Tree Matching

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).