





import math
def 		__magic_name__				( lowercase_				)		->					Optional[int]:


						'''simple docstring'''


						UpperCamelCase  							= 0
						UpperCamelCase  							= 0
						while num > 0:
												UpperCamelCase  							= num % 8
												UpperCamelCase  							= octal + (remainder * math.floor(math.pow(10						,		lowerCamelCase_				)				))
												counter += 1
												UpperCamelCase  							= math.floor(num / 8				)  # basically /= 8 without remainder if any
												# This formatting removes trailing '.0' from `octal`.
						return f'''0o{int(lowerCamelCase_				)}'''
def 		__magic_name__				( )		->					Any:


						'''simple docstring'''


						print("\n2 in octal is:"				)
						print(decimal_to_octal(2				)				)  # = 2
						print("\n8 in octal is:"				)
						print(decimal_to_octal(8				)				)  # = 10
						print("\n65 in octal is:"				)
						print(decimal_to_octal(65				)				)  # = 101
						print("\n216 in octal is:"				)
						print(decimal_to_octal(216				)				)  # = 330
						print("\n512 in octal is:"				)
						print(decimal_to_octal(512				)				)  # = 1000
						print("\n"				)


if __name__ == "__main__":
		main()












import heapq as hq
import math
from collections.abc import Iterator
class  _UpperCAmelCase   :

				"""simple docstring"""




				def __init__(	self		:       str,    lowerCamelCase		:       List[Any]    ):

								'''simple docstring'''
								lowercase__  					=     str(id_    )
								lowercase__  					=     None
								lowercase__  					=     None
								lowercase__  					=     []
								lowercase__  					=     {}  # {vertex:distance}




				def __lt__(	self		:       Dict,    lowerCamelCase		:       Tuple    ):

								'''simple docstring'''
								return self.key < other.key




				def __repr__(	self		:       Dict    ):

								'''simple docstring'''
								return self.id




				def 							lowercase__  (	self		:       str,    lowerCamelCase		:       List[str]    ):

								'''simple docstring'''
								self.neighbors.append(lowerCamelCase    )




				def 							lowercase__  (	self		:       Any,    lowerCamelCase		:       Dict,    lowerCamelCase		:       Optional[Any]    ):

								'''simple docstring'''
								lowercase__  					=     weight






def     a     (		lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				# 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]						,  lowerCamelCase_							)
				graph[b - 1].add_edge(graph[a - 1]						,  lowerCamelCase_							)






def     a     (		lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				lowercase__  					=     []
				for u in graph:
								lowercase__  					=     math.inf
								lowercase__  					=     None
				lowercase__  					=     0
				lowercase__  					=     graph[:]
				while q:
								lowercase__  					=     min(lowerCamelCase_							)
								q.remove(lowerCamelCase_							)
								for v in u.neighbors:
												if (v in q) and (u.edges[v.id] < v.key):
																lowercase__  					=     u
																lowercase__  					=     u.edges[v.id]
				for i in range(1						,  len(lowerCamelCase_							)							):
								a.append((int(graph[i].id							) + 1, int(graph[i].pi.id							) + 1)							)
				return a






def     a     (		lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				for u in graph:
								lowercase__  					=     math.inf
								lowercase__  					=     None
				lowercase__  					=     0

				lowercase__  					=     list(lowerCamelCase_							)
				hq.heapify(lowerCamelCase_							)

				while h:
								lowercase__  					=     hq.heappop(lowerCamelCase_							)
								for v in u.neighbors:
												if (v in h) and (u.edges[v.id] < v.key):
																lowercase__  					=     u
																lowercase__  					=     u.edges[v.id]
																hq.heapify(lowerCamelCase_							)

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






def     a     (		):






				'''simple docstring'''


if __name__ == "__main__":
							import doctest

							doctest.testmod()




