





'''simple docstring'''


from ..utils import DummyObject, requires_backends

class  lowerCAmelCase_		(		metaclass=__magic_name__		):
 __lowerCamelCase    :				Optional[Any]								=       ["torch", "scipy"]




 def __init__(						self      ,  *_lowerCAmelCase      ,  **_lowerCAmelCase		)     ->				Optional[int]:
     requires_backends(self      ,  ["torch", "scipy"]		)




 @classmethod
 def 				_snake_case (						cls      ,  *_lowerCAmelCase      ,  **_lowerCAmelCase		)     ->				Any:
     requires_backends(cls      ,  ["torch", "scipy"]		)





 @classmethod
 def 				_snake_case (						cls      ,  *_lowerCAmelCase      ,  **_lowerCAmelCase		)     ->				Union[str, Any]:
     requires_backends(cls      ,  ["torch", "scipy"]		)








from collections import defaultdict





def 				A__ (snake_case   :		int				)     ->						int:
					__UpperCamelCase					:	Optional[int]             =      1
					__UpperCamelCase					:	Tuple             =      True
					for v in tree[start]:
										if v not in visited:
															ret += dfs(snake_case				)
					if ret % 2 == 0:
										cuts.append(snake_case				)
					return ret





def 				A__ ()     ->						str:
					dfs(1				)


if __name__ == "__main__":
	a__     ,							a__		     =     10, 9
	a__		     =     defaultdict(list)
	a__		     =     {}
	a__		     =     []
	a__		     =     0
	a__		     =     [(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)






