```
"""
You are given a tree(a simple connected graph with no cycles). The tree has N
nodes numbered from 1 to N and is rooted at node 1.
Find the maximum number of edges you can remove from the tree to get a forest
such that each connected component of the forest contains an even number of
nodes.
Constraints
2 <= 2 <= 100
Note: The tree input will be such that it can always be decomposed into
components containing an even number of nodes.
"""
# pylint: disable=invalid-name
from collections import defaultdict
def dfs(start: int) -> int:
"""DFS traversal"""
# pylint: disable=redefined-outer-name
ret = 1
visited[start] = True
for v in tree[start]:
if v not in visited:
ret += dfs(v)
if ret % 2 == 0:
cuts.append(start)
return ret
def even_tree():
"""
2 1
3 1
4 3
5 2
6 1
7 2
8 6
9 8
10 8
On removing edges (1,3) and (1,6), we can get the desired result 2.
"""
dfs(1)
if __name__ == "__main__":
n, m = 10, 9
tree = defaultdict(list)
visited: dict[int, bool] = {}
cuts: list[int] = []
count = 0
edges = [(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)
```