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.Globalization;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading;
using System.Numerics;

// (づ°ω°)づﾐe★゜・。。・゜゜・。。・゜☆゜・。。・゜゜・。。・゜
public class Solver
{
    public class Heap<T>
    {
        private readonly List<T> data;
        private readonly Comparison<T> compare;

        public Heap(Comparison<T> compare)
        {
            this.compare = compare;
            data = new List<T> { default(T) };
        }

        public int Count
        {
            get { return data.Count - 1; }
        }

        public T Peek()
        {
            return data[1];
        }

        public void Push(T item)
        {
            data.Add(item);
            var curPlace = Count;
            while (curPlace > 1 && compare(item, data[curPlace / 2]) < 0)
            {
                data[curPlace] = data[curPlace / 2];
                data[curPlace / 2] = item;
                curPlace /= 2;
            }
        }

        public T Pop()
        {
            var ret = data[1];
            data[1] = data[Count];
            data.RemoveAt(Count);
            var curPlace = 1;
            while (true)
            {
                var max = curPlace;
                if (Count >= curPlace * 2 && compare(data[max], data[2 * curPlace]) > 0)
                    max = 2 * curPlace;
                if (Count >= curPlace * 2 + 1 && compare(data[max], data[2 * curPlace + 1]) > 0)
                    max = 2 * curPlace + 1;
                if (max == curPlace)
                    break;
                var item = data[max];
                data[max] = data[curPlace];
                data[curPlace] = item;
                curPlace = max;
            }

            return ret;
        }
    }

    class Edge
    {
        public int to, weight;
        public Edge(int to, int weight)
        {
            this.to = to;
            this.weight = weight;
        }
    }

    public void Solve()
    {
        int n = ReadInt();
        
        var g = new List<List<Edge>>();
        var d = Init<Dictionary<int, int>>(n);
        for (int m = ReadInt(); m > 0; m--)
        {
            int u = ReadInt() - 1;
            int v = ReadInt() - 1;
            int c = ReadInt();

            if (!d[u].ContainsKey(c))
            {
                d[u][c] = g.Count;
                g.Add(new List<Edge>());
            }
            if (!d[v].ContainsKey(c))
            {
                d[v][c] = g.Count;
                g.Add(new List<Edge>());
            }

            int xu = d[u][c];
            int xv = d[v][c];
            g[xu].Add(new Edge(xv, 0));
            g[xv].Add(new Edge(xu, 0));
        }

        var q = new Heap<Tuple<int, int>>((t1, t2) => t1.Item1.CompareTo(t2.Item1));
        q.Push(Tuple.Create(0, g.Count));
        var dist = Enumerable.Repeat(int.MaxValue, g.Count + n).ToArray();
        dist[g.Count] = 0;
        for (int i = 0; i < n; i++)
        {
            var list = d[i].Values;
            int x = g.Count;
            g.Add(new List<Edge>());
            foreach (int e in list)
            {
                g[e].Add(new Edge(x, 0));
                g[x].Add(new Edge(e, 1));
            }
        }

        while (q.Count > 0)
        {
            var t = q.Pop();
            if (dist[t.Item2] < t.Item1)
                continue;
            int x = t.Item2;
            foreach (var e in g[x])
            {
                int nd = dist[x] + e.weight;
                if (dist[e.to] > nd)
                {
                    dist[e.to] = nd;
                    q.Push(Tuple.Create(nd, e.to));
                }
            }
        }

        int ans = dist[g.Count - 1];
        Write(ans < int.MaxValue ? ans : -1);
    }

    #region Main

    protected static TextReader reader;
    protected static TextWriter writer;
    static void Main()
    {
#if DEBUG
        reader = new StreamReader("..\\..\\input.txt");
        //reader = new StreamReader(Console.OpenStandardInput());
        writer = Console.Out;
        //writer = new StreamWriter("..\\..\\output.txt");
#else
        reader = new StreamReader(Console.OpenStandardInput());
        writer = new StreamWriter(Console.OpenStandardOutput());
        //reader = new StreamReader("input.txt");
        //writer = new StreamWriter("output.txt");
#endif
        try
        {
            new Solver().Solve();
            //var thread = new Thread(new Solver().Solve, 1024 * 1024 * 128);
            //thread.Start();
            //thread.Join();
        }
        catch (Exception ex)
        {
#if DEBUG
            Console.WriteLine(ex);
#else
            throw;
#endif
        }
        reader.Close();
        writer.Close();
    }

    #endregion

    #region Read / Write
    private static Queue<string> currentLineTokens = new Queue<string>();
    private static string[] ReadAndSplitLine() { return reader.ReadLine().Split(new[] { ' ', '\t', }, StringSplitOptions.RemoveEmptyEntries); }
    public static string ReadToken() { while (currentLineTokens.Count == 0)currentLineTokens = new Queue<string>(ReadAndSplitLine()); return currentLineTokens.Dequeue(); }
    public static int ReadInt() { return int.Parse(ReadToken()); }
    public static long ReadLong() { return long.Parse(ReadToken()); }
    public static double ReadDouble() { return double.Parse(ReadToken(), CultureInfo.InvariantCulture); }
    public static int[] ReadIntArray() { return ReadAndSplitLine().Select(int.Parse).ToArray(); }
    public static long[] ReadLongArray() { return ReadAndSplitLine().Select(long.Parse).ToArray(); }
    public static double[] ReadDoubleArray() { return ReadAndSplitLine().Select(s => double.Parse(s, CultureInfo.InvariantCulture)).ToArray(); }
    public static int[][] ReadIntMatrix(int numberOfRows) { int[][] matrix = new int[numberOfRows][]; for (int i = 0; i < numberOfRows; i++)matrix[i] = ReadIntArray(); return matrix; }
    public static int[][] ReadAndTransposeIntMatrix(int numberOfRows)
    {
        int[][] matrix = ReadIntMatrix(numberOfRows); int[][] ret = new int[matrix[0].Length][];
        for (int i = 0; i < ret.Length; i++) { ret[i] = new int[numberOfRows]; for (int j = 0; j < numberOfRows; j++)ret[i][j] = matrix[j][i]; } return ret;
    }
    public static string[] ReadLines(int quantity) { string[] lines = new string[quantity]; for (int i = 0; i < quantity; i++)lines[i] = reader.ReadLine().Trim(); return lines; }
    public static void WriteArray<T>(IEnumerable<T> array) { writer.WriteLine(string.Join(" ", array)); }
    public static void Write(params object[] array) { WriteArray(array); }
    public static void WriteLines<T>(IEnumerable<T> array) { foreach (var a in array)writer.WriteLine(a); }
    private class SDictionary<TKey, TValue> : Dictionary<TKey, TValue>
    {
        public new TValue this[TKey key]
        {
            get { return ContainsKey(key) ? base[key] : default(TValue); }
            set { base[key] = value; }
        }
    }
    private static T[] Init<T>(int size) where T : new() { var ret = new T[size]; for (int i = 0; i < size; i++)ret[i] = new T(); return ret; }
    #endregion
}