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

Example Output

2

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