**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).