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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.HashMap;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
		int n = sc.nextInt();
		int m = sc.nextInt();
		HashMap<Edge, Integer> map = new HashMap<>();
		ArrayList<Edge>[] adj= new ArrayList[n];
		for(int i=0;i<n;i++) {
			adj[i] = new ArrayList<>();
		}
		for(int i=0;i<m;i++) {
			int p = sc.nextInt()-1;
			int q = sc.nextInt()-1;
			int c = sc.nextInt()-1;
			adj[p].add(new Edge(q,c));
			adj[q].add(new Edge(p,c));
		}
		HashMap<Edge, Integer> dp = new HashMap<Edge, Integer>();
		PriorityQueue<Edge> pq = new PriorityQueue<>(new Comparator<Edge>() {

			@Override
			public int compare(Edge o1, Edge o2) {
				// TODO Auto-generated method stub
				return dp.get(o1)-dp.get(o2);
			}
			
		});
		for(Edge x : adj[0]) {
			dp.put(x,1);
			pq.add(x);
		}
		while(!pq.isEmpty()) {
			Edge curr = pq.poll();
			int steps = dp.get(curr);
			for(Edge next : adj[curr.dest]) {
				if(next.c==curr.c) {
					if(steps<dp.getOrDefault(next,1000000000)) {
						dp.put(next, steps);
						pq.add(next);
					}
				}
				else {
					if(steps+1<dp.getOrDefault(next,1000000000)) {
						dp.put(next,steps+1);
						pq.add(next);
					}
				}
			}
		}
		int min = 1000000000;
		for(int c=0;c<1000000;c++) {
			min = Math.min(min,dp.getOrDefault(new Edge(n-1,c),1000000000));
		}
		if(min>=1000000000) {
			System.out.println(-1);
		}
		else {
			System.out.println(min);
		}
		
	}
	static class Edge{
		int dest;
		int c;
		public Edge(int dest,int c) {
			this.dest = dest;
			this.c = c;
		}
		@Override
		public int hashCode() {
			return dest*1299827+c*1299821;
		}
		@Override
		public boolean equals(Object o) {
			Edge e = (Edge)o;
			return (e.dest==dest && e.c==c);
		}
		
	}
}
class MyScanner
{
   BufferedReader br;
   StringTokenizer st;

   public MyScanner() {
      br = new BufferedReader(new InputStreamReader(System.in));
   }

   String next() {
       while (st == null || !st.hasMoreElements()) {
           try {
               st = new StringTokenizer(br.readLine());
           } catch (IOException e) {
               e.printStackTrace();
           }
       }
       return st.nextToken();
   }

   int nextInt() {
       return Integer.parseInt(next());
   }

   long nextLong() {
       return Long.parseLong(next());
   }

   double nextDouble() {
       return Double.parseDouble(next());
   }

   String nextLine(){
       String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
   }
   
   

}