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::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let m: usize = it.next().unwrap().parse().unwrap();
    let mut e = Vec::with_capacity(m);
    let mut z = Vec::with_capacity(2 * m + n);
    for _ in 0..m {
        let p: usize = it.next().unwrap().parse().unwrap();
        let q: usize = it.next().unwrap().parse().unwrap();
        let c: u32 = it.next().unwrap().parse().unwrap();
        e.push((p, q, c));
        z.push((p, c));
        z.push((q, c));
    }
    for i in 1..(n + 1) {
        z.push((i, 0));
    }
    z.sort();
    z.dedup();
    let size = z.len();
    let mut g = vec![vec![]; size];
    for (p, q, c) in e {
        let a = z.binary_search(&(p, c)).unwrap();
        let b = z.binary_search(&(q, c)).unwrap();
        g[a].push((b, 0));
        g[b].push((a, 0));
    }
    for i in 0..size {
        if z[i].1 != 0 {
            continue;
        }
        for j in (i + 1)..size {
            if z[j].0 != z[i].0 {
                break;
            }
            g[i].push((j, 1));
            g[j].push((i, 0));
        }
    }
    let mut dp = vec![size; size];
    dp[0] = 0;
    let mut q = std::collections::VecDeque::new();
    q.push_back(0);
    while let Some(v) = q.pop_front() {
        for &(u, c) in &g[v] {
            if c == 0 && dp[u] > dp[v] {
                dp[u] = dp[v];
                q.push_front(u);
            }
            if c == 1 && dp[u] > dp[v] + 1 {
                dp[u] = dp[v] + 1;
                q.push_back(u);
            }
        }
    }
    let ans = dp[z.binary_search(&(n, 0)).unwrap()];
    if ans == size {
        println!("-1");
    } else {
        println!("{}", ans);
    }
}

fn main() {
    run();
}