






"""simple docstring"""



import sys
from collections import defaultdict





class 					_UpperCAmelCase       :




					def __init__(				self     :						Optional[Any]   )  ->  Any:
							lowercase_ : Tuple							       =   []




					def   A  (				self     :						int    ,						A     :						Tuple   )  ->  str:
							return self.node_position[vertex]




					def   A  (				self     :						int    ,						A     :						List[str]    ,						A     :						List[Any]   )  ->  List[str]:
							lowercase_ : Dict							       =   pos




					def   A  (				self     :						Any    ,						A     :						Tuple    ,						A     :						Any    ,						A     :						Optional[Any]    ,						A     :						List[Any]   )  ->  int:
							if start > size // 2 - 1:
									return
							else:
									if 2 * start + 2 >= size:
											lowercase_ : Optional[int]							       =   2 * start + 1
									else:
											if heap[2 * start + 1] < heap[2 * start + 2]:
													lowercase_ : Optional[Any]							       =   2 * start + 1
											else:
													lowercase_ : str							       =   2 * start + 2
									if heap[smallest_child] < heap[start]:
											lowercase_ : List[str]							       =   heap[smallest_child], positions[smallest_child]
											lowercase_ : List[Any]							       =   (
											    heap[start],
											    positions[start],
											)
											lowercase_ : Union[str, Any]							       =   temp, tempa

											lowercase_ : Optional[int]							       =   self.get_position(positions[smallest_child]   )
											self.set_position(
											    positions[smallest_child]    ,						self.get_position(positions[start]   )   )
											self.set_position(positions[start]    ,						__lowercase   )

											self.top_to_bottom(__lowercase    ,						__lowercase    ,						__lowercase    ,						__lowercase   )




					def   A  (				self     :						int    ,						A     :						Any    ,						A     :						Optional[Any]    ,						A     :						Optional[int]    ,						A     :						str   )  ->  Any:
							lowercase_ : Optional[int]							       =   position[index]

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

									if val < heap[parent]:
											lowercase_ : str							       =   heap[parent]
											lowercase_ : int							       =   position[parent]
											self.set_position(position[parent]    ,						__lowercase   )
									else:
											lowercase_ : Any							       =   val
											lowercase_ : Tuple							       =   temp
											self.set_position(__lowercase    ,						__lowercase   )
											break
									lowercase_ : Union[str, Any]							       =   parent
							else:
									lowercase_ : Dict							       =   val
									lowercase_ : Any							       =   temp
									self.set_position(__lowercase    ,						0   )




					def   A  (				self     :						Union[str, Any]    ,						A     :						str    ,						A     :						List[str]   )  ->  Optional[int]:
							lowercase_ : Tuple							       =   len(__lowercase   ) // 2 - 1
							for i in range(__lowercase    ,						-1    ,						-1   ):
									self.top_to_bottom(__lowercase    ,						__lowercase    ,						len(__lowercase   )    ,						__lowercase   )






					def   A  (				self     :						Dict    ,						A     :						Dict    ,						A     :						int   )  ->  Any:
							lowercase_ : str							       =   positions[0]
							lowercase_ : str							       =   sys.maxsize
							self.top_to_bottom(__lowercase    ,						0    ,						len(__lowercase   )    ,						__lowercase   )
							return temp



def 						lowercase    (				__snake_case				: Tuple	):
		lowercase_ : Union[str, Any]							       =   Heap()

		lowercase_ : Tuple							       =   [0] * len(__lowerCamelCase	)
		lowercase_ : Optional[int]							       =   [-1] * len(__lowerCamelCase	)  # Neighboring Tree Vertex of selected vertex
		# Minimum Distance of explored vertex with neighboring vertex of partial tree
		# formed in graph
		lowercase_ : Optional[int]							       =   []  # Heap of Distance of vertices from their neighboring vertex
		lowercase_ : Dict							       =   []

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

		lowercase_ : Any							       =   []
		lowercase_ : Tuple							       =   1
		lowercase_ : Optional[int]							       =   sys.maxsize
		for neighbor, distance in adjacency_list[0]:
				lowercase_ : int							       =   0
				lowercase_ : Union[str, Any]							       =   distance
		heap.heapify(__lowerCamelCase		,					__lowerCamelCase	)

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


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











from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_DEFAULT_MEAN,
    IMAGENET_DEFAULT_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
       import PIL


a		:       Union[str, Any]			     = logging.get_logger(__name__)
class     a    ( lowercase__   ):



