Problem Statement

You are given a tree with $N$ vertices. The vertices of the tree are numbered from $1$ to $N$, and the edges are numbered up to $N-1$.

Edge $i$ connects vertices $u_i, v_i$. Initially, all vertices are painted white.

A-kun and B-kun play a game using this tree.

A-kun performs A-kun's operation below, and B-kun performs B-kun's operation below. The two of them perform these operations alternately. A-kun goes first.

A-kun's operation
Choose one edge whose 2 connected vertices are both painted white, and paint both of those vertices black.

B-kun's operation
Choose one vertex painted black, and paint that vertex white.

These operations are repeated alternately until A-kun can no longer perform his operation (that is, when, at the time A-kun is to perform his operation, there is no edge whose 2 connected vertices are both painted white).

A-kun tries to make the final number of vertices painted black as large as possible, and B-kun tries to make the final number of vertices painted white as large as possible.

Find the number of vertices that are painted black in the end.

Input

$N$
$u_1\ \ v_1$
$u_2\ \ v_2$
$:$
$u_{N-1}\ \ v_{N-1}$

• $2 \leq N \leq 10^5$
• $1 \leq u_i, v_i \leq N$
• $u_i \neq v_i$
• All input values are integers
• The graph represented by the input is a tree

Output

Print the computed value, followed by a newline.

Sample

4
1 2
1 3
1 4

1

2
1 2

1

12
1 7
8 2
3 12
6 7
7 11
9 1
4 10
12 2
10 1
1 2
5 10

5