



"""simple docstring"""






from collections import defaultdict






def        snake_case_  (      A_					:		int						):


       '''simple docstring'''





       _lowerCamelCase						:				Dict    			= 1
       _lowerCamelCase						:				List[Any]    			= True
       for v in tree[start]:
              if v not in visited:
                     ret += dfs(A_						)
       if ret % 2 == 0:
              cuts.append(A_						)
       return ret






def        snake_case_  (      ):


       '''simple docstring'''





       dfs(1						)


if __name__ == "__main__":
   lowerCAmelCase__    ,  lowerCAmelCase__        =				10, 9
   lowerCAmelCase__        =				defaultdict(list)
   lowerCAmelCase__        =				{}
   lowerCAmelCase__        =				[]
   lowerCAmelCase__        =				0
   lowerCAmelCase__        =				[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
   for u, v in edges:
      tree[u].append(v)
      tree[v].append(u)
   even_tree()
   print(len(cuts) - 1)






"""simple docstring"""


class   _UpperCamelCase  (   lowerCAmelCase__		):
							'''simple docstring'''







							pass
class   _UpperCamelCase  (   lowerCAmelCase__		):
							'''simple docstring'''







							pass
class   _UpperCamelCase  :
							'''simple docstring'''







							def __init__(     self	):
										__lowerCAmelCase				    =			[
										    [],
										    [],
										    [],
										]

							def 			snake_case				(     self    ,   __a    ,   __a	):
										try:
													if len(self.queues[priority]	) >= 1_00:
																raise OverflowError("Maximum queue size is 100"	)
													self.queues[priority].append(__a	)
										except IndexError:
													raise ValueError("Valid priorities are 0, 1, and 2"	)

							def 			snake_case				(     self	):
										for queue in self.queues:
													if queue:
																return queue.pop(0	)
										raise UnderFlowError("All queues are empty"	)



							def __str__(     self	):
										return "\n".join(f"Priority {i}: {q}" for i, q in enumerate(self.queues	)	)
class   _UpperCamelCase  :
							'''simple docstring'''







							def __init__(     self	):
										__lowerCAmelCase				    =			[]

							def 			snake_case				(     self    ,   __a	):
										if len(self.queue	) == 1_00:
													raise OverFlowError("Maximum queue size is 100"	)
										self.queue.append(__a	)

							def 			snake_case				(     self	):
										if not self.queue:
													raise UnderFlowError("The queue is empty"	)
										else:
													__lowerCAmelCase				    =			min(self.queue	)
													self.queue.remove(__a	)
													return data



							def __str__(     self	):
										return str(self.queue	)


def _lowerCamelCase	(		):

			'''simple docstring'''




			__lowerCAmelCase				    =			FixedPriorityQueue()
			fpq.enqueue(0    , 10      )
			fpq.enqueue(1    , 70      )
			fpq.enqueue(0    , 100      )
			fpq.enqueue(2    , 1      )
			fpq.enqueue(2    , 5      )
			fpq.enqueue(1    , 7      )
			fpq.enqueue(2    , 4      )
			fpq.enqueue(1    , 64      )
			fpq.enqueue(0    , 128      )
			print(_UpperCamelCase      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )
			print(_UpperCamelCase      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )
			print(fpq.dequeue()      )


def _lowerCamelCase	(		):

			'''simple docstring'''




			__lowerCAmelCase				    =			ElementPriorityQueue()
			epq.enqueue(10      )
			epq.enqueue(70      )
			epq.enqueue(100      )
			epq.enqueue(1      )
			epq.enqueue(5      )
			epq.enqueue(7      )
			epq.enqueue(4      )
			epq.enqueue(64      )
			epq.enqueue(128      )
			print(_UpperCamelCase      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )
			print(_UpperCamelCase      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )
			print(epq.dequeue()      )


if __name__ == "__main__":
	fixed_priority_queue()
	element_priority_queue()




