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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
 
struct Z2 {
	public int x, y;
	public Z2(int x, int y){
		this.x = x; this.y = y;
	}
}
 
struct Z3 {
	public int x;
	public Z2 z;
	public Z3(int x, Z2 z){
		this.x = x; this.z = z;
	}
}
 
public class A {
	int N,M;
	Dictionary<Z2,List<Z2>> edges;
    
	
	public A(){
		edges = new Dictionary<Z2,List<Z2>>();
	}
	
	string[] Rs(){
		return Console.ReadLine().Split(' ');
	}
	public void run(){
		string[] str = Rs();
		N = int.Parse(str[0]); M = int.Parse(str[1]);
		for(int i=0;i<N;i++){
            edges.Add(new Z2(i,-1), new List<Z2>());
        }
        
        Action<Z2,Z2> f = (p1,p2) => {
            Z2 ne = new Z2(p1.x, -1);
			if(edges.ContainsKey(p1)){
                edges[p1].Add(p2);
            } else {
                var l = new List<Z2>(); l.Add(p2); l.Add(ne); 
                edges.Add( p1,  l);
            }
            edges[ne].Add(p2);
        };
        
        for(int i=0;i<M;i++){
			int[] inp = Rs().Select( x => int.Parse(x)-1 ).ToArray();
            Z2 e0 = new Z2(inp[0], inp[2]), e1 = new Z2(inp[1], inp[2]);
            f(e0,e1);
            f(e1,e0);
        }
        
        Dictionary<Z2, int> dis = new Dictionary<Z2,int>(2*(M+N));
		LinkedList<Z2> que = new LinkedList<Z2>();
		LinkedList<int> que2 = new LinkedList<int>();
		
		que.AddLast(new Z2(0,-1) );
		que2.AddLast(0); 
		dis.Add( new Z2(0, -1), 0);
        Z2 end = new Z2(N-1,-1);
        
		while(que.Count!=0){
			Z2 nz = que.First(); que.RemoveFirst();
			int d = que2.First(); que2.RemoveFirst();
			if(nz.x==N-1 && nz.y==-1){ 
				Console.WriteLine(dis[end]);
				return;
			}
			if(d > dis[nz]) continue;
            foreach(Z2 e in edges[nz]){
					if(nz.y==-1){
						int nv = dis[nz] + 1;
	                    if(!dis.ContainsKey(e)){
							dis.Add(e, nv);
							que.AddLast(e);
							que2.AddLast(nv);
	                    } else if(nv < dis[e]){
							dis[e] = nv;
							que.AddLast(e);
							que2.AddLast(nv);
						}
					} else {
						if(!dis.ContainsKey(e)){
							dis.Add(e, dis[nz]);
							que.AddFirst(e);
							que2.AddFirst(dis[nz]);
	                    } else if(dis[nz] < dis[e]){
							dis[e] = dis[nz];
							que.AddFirst( e);
							que2.AddFirst(dis[nz]);
						}
					}
            }
        }
		Console.WriteLine("-1");
	}
}
 
public class Program {
	static void Main(string[] args){
		A a = new A();
		a.run();
	}
}