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::str::FromStr;
use std::io::*;
use std::collections::*;
use utils::*;

pub fn main() {
    let i = stdin();
    let mut o = Vec::new();
    run(i.lock(), &mut o);
    stdout().write_all(&o).unwrap();
}
#[derive(Copy, Clone, Hash, Eq, PartialEq)]
struct S {
    s: usize, // 駅
    c: usize, // 運営会社
}

fn run<R: BufRead, W: Write>(i: R, o: &mut W) {
    let mut i = AtRead::from(i);
    let (n, m) = i.read2::<usize, usize>();

    let mut edges = vec![Vec::new(); n];
    for _ in 0..m {
        let (p, q, c) = i.read3::<usize, usize, usize>();
        let (p, q) = (p - 1, q - 1);
        edges[p].push(S { s: q, c: c });
        edges[q].push(S { s: p, c: c });
    }
    let result = if let Some(cost) = solve(n, &edges) {
        format!("{}", cost)
    } else {
        "-1".to_string()
    };
    writeln!(o, "{}", result).unwrap();
}
fn solve(n: usize, edges: &[Vec<S>]) -> Option<usize> {
    let mut costs = vec![usize::max_value(); n];
    let mut s = (HashSet::new(), HashSet::new());
    let mut visits = HashSet::new();
    let mut q = Vec::new();
    s.0.insert(0);
    costs[0] = 0;

    for cost in 1.. {
        if s.0.is_empty() {
            return None;
        }
        for &s0 in &s.0 {
            for &sc in &edges[s0] {
                q.push(sc);
            }
        }
        visits.clear();
        while let Some(sc0) = q.pop() {
            if costs[sc0.s] < cost || !visits.insert(sc0) {
                continue;
            }
            if sc0.s == n - 1 {
                return Some(cost);
            }
            s.1.insert(sc0.s);
            costs[sc0.s] = cost;
            for &sc1 in &edges[sc0.s] {
                if sc1.c == sc0.c {
                    q.push(sc1);
                }
            }
        }
        s.0.clear();
        s = (s.1, s.0);
    }
    unreachable!()
}

mod utils {
    use super::*;

    pub struct AtRead<R: BufRead> {
        r: R,
        s: String,
    }

    macro_rules! fn_read {
        {$f:ident($($v:ident: $t:ident),*)} => {
            pub fn $f<$($t: FromStr),*>(&mut self) -> ($($t),*) {
                let i = &mut self.read_line().split(' ');
                $(
                    let $v = next(i);
                )*
                ($($v),*)
            }
        };
    }

    impl<R: BufRead> AtRead<R> {
        pub fn from(r: R) -> Self {
            AtRead {
                r: r,
                s: String::new(),
            }
        }
        pub fn read_line(&mut self) -> &str {
            self.s.clear();
            self.r.read_line(&mut self.s).unwrap();
            self.s.trim()
        }

        fn_read! { read2(v1: T1, v2: T2) }
        fn_read! { read3(v1: T1, v2: T2, v3: T3) }
    }

    fn next<'a, T: FromStr, I: std::iter::Iterator<Item = &'a str>>(i: &mut I) -> T {
        i.next().unwrap().parse().ok().unwrap()
    }
}