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: Memory Limit Exceeded)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet, BinaryHeap, VecDeque, BTreeSet};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_imports)]
use std::io::stdin;

mod util {
    use std::io::stdin;
    use std::str::FromStr;
    use std::fmt::Debug;

    #[allow(dead_code)]
    pub fn line() -> String {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn gets<T: FromStr>() -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        let mut line: String = String::new();
        stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|t| t.parse().unwrap())
            .collect()
    }
}

#[allow(unused_macros)]
macro_rules! get {
    ($t:ty) => {
        {
            let mut line: String = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
}

#[derive(Eq, PartialEq, Clone, Debug)]
struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}


fn main() {
    let (n, m) = get!(usize, usize);
    let pqc: Vec<(usize, usize, usize)> = (0..m).map(|_| get!(usize, usize, usize)).collect();

    let mut edges = HashMap::new();

    for &(p, q, c) in &pqc {
        let p = p - 1;
        let q = q - 1;
        edges
            .entry((p, Some(c)))
            .or_insert(BTreeSet::new())
            .insert(((q, Some(c)), 0));
        edges
            .entry((q, Some(c)))
            .or_insert(BTreeSet::new())
            .insert(((p, Some(c)), 0));
        edges
            .entry((p, Some(c)))
            .or_insert(BTreeSet::new())
            .insert(((p, None), 0));
        edges
            .entry((q, Some(c)))
            .or_insert(BTreeSet::new())
            .insert(((q, None), 0));
        edges.entry((p, None)).or_insert(BTreeSet::new()).insert((
            (
                p,
                Some(c),
            ),
            1,
        ));
        edges.entry((q, None)).or_insert(BTreeSet::new()).insert((
            (
                q,
                Some(c),
            ),
            1,
        ));
    }


    let mut que = BinaryHeap::new();
    let mut cost = HashMap::new();
    que.push(Rev((0, (0, None))));

    while !que.is_empty() {
        let Rev((c, here)) = que.pop().unwrap();

        if here.0 == n - 1 {
            println!("{}", c);
            return;
        }
        if let Some(e) = edges.get(&here) {
            for &(to, d) in e.iter() {
                let new_cost = c + d;
                if cost.get(&to).cloned().unwrap_or(u64::max_value()) > new_cost {
                    cost.insert(to, new_cost);
                    que.push(Rev((new_cost, to)));
                }
            }
        }
    }

    println!("-1");
}