"""
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)