCamelCase__         =    self.movq.encode(snake_case_      )['latents']
       UpperCamelCase__         =    latents.repeat_interleave(snake_case_ ,				dim=0      )
       self.scheduler.set_timesteps(snake_case_ ,				device=snake_case_      )
       UpperCamelCase__       ,						UpperCamelCase__         =    self.get_timesteps(snake_case_ ,				snake_case_ ,				snake_case_      )
       UpperCamelCase__         =    timesteps[:1].repeat(batch_size * num_images_per_prompt      )
       UpperCamelCase__       ,						UpperCamelCase__         =    downscale_height_and_width(snake_case_ ,				snake_case_ ,				self.movq_scale_factor      )
       UpperCamelCase__         =    self.prepare_latents(
           snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				image_embeds.dtype ,				snake_case_ ,				snake_case_      )
       for i, t in enumerate(self.progress_bar(snake_case_      )      ):
           # expand the latents if we are doing classifier free guidance
           UpperCamelCase__         =    torch.cat([latents] * 2      ) if do_classifier_free_guidance else latents

           UpperCamelCase__         =    {'image_embeds': image_embeds}
           UpperCamelCase__         =    self.unet(
               sample=snake_case_ ,				timestep=snake_case_ ,				encoder_hidden_states=snake_case_ ,				added_cond_kwargs=snake_case_ ,				return_dict=snake_case_ ,				)[0]

           if do_classifier_free_guidance:
               UpperCamelCase__       ,						UpperCamelCase__         =    noise_pred.split(latents.shape[1] ,				dim=1      )
               UpperCamelCase__       ,						UpperCamelCase__         =    noise_pred.chunk(2      )
               UpperCamelCase__       ,						UpperCamelCase__         =    variance_pred.chunk(2      )
               UpperCamelCase__         =    noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
               UpperCamelCase__         =    torch.cat([noise_pred, variance_pred_text] ,				dim=1      )

           if not (
               hasattr(self.scheduler.config ,				'variance_type'      )
               and self.scheduler.config.variance_type in ["learned", "learned_range"]
           ):
               UpperCamelCase__       ,						UpperCamelCase__         =    noise_pred.split(latents.shape[1] ,				dim=1      )

           # compute the previous noisy sample x_t -> x_t-1
           UpperCamelCase__         =    self.scheduler.step(
               snake_case_ ,				snake_case_ ,				snake_case_ ,				generator=snake_case_ ,				)[0]

       # post-processing
       UpperCamelCase__         =    self.movq.decode(snake_case_ ,				force_not_quantize=snake_case_      )['sample']

       if output_type not in ["pt", "np", "pil"]:
           raise ValueError(F'Only the output types `pt`, `pil` and `np` are supported not output_type={output_type}'      )

       if output_type in ["np", "pil"]:
           UpperCamelCase__         =    image * 0.5 + 0.5
           UpperCamelCase__         =    image.clamp(0 ,				1      )
           UpperCamelCase__         =    image.cpu().permute(0 ,				2 ,				3 ,				1      ).float().numpy()

       if output_type == "pil":
           UpperCamelCase__         =    self.numpy_to_pil(snake_case_      )

       if not return_dict:
           return (image,)

       return ImagePipelineOutput(images=snake_case_      )












"""simple docstring"""





import sys
from collections import defaultdict
class    __lowerCamelCase    :

   def __init__(					self      )		->       Tuple:
       UpperCamelCase__         =    []

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       List[str]:
       return self.node_position[vertex]

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       Optional[int]:
       UpperCamelCase__         =    pos

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_      )		->       List[Any]:
       if start > size // 2 - 1:
           return
       else:
           if 2 * start + 2 >= size:
               UpperCamelCase__         =    2 * start + 1
           else:
               if heap[2 * start + 1] < heap[2 * start + 2]:
                   UpperCamelCase__         =    2 * start + 1
               else:
                   UpperCamelCase__         =    2 * start + 2
           if heap[smallest_child] < heap[start]:
               UpperCamelCase__       ,						UpperCamelCase__         =    heap[smallest_child], positions[smallest_child]
               UpperCamelCase__       ,						UpperCamelCase__         =    (
                   heap[start],
                   positions[start],
               )
               UpperCamelCase__       ,						UpperCamelCase__         =    temp, tempa

               UpperCamelCase__         =    self.get_position(positions[smallest_child]      )
               self.set_position(
                   positions[smallest_child] ,				self.get_position(positions[start]      )      )
               self.set_position(positions[start] ,				snake_case_      )

               self.top_to_bottom(snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_      )		->       Any:
       UpperCamelCase__         =    position[index]

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

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

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       Any:
       UpperCamelCase__         =    len(snake_case_      ) // 2 - 1
       for i in range(snake_case_ ,				-1 ,				-1      ):
           self.top_to_bottom(snake_case_ ,				snake_case_ ,				len(snake_case_      ) ,				snake_case_      )







   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       List[Any]:
       UpperCamelCase__         =    positions[0]
       UpperCamelCase__         =    sys.maxsize
       self.top_to_bottom(snake_case_ ,				0 ,				len(snake_case_      ) ,				snake_case_      )
       return temp







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE					)					->	Tuple:
    """simple docstring"""

    UpperCamelCase__         =    Heap()

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

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

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

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


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




