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.

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.

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.

Sample Input 1

4
1 2
1 3
1 4

Sample Output 1

3

Here is an example of Alice's procedure. Let (u, v) denote the state where the piece is at vertex u and the gate is at vertex v.

• Place the piece and the gate at vertex 4.

• The state is now (4, 4).

• Perform action 1.

• Vertex 4 is painted black.

• The state is now (4, 4).

• Perform action 2 and move the piece to vertex 1.

• This costs 1.

• The state is now (1, 4).

• Perform action 1.

• Vertex 1 is painted black.

• Perform action 4.

• The state is now (1, 1).

• Perform action 2 and move the piece to vertex 2.

• This costs 1.

• The state is now (2, 1).

• Perform action 1.

• Vertex 2 is painted black.

• Perform action 3.

• The state is now (1, 1).

• Perform action 2 and move the piece to vertex 3.

• This costs 1.

• The state is now (3, 1).

• Perform action 1.

• Vertex 3 is painted black.
• All vertices are now painted black, so the procedure ends.

The total cost of performing action 2 is 3, and there is no procedure with a smaller cost.

Sample Input 2

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

Sample Output 2

10

见题面 Input 部分

见题面 Output 部分