






import sys
from collections import defaultdict
class 		SCREAMING_SNAKE_CASE__	:

  '''simple docstring'''







  def __init__(      self		:			List[Any]							)						->	Optional[Any]:


         """simple docstring"""
         _UpperCAmelCase							=    []


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


         """simple docstring"""
         return self.node_position[vertex]


  def  lowerCamelCase       (      self		:			Dict       ,				lowerCamelCase		:			Any       ,				lowerCamelCase		:			Any							)						->	Tuple:


         """simple docstring"""
         _UpperCAmelCase							=    pos


  def  lowerCamelCase       (      self		:			Optional[int]       ,				lowerCamelCase		:			Any       ,				lowerCamelCase		:			Tuple       ,				lowerCamelCase		:			str       ,				lowerCamelCase		:			List[str]							)						->	List[str]:


         """simple docstring"""
         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							=    heap[smallest_child], positions[smallest_child]
                       _UpperCAmelCase							=    (
                           heap[start],
                           positions[start],
                       )
                       _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]       ,				__lowerCAmelCase							)

                       self.top_to_bottom(__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase							)


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


         """simple docstring"""
         _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]       ,				__lowerCAmelCase							)
                else:
                       _UpperCAmelCase							=    val
                       _UpperCAmelCase							=    temp
                       self.set_position(__lowerCAmelCase       ,				__lowerCAmelCase							)
                       break
                _UpperCAmelCase							=    parent
         else:
                _UpperCAmelCase							=    val
                _UpperCAmelCase							=    temp
                self.set_position(__lowerCAmelCase       ,				0							)


  def  lowerCamelCase       (      self		:			int       ,				lowerCamelCase		:			Dict       ,				lowerCamelCase		:			Union[str, Any]							)						->	List[Any]:


         """simple docstring"""
         _UpperCAmelCase							=    len(__lowerCAmelCase							) // 2 - 1
         for i in range(__lowerCAmelCase       ,				-1       ,				-1							):
                self.top_to_bottom(__lowerCAmelCase       ,				__lowerCAmelCase       ,				len(__lowerCAmelCase							)       ,				__lowerCAmelCase							)





  def  lowerCamelCase       (      self		:			Tuple       ,				lowerCamelCase		:			int       ,				lowerCamelCase		:			Tuple							)						->	int:


         """simple docstring"""
         _UpperCAmelCase							=    positions[0]
         _UpperCAmelCase							=    sys.maxsize
         self.top_to_bottom(__lowerCAmelCase       ,				0       ,				len(__lowerCAmelCase							)       ,				__lowerCAmelCase							)
         return temp




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						List[str]:
       _UpperCAmelCase							=    Heap()

       _UpperCAmelCase							=    [0] * len(a_ )
       _UpperCAmelCase							=    [-1] * len(a_ )  # 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(a_ ) ):
              distance_tv.append(sys.maxsize )
              positions.append(a_ )
              heap.node_position.append(a_ )

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

       for _ in range(1   ,      len(a_ ) ):
              _UpperCAmelCase							=    heap.delete_minimum(a_   ,      a_ )
              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(a_ )]
                            ):
                                   _UpperCAmelCase							=    distance
                                   heap.bottom_to_top(
                                       a_   ,      heap.get_position(a_ )   ,      a_   ,      a_ )
                                   _UpperCAmelCase							=    vertex
       return tree_edges


if __name__ == "__main__":  # pragma: no cover
  # < --------- Prims Algorithm --------- >
  __a:     List[Any]   					=					int(input('''Enter number of edges: ''').strip())
  __a:     int   					=					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))







'''simple docstring'''

from collections import defaultdict
from typing import Optional

from ..image_utils import load_image
from ..utils import (
    add_end_docstrings,
    is_torch_available,
    logging,
    requires_backends,
)
from .base import PIPELINE_INIT_ARGS, ChunkPipeline


if is_torch_available():
      import torch

      from ..models.auto.modeling_auto import MODEL_FOR_MASK_GENERATION_MAPPING

UpperCamelCase      					=logging.get_logger(__name__)




