Attraction on Tree

AtCoder

IDarc152_f

Time2000ms

Memory256MB

Difficulty—

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: $N$ $a_1$ $b_1$ $a_2$ $b_2$ $\vdots$ $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

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.

Input #2

Output #2

\-1

There is no good procedure.

Input #3

Output #3

API Response (JSON)

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