      """simple docstring"""


      a  : Any							       =	['pixel_values']
      def __init__(      self					:			Optional[int]		,      __lowercase					:			bool = True		,      __lowercase					:			Dict[str, int] = None		,      __lowercase					:			int = 0.9		,      __lowercase					:			PILImageResampling = PILImageResampling.BICUBIC		,      __lowercase					:			bool = True		,      __lowercase					:			Dict[str, int] = None		,      __lowercase					:			Union[int, float] = 1 / 255		,      __lowercase					:			bool = True		,      __lowercase					:			bool = True		,      __lowercase					:			Optional[Union[float, List[float]]] = None		,      __lowercase					:			Optional[Union[float, List[float]]] = None		,      **__lowercase					:			Any		,      )							->      None:
        super().__init__(**__lowercase					)
        __UpperCAmelCase							:	Tuple           =  size if size is not None else {"""shortest_edge""": 224}
        __UpperCAmelCase							:	Union[str, Any]           =  get_size_dict(__lowercase		,      default_to_square=__lowercase					)
        __UpperCAmelCase							:	Union[str, Any]           =  crop_size if crop_size is not None else {"""height""": 224, """width""": 224}
        __UpperCAmelCase							:	Any           =  get_size_dict(__lowercase		,      param_name="""crop_size"""					)

        __UpperCAmelCase							:	Dict           =  do_resize
        __UpperCAmelCase							:	Dict           =  size
        __UpperCAmelCase							:	Tuple           =  crop_pct
        __UpperCAmelCase							:	List[Any]           =  resample
        __UpperCAmelCase							:	List[Any]           =  do_center_crop
        __UpperCAmelCase							:	List[Any]           =  crop_size
        __UpperCAmelCase							:	Any           =  do_rescale
        __UpperCAmelCase							:	Tuple           =  rescale_factor
        __UpperCAmelCase							:	int           =  do_normalize
        __UpperCAmelCase							:	List[Any]           =  image_mean if image_mean is not None else IMAGENET_DEFAULT_MEAN
        __UpperCAmelCase							:	List[str]           =  image_std if image_std is not None else IMAGENET_DEFAULT_STD
      def 	UpperCAmelCase      (      self					:			Tuple		,      __lowercase					:			np.ndarray		,      __lowercase					:			Dict[str, int]		,      __lowercase					:			Optional[float] = None		,      __lowercase					:			PILImageResampling = PILImageResampling.BICUBIC		,      __lowercase					:			Optional[Union[str, ChannelDimension]] = None		,      **__lowercase					:			Optional[int]		,      )							->      np.ndarray:
        __UpperCAmelCase							:	Tuple           =  get_size_dict(__lowercase		,      default_to_square=__lowercase					)
        if "shortest_edge" not in size and ("height" not in size or "width" not in size):
          raise ValueError(f"""size must contain 'height' and 'width' or 'shortest_edge' as keys. Got {size.keys()}"""					)
        if crop_pct is not None:
          if "shortest_edge" in size:
            __UpperCAmelCase							:	Union[str, Any]           =  int(size["""shortest_edge"""] / crop_pct					)
          elif "height" in size and "width" in size:
            if size["height"] == size["width"]:
              __UpperCAmelCase							:	Tuple           =  int(size["""height"""] / crop_pct					)
            else:
              __UpperCAmelCase							:	str           =  (int(size["""height"""] / crop_pct					), int(size["""width"""] / crop_pct					))
          else:
            raise ValueError("""Invalid size for resize: {}""".format(__lowercase					)					)

          __UpperCAmelCase							:	str           =  get_resize_output_image_size(__lowercase		,      size=__lowercase		,      default_to_square=__lowercase					)
        else:
          if "shortest_edge" in size:
            __UpperCAmelCase							:	List[str]           =  get_resize_output_image_size(__lowercase		,      size=size["""shortest_edge"""]		,      default_to_square=__lowercase					)
          elif "height" in size and "width" in size:
            __UpperCAmelCase							:	int           =  (size["""height"""], size["""width"""])
          else:
            raise ValueError("""Invalid size for resize: {}""".format(__lowercase					)					)

        return resize(__lowercase		,      size=__lowercase		,      resample=__lowercase		,      data_format=__lowercase		,      **__lowercase					)
      def 	UpperCAmelCase      (      self					:			Dict		,      __lowercase					:			np.ndarray		,      __lowercase					:			Dict[str, int]		,      __lowercase					:			Optional[Union[str, ChannelDimension]] = None		,      **__lowercase					:			Union[str, Any]		,      )							->      np.ndarray:
        __UpperCAmelCase							:	Optional[Any]           =  get_size_dict(__lowercase					)
        if "height" not in size or "width" not in size:
          raise ValueError(f"""size must contain 'height' and 'width' as keys. Got {size.keys()}"""					)
        return center_crop(__lowercase		,      size=(size["""height"""], size["""width"""])		,      data_format=__lowercase		,      **__lowercase					)
      def 	UpperCAmelCase      (      self					:			List[str]		,      __lowercase					:			np.ndarray		,      __lowercase					:			Union[int, float]		,      __lowercase					:			Optional[Union[str, ChannelDimension]] = None		,      **__lowercase					:			int		,      )							->      int:
        return rescale(__lowercase		,      scale=__lowercase		,      data_format=__lowercase		,      **__lowercase					)
      def 	UpperCAmelCase      (      self					:			List[Any]		,      __lowercase					:			np.ndarray		,      __lowercase					:			Union[float, List[float]]		,      __lowercase					:			Union[float, List[float]]		,      __lowercase					:			Optional[Union[str, ChannelDimension]] = None		,      **__lowercase					:			List[Any]		,      )							->      np.ndarray:
        return normalize(__lowercase		,      mean=__lowercase		,      std=__lowercase		,      data_format=__lowercase		,      **__lowercase					)




