Problem Statement

You are given a tree with $N$ vertices numbered $1, 2, \dots, N$. The $i$-th edge connects vertices $u_i$ and $v_i$ bidirectionally.

Initially, all vertices are painted white.

To efficiently visit all vertices of this tree, Alice has invented a magical gate. She uses one piece and one gate to travel according to the following procedure.

First, she chooses a vertex and places both the piece and the gate on that vertex. Then, she repeatedly performs the following operations until all vertices are painted black.

• Choose one of the following actions:
• Paint the vertex where the piece is placed black.
  • Choose a vertex adjacent to the vertex where the piece is placed and move the piece to that vertex. The cost of this action is $1$.
  • Move the piece to the vertex where the gate is placed.
  • Move the gate to the vertex where the piece is placed.

Note that only the second action incurs a cost.

It can be proved that it is possible to paint all vertices black in a finite number of operations. Find the minimum total cost required.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq u_i, v_i \leq N$
• The given graph is a tree.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
u_1 v_1
\vdots
u_{N-1} v_{N-1}

Output

Print the answer.