Tree Matching

• Time limit: 1.00 s
• Memory limit: 512 MB

You are given a tree consisting 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 describing 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

• $1 \le n \le 2 \cdot 10^5$
  
• $1 \le a,b \le n$
  

Example

Input:
5
1 2
1 3
3 4
3 5

Output:
2

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