



import heapq as hq
import math
from collections.abc import Iterator



class 				__snake_case						:




							def __init__(       self     :       str				,				A_     :       int):
									lowerCAmelCase_			:     Optional[int]									= str(id_)
									lowerCAmelCase_			:     List[str]									= None
									lowerCAmelCase_			:     Optional[int]									= None
									lowerCAmelCase_			:     Tuple									= []
									lowerCAmelCase_			:     Any									= {}  # {vertex:distance}




							def __lt__(       self     :       Tuple				,				A_     :       Optional[int]):
									return self.key < other.key




							def __repr__(       self     :       List[Any]):
									return self.id




							def    UpperCAmelCase__			(       self     :       int				,				A_     :       str):
									self.neighbors.append(A_)







							def    UpperCAmelCase__			(       self     :       Dict				,				A_     :       List[Any]				,				A_     :       Tuple):
									lowerCAmelCase_			:     List[Any]									= weight





def 			UpperCamelCase(  __UpperCamelCase							:		List[str]     ,__UpperCamelCase							:		Any     ,__UpperCamelCase							:		int     ,__UpperCamelCase							:		Union[str, Any] ):
		# add the neighbors:
		graph[a - 1].add_neighbor(graph[b - 1] )
		graph[b - 1].add_neighbor(graph[a - 1] )
		# add the edges:
		graph[a - 1].add_edge(graph[b - 1]     ,__UpperCamelCase )
		graph[b - 1].add_edge(graph[a - 1]     ,__UpperCamelCase )


def 			UpperCamelCase(  __UpperCamelCase							:		list     ,__UpperCamelCase							:		Vertex ):
		lowerCAmelCase_			:     int									= []
		for u in graph:
				lowerCAmelCase_			:     Union[str, Any]									= math.inf
				lowerCAmelCase_			:     Union[str, Any]									= None
		lowerCAmelCase_			:     Optional[Any]									= 0
		lowerCAmelCase_			:     Tuple									= graph[:]
		while q:
				lowerCAmelCase_			:     Any									= min(__UpperCamelCase )
				q.remove(__UpperCamelCase )
				for v in u.neighbors:
						if (v in q) and (u.edges[v.id] < v.key):
								lowerCAmelCase_			:     Optional[Any]									= u
								lowerCAmelCase_			:     Any									= u.edges[v.id]
		for i in range(1     ,len(__UpperCamelCase ) ):
				a.append((int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1) )
		return a


def 			UpperCamelCase(  __UpperCamelCase							:		list     ,__UpperCamelCase							:		Vertex ):
		for u in graph:
				lowerCAmelCase_			:     List[Any]									= math.inf
				lowerCAmelCase_			:     Union[str, Any]									= None
		lowerCAmelCase_			:     Optional[Any]									= 0

		lowerCAmelCase_			:     List[Any]									= list(__UpperCamelCase )
		hq.heapify(__UpperCamelCase )

		while h:
				lowerCAmelCase_			:     List[str]									= hq.heappop(__UpperCamelCase )
				for v in u.neighbors:
						if (v in h) and (u.edges[v.id] < v.key):
								lowerCAmelCase_			:     Dict									= u
								lowerCAmelCase_			:     List[Any]									= u.edges[v.id]
								hq.heapify(__UpperCamelCase )

		for i in range(1     ,len(__UpperCamelCase ) ):
				yield (int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1)


def 			UpperCamelCase(  ):
		pass


if __name__ == "__main__":
						import doctest

						doctest.testmod()










import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp


def 			UpperCamelCase(  ):
		lowerCAmelCase_			:     List[str]									= ArgumentParser(
		    description=(
		        '''PyTorch TPU distributed training launch '''
		        '''helper utility that will spawn up '''
		        '''multiple distributed processes'''
		    ) )

		# Optional arguments for the launch helper
		parser.add_argument('''--num_cores'''     ,type=__UpperCamelCase     ,default=1     ,help='''Number of TPU cores to use (1 or 8).''' )

		# positional
		parser.add_argument(
		    '''training_script'''     ,type=__UpperCamelCase     ,help=(
		        '''The full path to the single TPU training '''
		        '''program/script to be launched in parallel, '''
		        '''followed by all the arguments for the '''
		        '''training script'''
		    )     ,)

		# rest from the training program
		parser.add_argument('''training_script_args'''     ,nargs=__UpperCamelCase )

		return parser.parse_args()


def 			UpperCamelCase(  ):
		lowerCAmelCase_			:     str									= parse_args()

		# Import training_script as a module.
		lowerCAmelCase_			:     str									= Path(args.training_script )
		sys.path.append(str(script_fpath.parent.resolve() ) )
		lowerCAmelCase_			:     Tuple									= script_fpath.stem
		lowerCAmelCase_			:     Union[str, Any]									= importlib.import_module(__UpperCamelCase )

		# Patch sys.argv
		lowerCAmelCase_			:     Optional[int]									= [args.training_script] + args.training_script_args + ['''--tpu_num_cores''', str(args.num_cores )]
		xmp.spawn(mod._mp_fn     ,args=()     ,nprocs=args.num_cores )


if __name__ == "__main__":
						main()





