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.io.*;
import java.util.*;
 
public class Main{
	
	class Node{
		ArrayList<Path> next;
		HashMap<Integer, ArrayList<Path>> hash;
		int idx;
		int cost = Integer.MAX_VALUE;
		int flg = 0;
		public Node(int idx){
			this.idx = idx;
			next = new ArrayList<>();
			hash = new HashMap<>();
		}
		public void add(Path p){
			next.add(p);
			if(!hash.containsKey(p.c)){
				hash.put(p.c, new ArrayList<>());
			}
			hash.get(p.c).add(p);
		}
	}
	
	class Path{
		Node from;
		Node to;
		int c;
		public Path(int c, Node from, Node to){
			this.c = c;
			this.from = from;
			this.to = to;
		}
	}
	int N;
	int M;
	Node[] nodes;
	
	public void solve(){
		N = nextInt();
		M = nextInt();
		nodes = new Node[N];
		for(int i = 0; i < N; i++){
			nodes[i] = new Node(i);
		}
		for(int i = 0; i < M; i++){
			int p = nextInt() - 1;
			int q = nextInt() - 1;
			int c = nextInt() - 1;
			nodes[p].add(new Path(c, nodes[p], nodes[q]));
			nodes[q].add(new Path(c, nodes[q], nodes[p]));
		}
		ArrayDeque<Node> queue = new ArrayDeque<>();
		nodes[0].cost = 0;
		queue.add(nodes[0]);
		while(!queue.isEmpty()){
			Node n = queue.removeFirst();
			if(n.idx == N - 1) break;
			int c = n.cost;
			for(Path p : n.next){
				recur(queue, p, c + 1);
			}
			
		}
		if(nodes[N - 1].cost == Integer.MAX_VALUE){
			out.println(-1);
		}else{
			out.println(nodes[N - 1].cost);
		}
	}
	
	public void recur(ArrayDeque<Node> queue, Path p, int cost){
		Node n = p.to;
		if(n.flg == 1){
			return;
		}
		n.flg = 1;
		if(n.cost >= cost){
			if(n.cost > cost) queue.add(n);
			n.cost = cost;

			for(Path pp : n.hash.get(p.c)){
				recur(queue, pp, cost);
			}
		}
		n.flg = 0;
	}
	
	private static PrintWriter out;
	public static void main(String[] args){
		out = new PrintWriter(System.out);
		new Main().solve();
		out.flush();
	}
	
	
	
	public static int nextInt(){
		int num = 0;
		String str = next();
		boolean minus = false;
		int i = 0;
		if(str.charAt(0) == '-'){
			minus = true;
			i++;
		}
		int len = str.length();
		for(;i < len; i++){
			char c = str.charAt(i);
			if(!('0' <= c && c <= '9')) throw new RuntimeException();
			num = num * 10 + (c - '0');
		}
		return minus ? -num : num;
	}
	
	public static long nextLong(){
		long num = 0;
		String str = next();
		boolean minus = false;
		int i = 0;
		if(str.charAt(0) == '-'){
			minus = true;
			i++;
		}
		int len = str.length();
		for(;i < len; i++){
			char c = str.charAt(i);
			if(!('0' <= c && c <= '9')) throw new RuntimeException();
			num = num * 10l + (c - '0');
		}
		return minus ? -num : num;
	}
	public static String next(){
		int c;
		while(!isAlNum(c = read())){}
		StringBuilder build = new StringBuilder();
		build.append((char)c);
		while(isAlNum(c = read())){
			build.append((char)c);
		}
		return build.toString();
	}
	
	
	private static byte[] inputBuffer = new byte[1024];
	private static int bufferLength = 0;
	private static int bufferIndex = 0;
	private static int read(){
		if(bufferLength < 0) throw new RuntimeException();
		if(bufferIndex >= bufferLength){
			try{
				bufferLength = System.in.read(inputBuffer);
				bufferIndex = 0;
			}catch(IOException e){
				throw new RuntimeException(e);
			}
			if(bufferLength <= 0) return (bufferLength = -1);
		}
		return inputBuffer[bufferIndex++];
	}
	
	private static boolean isAlNum(int c){
		return '!' <= c && c <= '~';
	}
}