201525: [AtCoder]ARC152 F - Attraction on Tree

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.

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.

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.

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