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.