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: Wrong Answer)

#[allow(unused_macros)]
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)*}
    };
}

#[allow(unused_macros)]
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)*}
    };
}

#[allow(unused_macros)]
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<_>>()
    };

    ($next:expr, chars) => {
        read_value!($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_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

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

#[allow(unused_imports)]
use std::io::Write;
use std::cmp::Ordering;

#[derive(Debug, Copy, Clone, Eq, PartialEq)]
struct Rev(usize);

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

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


fn main() {
    input!{
      n: usize,
      m: usize,
      pqcs: [(usize,usize,usize); m],
    }
    let mut nodes = vec![];
    for i in 0..n {
        nodes.push((i+1, 0));
    }
    for &(p, q, c) in pqcs.iter() {
        nodes.push((p, c));
        nodes.push((q, c));
    }
    nodes.sort();
    nodes.dedup();

    let nn = nodes.len();
    let mut edges = vec![vec![]; nn];

    for &(p, q, c) in pqcs.iter() {
        // p.0 -> p.c 1
        // p.c -> q.c 0
        // q.c -> p.c 0
        // q.c -> q.0 0
        let p0 = nodes.binary_search(&(p, 0)).unwrap();
        let pc = nodes.binary_search(&(p, c)).unwrap();
        let qc = nodes.binary_search(&(q, c)).unwrap();
        let q0 = nodes.binary_search(&(q, 0)).unwrap();
        edges[p0].push((pc, 1));
        edges[pc].push((qc, 0));
        edges[qc].push((pc, 0));
        edges[qc].push((q0, 0));
    }

    let s = nodes.binary_search(&(1, 0)).unwrap();
    let e = nodes.binary_search(&(n, 0)).unwrap();

    use std::collections::BinaryHeap;
    let mut q = BinaryHeap::new();
    q.push((Rev(0),s));

    const INF: usize = 1 << 31;
    let mut costs = vec![INF; nn];
    costs[s] = 0;
    while q.len() > 0 {
        let (Rev(cur_cost), cur) = q.pop().unwrap();
        if costs[cur] < cur_cost {
            continue;
        }

        for &(next_node, cost) in edges[cur].iter() {
            let next_cost = costs[cur] + cost;
            if next_cost < costs[next_node] {
                costs[next_node] = next_cost;
                q.push((Rev(next_cost), next_node));
            }
        }
    }

    // debug!(nodes);
    // debug!(edges);
    // debug!(s, e);
    // debug!(costs);

    if costs[e] >= INF {
        println!("{}", -1);
    } else {
        println!("{}", costs[e]);
    }
}