      def 	UpperCAmelCase      (      self					:			Any		,      __lowercase					:			ImageInput		,      __lowercase					:			bool = None		,      __lowercase					:			Dict[str, int] = None		,      __lowercase					:			int = None		,      __lowercase					:			PILImageResampling = None		,      __lowercase					:			bool = None		,      __lowercase					:			Dict[str, int] = None		,      __lowercase					:			bool = None		,      __lowercase					:			float = None		,      __lowercase					:			bool = None		,      __lowercase					:			Optional[Union[float, List[float]]] = None		,      __lowercase					:			Optional[Union[float, List[float]]] = None		,      __lowercase					:			Optional[Union[str, TensorType]] = None		,      __lowercase					:			ChannelDimension = ChannelDimension.FIRST		,      **__lowercase					:			List[str]		,      )							->      PIL.Image.Image:
        __UpperCAmelCase							:	Any           =  do_resize if do_resize is not None else self.do_resize
        __UpperCAmelCase							:	Optional[int]           =  crop_pct if crop_pct is not None else self.crop_pct
        __UpperCAmelCase							:	Optional[Any]           =  resample if resample is not None else self.resample
        __UpperCAmelCase							:	List[Any]           =  do_center_crop if do_center_crop is not None else self.do_center_crop
        __UpperCAmelCase							:	Dict           =  do_rescale if do_rescale is not None else self.do_rescale
        __UpperCAmelCase							:	Tuple           =  rescale_factor if rescale_factor is not None else self.rescale_factor
        __UpperCAmelCase							:	Union[str, Any]           =  do_normalize if do_normalize is not None else self.do_normalize
        __UpperCAmelCase							:	Tuple           =  image_mean if image_mean is not None else self.image_mean
        __UpperCAmelCase							:	Any           =  image_std if image_std is not None else self.image_std

        __UpperCAmelCase							:	Optional[int]           =  size if size is not None else self.size
        __UpperCAmelCase							:	Dict           =  get_size_dict(__lowercase		,      default_to_square=__lowercase					)
        __UpperCAmelCase							:	Tuple           =  crop_size if crop_size is not None else self.crop_size
        __UpperCAmelCase							:	Tuple           =  get_size_dict(__lowercase		,      param_name="""crop_size"""					)

        __UpperCAmelCase							:	Dict           =  make_list_of_images(__lowercase					)

        if not valid_images(__lowercase					):
          raise ValueError(
              """Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, """
              """torch.Tensor, tf.Tensor or jax.ndarray."""					)

        if do_resize and size is None or resample is None:
          raise ValueError("""Size and resample must be specified if do_resize is True."""					)

        if do_center_crop and crop_pct is None:
          raise ValueError("""Crop_pct must be specified if do_center_crop is True."""					)

        if do_rescale and rescale_factor is None:
          raise ValueError("""Rescale factor must be specified if do_rescale is True."""					)

        if do_normalize and (image_mean is None or image_std is None):
          raise ValueError("""Image mean and std must be specified if do_normalize is True."""					)

        # All transformations expect numpy arrays.
        __UpperCAmelCase							:	str           =  [to_numpy_array(__lowercase					) for image in images]

        if do_resize:
          __UpperCAmelCase							:	str           =  [self.resize(image=__lowercase		,      size=__lowercase		,      crop_pct=__lowercase		,      resample=__lowercase					) for image in images]

        if do_center_crop:
          __UpperCAmelCase							:	Any           =  [self.center_crop(image=__lowercase		,      size=__lowercase					) for image in images]

        if do_rescale:
          __UpperCAmelCase							:	List[str]           =  [self.rescale(image=__lowercase		,      scale=__lowercase					) for image in images]

        if do_normalize:
          __UpperCAmelCase							:	str           =  [self.normalize(image=__lowercase		,      mean=__lowercase		,      std=__lowercase					) for image in images]

        __UpperCAmelCase							:	List[str]           =  [to_channel_dimension_format(__lowercase		,      __lowercase					) for image in images]

        __UpperCAmelCase							:	Any           =  {"""pixel_values""": images}
        return BatchFeature(data=__lowercase		,      tensor_type=__lowercase					)


