Problem Statement

You are given a tree with N vertices numbered 1 to N.
The i-th edge connects two vertices a_i and $b_i (1\leq i\leq N-1)$.
Initially, a piece is placed at vertex 1. You will perform the following operation exactly N times.

• Choose a vertex that is not occupied by the piece at that moment and is never chosen in the previous operations, and move the piece one vertex toward the chosen vertex.

A way to perform the operation N times is called a good procedure if the piece ends up at vertex N.
Additionally, a good procedure is called an ideal procedure if the number of vertices visited by the piece at least once during the procedure (including vertices 1 and N) is the minimum possible.
Find the number of vertices visited by the piece at least once during an ideal procedure.
If there is no good procedure, print -1 instead.

Input

The input is given from Standard Input in the following format:
N
a_1 b_1
a_2 b_2
$\vdots$
a_{N-1} b_{N-1}

Output

Print the answer as an integer.

Constraints

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

Sample Input 1

4
1 2
2 4
3 4

Sample Output 1

3

If you choose vertices 3, 1, 2, 4 in this order, the piece will go along the path 1 → 2 → 1 → 2 → 4. This is an ideal procedure.

Sample Input 2

6
1 6
2 6
2 3
3 4
4 5

Sample Output 2

-1

There is no good procedure.

Sample Input 3

14
1 2
1 3
3 4
3 5
5 6
6 7
5 8
8 9
8 14
14 10
10 11
14 12
12 13

Sample Output 3

5

见题面 Input 部分

见题面 Output 部分