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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

public class Heap<T>{
    private List<T> array;
    private Comparison<T> cmp;
    private int size;
    
    
    public Heap(int capacity, Comparison<T> cmp){
        this.array = new List<T>(capacity);
        this.size = 0;
        this.cmp = cmp;
    }
    public void Clear(){
        array.Clear();
        this.size = 0;
    }
    
    public bool Empty(){ return size==0; }
    protected int Parent(int i){ return (i-1)/2; }
    protected int Left(int i){ return 2*i+1; }
    protected int Right(int i){ return 2*i+2; }
    
    public T Front(){
        if(size!=0){
            return array[0];
        } else {
            return default(T);
        }
    }
    
    public void Heapify(int i){
        int l = Left(i);
        int r = Right(i);
        int largest = i;
        if(l<size && cmp(array[l], array[i]) > 0) largest = l;
        if(r<size && cmp(array[r], array[largest])>0) largest = r;
        if(largest != i){
            T tmp = array[i];
            array[i] = array[largest];
            array[largest] = tmp;
            Heapify(largest);
        } 
    }
    public T Pop(){
        if(size < 1) return default(T);
        T max = array[0];
        array[0] = array[size-1];
        size--;
        Heapify(0);
        return max;
    }
    public void Insert(T key){
        size = size + 1;
        if( array.Count < size){
            array.Add(key);
        }  else {
            array[size-1] = key;
        }
        int i = size-1;
        while(i>0 && cmp(array[Parent(i)],array[i])<0){
            T tmp = array[i];
            array[i] = array[Parent(i)];
            array[Parent(i)] = tmp;
            i = Parent(i);
        }
    }
}
 
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 MAX_N = 100008;
	int N,M;
	List<Z2>[] edges;
    
	
	public A(){
		edges = new List<Z2>[MAX_N];
		for(int i=0;i<MAX_N;i++) edges[i] = new 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<M;i++){
			int[] inp = Rs().Select( x => int.Parse(x)-1 ).ToArray();
			edges[ inp[0] ].Add( new Z2(inp[1],inp[2]) );
			edges[ inp[1] ].Add( new Z2(inp[0],inp[2]) );
        }
        edges[N-1].Add(new Z2(N-1,-1));
        Dictionary<Z2, int> dis = new Dictionary<Z2,int>();
		Heap<Z3> que = new Heap<Z3>(2*N+M, (x,y)=>y.x-x.x);
		
		que.Insert(new Z3(0, new Z2(0,-1)) ); 
		dis.Add( new Z2(0, -1), 0);
        Z2 end = new Z2(N-1,-1);
        
		while(!que.Empty()){
			Z3 n = que.Pop();
			Z2 nz = n.z;
			if(dis.ContainsKey(end)){ 
				Console.WriteLine(dis[end]-1);
				return;
			}
			if(n.x > dis[nz]) continue;
            foreach(Z2 e in edges[nz.x]){
                    if(!dis.ContainsKey(e) || dis[nz] + (e.y==nz.y?0:1) < dis[e]){
                        int nv = dis[nz] + (e.y==nz.y?0:1);
						dis.Add(e, nv);
						que.Insert(new Z3(nv, e));
                    }
            }
        }
		Console.WriteLine("-1");
	}
}
 
public class Program {
	static void Main(string[] args){
		A a = new A();
		a.run();
	}
}