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

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 $(3,4)$.