Problem:
Score : 600 points

Problem Statement

Snuke's town has a subway system, consisting of N stations and M railway lines. The stations are numbered 1 through N. Each line is operated by a company. Each company has an identification number.

The i-th ( 1 \leq i \leq M ) line connects station p_i and q_i bidirectionally. There is no intermediate station. This line is operated by company c_i.

You can change trains at a station where multiple lines are available.

The fare system used in this subway system is a bit strange. When a passenger only uses lines that are operated by the same company, the fare is 1 yen (the currency of Japan). Whenever a passenger changes to a line that is operated by a different company from the current line, the passenger is charged an additional fare of 1 yen. In a case where a passenger who changed from some company A's line to another company's line changes to company A's line again, the additional fare is incurred again.

Snuke is now at station 1 and wants to travel to station N by subway. Find the minimum required fare.

Constraints

2 \leq N \leq 10^5

0 \leq M \leq 2×10^5

1 \leq p_i \leq N (1 \leq i \leq M)

1 \leq q_i \leq N (1 \leq i \leq M)

1 \leq c_i \leq 10^6 (1 \leq i \leq M)

p_i \neq q_i (1 \leq i \leq M)

Input

The input is given from Standard Input in the following format:

N M
p_1 q_1 c_1
:
p_M q_M c_M

Output

Print the minimum required fare. If it is impossible to get to station N by subway, print -1 instead.

Sample Input 1

3 3
1 2 1
2 3 1
3 1 2

Sample Output 1

1

Use company 1's lines: 1 → 2 → 3. The fare is 1 yen.

Sample Input 2

8 11
1 3 1
1 4 2
2 3 1
2 5 1
3 4 3
3 6 3
3 7 3
4 8 4
5 6 1
6 7 5
7 8 5

Sample Output 2

2

First, use company 1's lines: 1 → 3 → 2 → 5 → 6. Then, use company 5's lines: 6 → 7 → 8. The fare is 2 yen.

Sample Input 3

2 0

Sample Output 3

-1

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::collections::VecDeque;
fn main() {
    let (n, m) = {
        let a = getvec::<usize>();
        (a[0], a[1])
    };
    let mut stations = vec![vec![]; n];
    let mut edges = vec![];
    for _ in 0..m {
        let (p, q, c) = {
            let a = getvec::<usize>();
            (a[0] - 1, a[1] - 1, a[2] - 1)
        };
        stations[p].push(c);
        stations[q].push(c);
        edges.push((p, q, c));
    }
    let mut offset : Vec<usize>= vec![0; n + 1];
    offset[0] = n;
    for i in 0..n {
        stations[i].sort();
        stations[i].dedup();
        offset[i + 1] = offset[i] + stations[i].len();
    }
    let mut adj = vec![vec![]; offset[n]];
    for i in 0..n {
        for j in offset[i]..offset[i + 1] {
            adj[j].push(i);
        }
    }
    for &e in &edges {
        let (u, v, c) = e;
        let x = offset[u] + stations[u].binary_search(&c).unwrap();
        let y = offset[v] + stations[v].binary_search(&c).unwrap();
        adj[x].push(y);
        adj[y].push(x);
    }
    let inf = 1000000000;
    let mut dist = vec![inf; offset[n]];
    let mut deq : VecDeque<usize> = VecDeque::new();
    deq.push_back(0); dist[0] = 0;
    while let Some(u) = deq.pop_front() {
        if u < n {
            for v in offset[u]..offset[u + 1] {
                if dist[v] > dist[u] + 1 {
                    dist[v] = dist[u] + 1;
                    deq.push_back(v);
                }
            }
        }
        else {
            for &v in &adj[u] {
                if dist[v] > dist[u] {
                    dist[v] = dist[u];
                    deq.push_front(v);
                }
            }
        }
    }
    println!("{}", if dist[n - 1] == inf {-1} else {dist[n - 1]});
}

fn next_line() -> String {
    let mut input = String::new();
    std::io::stdin().read_line(&mut input).unwrap();
    input
}
 
#[allow(dead_code)]
fn getnum<T : std::str::FromStr>() -> T {
    let res = next_line();
    let res = res.trim().parse::<T>().ok().unwrap();
    res
}
 
#[allow(dead_code)]
fn getvec<T : std::str::FromStr>() -> Vec<T> {
    let res = next_line();
    let res : Vec<T> = res.split_whitespace().map(|x| x.parse::<T>().ok().unwrap()).collect();
    return res;
}