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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};
use std::collections::HashMap;

fn main() {
    input!{
        n: usize,
        m: usize,
        v: [(usize1, usize1, usize); m]
    }
    let mut g: HashMap<(usize, usize), HashMap<(usize, usize), usize>> = HashMap::new();
    g.insert((0, 0), HashMap::new());
    for &(a, b, c) in &v {
        {
            let map = g.entry((a, c)).or_insert(HashMap::new());
            map.insert((b, c), 0);
            map.insert((a, 0), 0);
        }
        g.entry((a, 0)).or_insert(HashMap::new()).insert((a, c), 1);
        {
            let map = g.entry((b, c)).or_insert(HashMap::new());
            map.insert((a, c), 0);
            map.insert((b, 0), 0);
        }
        g.entry((b, 0)).or_insert(HashMap::new()).insert((b, c), 1);
    }
    if let Some(ans) = dijkstra((0, 0), (n - 1, 0), &g) {
        println!("{}", ans);
    } else {
        println!("-1");
    }
}

use std::collections::BinaryHeap;
use std::cmp::Ordering;

#[derive(Debug, PartialEq, Eq)]
struct State((usize, usize), usize);

impl Ord for State {
    fn cmp(&self, other: &Self) -> Ordering {
        other.1.cmp(&self.1)
    }
}

impl PartialOrd for State {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

fn dijkstra(s: (usize, usize), t: (usize, usize), g: &HashMap<(usize, usize), HashMap<(usize, usize), usize>>) -> Option<usize> {
    let mut pq = BinaryHeap::new();
    let mut dist = HashMap::new();
    pq.push(State(s, 0));
    dist.insert(s, 0);
    while let Some(st) = pq.pop() {
        if st.0 == t {
            return Some(st.1);
        }
        for (&q, c) in g.get(&st.0).unwrap().iter() {
            if let Some(&d) = dist.get(&q) {
                if d <= st.1 + c {
                    continue;
                }
            }
            dist.insert(q, st.1 + c);
            pq.push(State(q, st.1 + c));
        }
    }
    None
}