@add_end_docstrings(SCREAMING_SNAKE_CASE__    )
class      A     (   SCREAMING_SNAKE_CASE__    ):






 """simple docstring"""





 def __init__(				self      ,  **__lowerCAmelCase			):
       super().__init__(**__lowerCAmelCase			)
       requires_backends(self      ,  """vision"""			)
       requires_backends(self      ,  """torch"""			)

       if self.framework != "pt":
             raise ValueError(F"The {self.__class__} is only available in PyTorch."			)

       self.check_model_type(__lowerCAmelCase			)
 def 	_UpperCAmelCase							(				self      ,  **__lowerCAmelCase			):
       UpperCamelCase_					: int            =				{}
       UpperCamelCase_					: int            =				{}
       UpperCamelCase_					: Any            =				{}
       # preprocess args
       if "points_per_batch" in kwargs:
             UpperCamelCase_					: Dict            =				kwargs["""points_per_batch"""]
       if "points_per_crop" in kwargs:
             UpperCamelCase_					: str            =				kwargs["""points_per_crop"""]
       if "crops_n_layers" in kwargs:
             UpperCamelCase_					: Any            =				kwargs["""crops_n_layers"""]
       if "crop_overlap_ratio" in kwargs:
             UpperCamelCase_					: str            =				kwargs["""crop_overlap_ratio"""]
       if "crop_n_points_downscale_factor" in kwargs:
             UpperCamelCase_					: Tuple            =				kwargs["""crop_n_points_downscale_factor"""]
       # postprocess args
       if "pred_iou_thresh" in kwargs:
             UpperCamelCase_					: Any            =				kwargs["""pred_iou_thresh"""]
       if "stability_score_offset" in kwargs:
             UpperCamelCase_					: List[str]            =				kwargs["""stability_score_offset"""]
       if "mask_threshold" in kwargs:
             UpperCamelCase_					: Tuple            =				kwargs["""mask_threshold"""]
       if "stability_score_thresh" in kwargs:
             UpperCamelCase_					: Optional[Any]            =				kwargs["""stability_score_thresh"""]
       if "crops_nms_thresh" in kwargs:
             UpperCamelCase_					: Dict            =				kwargs["""crops_nms_thresh"""]
       if "output_rle_mask" in kwargs:
             UpperCamelCase_					: Optional[int]            =				kwargs["""output_rle_mask"""]
       if "output_bboxes_mask" in kwargs:
             UpperCamelCase_					: List[Any]            =				kwargs["""output_bboxes_mask"""]
       return preprocess_kwargs, forward_params, postprocess_kwargs
 def __call__(				self      ,  __lowerCAmelCase      ,  *__lowerCAmelCase      ,  __lowerCAmelCase=None      ,  __lowerCAmelCase=None      ,  **__lowerCAmelCase			):
       return super().__call__(__lowerCAmelCase      ,  *__lowerCAmelCase      ,  num_workers=__lowerCAmelCase      ,  batch_size=__lowerCAmelCase      ,  **__lowerCAmelCase			)
 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase=64      ,  __lowerCAmelCase = 0      ,  __lowerCAmelCase = 5_12 / 15_00      ,  __lowerCAmelCase = 32      ,  __lowerCAmelCase = 1      ,  ):
       UpperCamelCase_					: Tuple            =				load_image(__lowerCAmelCase			)
       UpperCamelCase_					: Tuple            =				self.image_processor.size["""longest_edge"""]
       UpperCamelCase_     ,      UpperCamelCase_     ,      UpperCamelCase_     ,      UpperCamelCase_					: Dict            =				self.image_processor.generate_crop_boxes(
           __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase			)
       UpperCamelCase_					: Any            =				self.image_processor(images=__lowerCAmelCase      ,  return_tensors="""pt"""			)

       with self.device_placement():
             if self.framework == "pt":
                   UpperCamelCase_					: str            =				self.get_inference_context()
                   with inference_context():
                         UpperCamelCase_					: Optional[int]            =				self._ensure_tensor_on_device(__lowerCAmelCase      ,  device=self.device			)
                         UpperCamelCase_					: Tuple            =				self.model.get_image_embeddings(model_inputs.pop("""pixel_values"""			)			)
                         UpperCamelCase_					: List[Any]            =				image_embeddings

