



'''simple docstring'''




from collections import defaultdict



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



def    __lowerCamelCase						(      )   ->    Dict:
       dfs(1	)


if __name__ == "__main__":
       a						,   a     :    Optional[Any]      						=					1_0, 9
       a     :    Dict      						=					defaultdict(list)
       a     :    List[Any]      						=					{}
       a     :    List[Any]      						=					[]
       a     :    Union[str, Any]      						=					0
       a     :    List[str]      						=					[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (1_0, 8)]
       for u, v in edges:
              tree[u].append(v)
              tree[v].append(u)
       even_tree()
       print(len(cuts) - 1)






'''simple docstring'''




from collections.abc import Callable

import numpy as np



def    __lowerCamelCase						(      _lowercase			,       _lowercase			,       _lowercase			,       _lowercase			,       _lowercase	)   ->    np.array:
							UpperCAmelCase  :	Optional[Any]							  =	int(np.ceil((x_end - xa) / step_size	)	)
							UpperCAmelCase  :	str							  =	np.zeros((n + 1,)	)
							UpperCAmelCase  :	Optional[Any]							  =	ya
							UpperCAmelCase  :	Union[str, Any]							  =	xa

							for k in range(_lowercase	):
														UpperCAmelCase  :	Dict							  =	y[k] + step_size * ode_func(_lowercase			,       y[k]	)
														UpperCAmelCase  :	Optional[int]							  =	y[k] + (
														    (step_size / 2) * (ode_func(_lowercase			,       y[k]	) + ode_func(x + step_size			,       _lowercase	))
														)
														x += step_size

							return y


if __name__ == "__main__":
							import doctest

							doctest.testmod()

