Problem Statement

You are given a tree with $N$ vertices. The $i$-th edge connects vertex $u_i$ and vertex $v_i$ bidirectionally.
Each vertex of the tree is painted either black or white, and initially all vertices are painted white.
Hijiri wants to make all vertices black by performing the following two operations any number of times in any order.

Operation 1: Choose one white vertex and make it black. This costs 1.
Operation 2: Choose one white vertex. If a majority of the vertices adjacent to it are black, make it black. This costs nothing.

Find the minimum cost required to make all vertices black.

Constraints

• $1 \le N \le 100000$
• $1 \le u_i,v_i \le N$
• All inputs are integers
• The given graph is a tree

Input

$N$
$u_1\ v_1$
$u_2\ v_2$
$u_3\ v_3$
$\vdots$
$u_{N-1}\ v_{N-1}$

Output

Output the minimum cost required for Hijiri to make all vertices black.

Sample

8
1 2
1 3
1 4
2 5
2 6
3 7
3 8

2

3
1 2
2 3

1