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CSES Problem Set

Tree Matching


Task | Statistics


CSES - Tree Matching

Time limit:1.00 s Memory limit:512 MB

You are given a tree that consists of $n$ nodes.

A matching is a set of edges where each node is an endpoint of at most one edge. What is the maximum number of edges in a matching?

Input

The first input line contains an integer $n$: the number of nodes. The nodes are numbered $1,2,\ldots,n$.

Then there are $n-1$ lines that describe the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Output

Print one integer: the maximum number of pairs.

Constraints
Example

Input:
5
1 2
1 3
3 4
3 5


Output:
2

Explanation: One possible matching is $(1,2)$ and $(3,4)$.