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)

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

struct IdRegister {
    registered_ids: HashMap<(usize, usize), usize>,
    unused_id: usize,
}

impl IdRegister {
    fn new() -> IdRegister {
        IdRegister {
            registered_ids: HashMap::new(),
            unused_id: 0,
        }
    }

    fn query(&mut self, company: usize, station: usize) -> usize {
        if !self.registered_ids.contains_key(&(company, station)) {
            self.registered_ids
                .insert((company, station), self.unused_id);
            self.unused_id += 1;
        }
        self.registered_ids[&(company, station)]
    }
}

fn main() {
    let v: Vec<usize> = read_vec();
    let (n, m) = (v[0], v[1]);

    let mut lines = HashMap::new();
    let mut edges = Vec::new();
    let mut id_register = IdRegister::new();
    for _ in 0..m {
        let v: Vec<usize> = read_vec();
        let (s, t, c) = (v[0] - 1, v[1] - 1, v[2]);
        let s_edge_idx = id_register.query(c, s);
        let t_edge_idx = id_register.query(c, t);
        if edges.len() == s_edge_idx {
            edges.push(Vec::new());
        }
        if edges.len() == t_edge_idx {
            edges.push(Vec::new());
        }

        edges[s_edge_idx].push(Edge {
            to: t_edge_idx,
            cost: 0,
        });
        edges[t_edge_idx].push(Edge {
            to: s_edge_idx,
            cost: 0,
        });

        lines.entry(s).or_insert(HashSet::new()).insert(c);
        lines.entry(t).or_insert(HashSet::new()).insert(c);
    }

    // changable stations
    for station in lines.keys() {
        if lines[station].len() < 2 {
            continue;
        }
        let new_edges_idx = edges.len();
        edges.push(Vec::new());
        for &company in lines[station].iter() {
            edges[new_edges_idx].push(Edge {
                to: id_register.query(company, *station),
                cost: 1,
            });
            edges[id_register.query(company, *station)].push(Edge {
                to: new_edges_idx,
                cost: 1,
            });
        }
    }

    let new_edges_idx = edges.len();
    edges.push(Vec::new());
    if !lines.contains_key(&0) || !lines.contains_key(&(n - 1)) {
        println!("-1");
        return;
    }
    for &company in lines[&0].iter() {
        edges[new_edges_idx].push(Edge {
            to: id_register.query(company, 0),
            cost: 2,
        });
    }
    let d = dijkstra(&edges, new_edges_idx, new_edges_idx + 1);

    let mut ans = INF;
    for &company in lines[&(n - 1)].iter() {
        ans = min(ans, d[id_register.query(company, n - 1)]);
    }
    if ans == INF {
        println!("-1");
    } else {
        println!("{}", ans / 2);
    }
}

const INF: i32 = std::i32::MAX;

#[derive(PartialEq, Debug)]
struct MinInt {
    value: i32,
}

impl Eq for MinInt {}

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

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

fn make_pair(x: i32, y: usize) -> (MinInt, usize) {
    (MinInt { value: x }, y)
}

#[derive(Debug, Clone)]
struct Edge {
    to: usize,
    cost: i32,
}

fn dijkstra(edges: &Vec<Vec<Edge>>, start_idx: usize, num_apexes: usize) -> Vec<i32> {
    let mut d = vec![INF; num_apexes];
    d[start_idx] = 0;
    let mut que = BinaryHeap::new();
    que.push(make_pair(0, start_idx));

    while let Some((u, v)) = que.pop() {
        if d[v] < u.value {
            continue;
        }
        for e in &edges[v] {
            if d[e.to] > d[v] + e.cost {
                d[e.to] = d[v] + e.cost;
                que.push(make_pair(d[e.to], e.to));
            }
        }
    }
    d
}