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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		ArrayList<ArrayList<Route>> graph = new ArrayList<>();
		ArrayList<HashSet<Integer>> used = new ArrayList<>();
		for (int i = 0; i <= n; i++) {
		    graph.add(new ArrayList<>());
		    used.add(new HashSet<>());
		}
		for (int i = 0; i < m; i++) {
		    int a = sc.nextInt();
		    int b = sc.nextInt();
		    int c = sc.nextInt();
		    graph.get(a).add(new Route(b, c));
		    graph.get(b).add(new Route(a, c));
		}
		PriorityQueue<Path> queue = new PriorityQueue<>();
		queue.add(new Path(1, 0, 0));
		int[] costs = new int[n + 1];
		Arrays.fill(costs, Integer.MAX_VALUE);
		while (queue.size() > 0) {
		    Path p = queue.poll();
		    if (costs[p.idx] < p.value) {
		        continue;
		    }
		    if (costs[p.idx] == p.value) {
		        if (used.get(p.idx).contains(p.company)) {
		            continue;
		        } else {
		            used.get(p.idx).add(p.company);
		        }
		    } else {
		        costs[p.idx] = p.value;
		        used.get(p.idx).add(p.company);
		    }
		    for (Route r : graph.get(p.idx)) {
		        int next = p.value;
		        if (r.company != p.company) {
		            next++;
		        }
		        if (costs[r.idx] >= next) {
		            queue.add(new Path(r.idx, next, r.company));
		        }
		    }
		}
		if (costs[n] == Integer.MAX_VALUE) {
		    System.out.println(-1);
		} else {
		    System.out.println(costs[n]);
		}
    }
    
    static class Path implements Comparable<Path> {
        int idx;
        int value;
        int company;
        
        public Path(int idx, int value, int company) {
            this.idx = idx;
            this.value = value;
            this.company = company;
        }
        
        public int compareTo(Path another) {
            return value - another.value;
        }
    }
    
    static class Route {
        int idx;
        int company;
        
        public Route(int idx, int company) {
            this.idx = idx;
            this.company = company;
        }
    }
}