       UpperCamelCase_					: Any            =				grid_points.shape[1]
       UpperCamelCase_					: List[str]            =				points_per_batch if points_per_batch is not None else n_points

       if points_per_batch <= 0:
             raise ValueError(
                 """Cannot have points_per_batch<=0. Must be >=1 to returned batched outputs. """
                 """To return all points at once, set points_per_batch to None"""			)

       for i in range(0      ,  __lowerCAmelCase      ,  __lowerCAmelCase			):
             UpperCamelCase_					: Dict            =				grid_points[:, i : i + points_per_batch, :, :]
             UpperCamelCase_					: List[Any]            =				input_labels[:, i : i + points_per_batch]
             UpperCamelCase_					: Dict            =				i == n_points - points_per_batch
             yield {
                 "input_points": batched_points,
                 "input_labels": labels,
                 "input_boxes": crop_boxes,
                 "is_last": is_last,
                 **model_inputs,
             }
 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase=0.88      ,  __lowerCAmelCase=0.95      ,  __lowerCAmelCase=0      ,  __lowerCAmelCase=1      ,  ):
       UpperCamelCase_					: Union[str, Any]            =				model_inputs.pop("""input_boxes"""			)
       UpperCamelCase_					: Tuple            =				model_inputs.pop("""is_last"""			)
       UpperCamelCase_					: Dict            =				model_inputs.pop("""original_sizes"""			).tolist()
       UpperCamelCase_					: int            =				model_inputs.pop("""reshaped_input_sizes"""			).tolist()

       UpperCamelCase_					: Optional[Any]            =				self.model(**__lowerCAmelCase			)

       # post processing happens here in order to avoid CPU GPU copies of ALL the masks
       UpperCamelCase_					: List[str]            =				model_outputs["""pred_masks"""]
       UpperCamelCase_					: Optional[int]            =				self.image_processor.post_process_masks(
           __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  binarize=__lowerCAmelCase			)
       UpperCamelCase_					: List[str]            =				model_outputs["""iou_scores"""]
       UpperCamelCase_     ,      UpperCamelCase_     ,      UpperCamelCase_					: Optional[Any]            =				self.image_processor.filter_masks(
           masks[0]      ,  iou_scores[0]      ,  original_sizes[0]      ,  input_boxes[0]      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  )
       return {
           "masks": masks,
           "is_last": is_last,
           "boxes": boxes,
           "iou_scores": iou_scores,
       }





 def 	_UpperCAmelCase							(				self      ,  __lowerCAmelCase      ,  __lowerCAmelCase=False      ,  __lowerCAmelCase=False      ,  __lowerCAmelCase=0.7      ,  ):
       UpperCamelCase_					: Tuple            =				[]
       UpperCamelCase_					: Optional[Any]            =				[]
       UpperCamelCase_					: Tuple            =				[]
       for model_output in model_outputs:
             all_scores.append(model_output.pop("""iou_scores"""			)			)
             all_masks.extend(model_output.pop("""masks"""			)			)
             all_boxes.append(model_output.pop("""boxes"""			)			)

       UpperCamelCase_					: Any            =				torch.cat(__lowerCAmelCase			)
       UpperCamelCase_					: Union[str, Any]            =				torch.cat(__lowerCAmelCase			)
       UpperCamelCase_     ,      UpperCamelCase_     ,      UpperCamelCase_     ,      UpperCamelCase_					: Any            =				self.image_processor.post_process_for_mask_generation(
           __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase      ,  __lowerCAmelCase			)

       UpperCamelCase_					: List[Any]            =				defaultdict(__lowerCAmelCase			)
       for output in model_outputs:
             for k, v in output.items():
                   extra[k].append(__lowerCAmelCase			)

       UpperCamelCase_					: Optional[Any]            =				{}
       if output_rle_mask:
             UpperCamelCase_					: int            =				rle_mask

       if output_bboxes_mask:
             UpperCamelCase_					: int            =				bounding_boxes

       return {"masks": output_masks, "scores": iou_scores, **optional, **extra}






