This is an unusual problem in an unusual contest, here is the announcement: http://codeforces.com/blog/entry/73543

Find the distance between vertices $1$ and $n$ in an undirected weighted graph.

Input

The first line contains two integers $n, m$ ($1 \leq n, m \leq 2 \cdot 10^5$) — the number of vertices and the number of edges.

Each of the next $m$ lines contain description of an edge $a_i~b_i~cost_i$ ($1 \leq a_i, b_i \leq n$, $1 \leq cost_i \leq 10^9$).

Loops and multiple edges? Hmm, why not?

Output

Print one integer — the answer to the problem. If there is no path, print $-1$ instead.

见题面 Input 部分

见题面 Output 部分