Problem: 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.

Examples

Input

3 3
1 2 1
2 3 1
3 1 2


Output

1


Input

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


Output

2


Input

2 0


Output

-1

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {
	public static final long BIG = 10000000;
	public static final int INF = 1 << 29;
	public static void main(String[] args) {
		IO io = new IO();
		int n = io.nextInt();
		int m = io.nextInt();
		int[] a = new int[m*2];
		int[] b = new int[m*2];
		int[] c = new int[m*2];
		for(int i=0;i<m;i++) {
			int aa = io.nextInt() - 1;
			int bb = io.nextInt() - 1;
			int cc = io.nextInt() - 1;
			a[i] = aa;
			b[i] = bb;
			c[i] = cc;
			a[m+i] = bb;
			b[m+i] = aa;
			c[m+i] = cc;
		}
		int m2 = m * 2;
		//pos,col -> id
		HashMap<Long, Integer> zip = new HashMap<>();
		int[] unzipPos = new int[m2];
		int k = 0;
		for(int i=0;i<m2;i++) {
			long key = b[i] * BIG + c[i];
			Integer x = zip.get(key);
			if (x == null) {
				unzipPos[k] = b[i];
				zip.put(key, k);
				k++;
			}
		}
		Graph g = new Graph(n+k);
		for(int i=0;i<k;i++) {
			g.addEdge(unzipPos[i], n + i, 1);
			g.addEdge(n + i, unzipPos[i], 0);
		}
		for(int i=0;i<m2;i++) {
			int k1 = zip.get(a[i] * BIG + c[i]);
			int k2 = zip.get(b[i] * BIG + c[i]);
			g.addEdge(n + k1, n + k2, 0);
		}
		int[] dist = g.minDistQueue(0);
		System.out.println(dist[n-1] == Graph.INF ? -1 : dist[n-1]);
	}
	
	public static void addEdge(HashMap<Long, ArrayList<Integer>> hm,int pos, int col, int edge) {
		long key = pos * BIG + col;
		ArrayList<Integer> al = hm.get(key);
		if (al == null) {
			al = new ArrayList<>();
		}
		al.add(edge);
		hm.put(key, al);
	}
}
class Graph {
	public static final int INF = 1<<29;
	int n;
	ArrayList<Edge>[] graph;

	@SuppressWarnings("unchecked")
	public Graph(int n) {
		this.n = n;
		this.graph = new ArrayList[n];
		for(int i=0;i<n;i++) {
			graph[i] = new ArrayList<Edge>();
		}
	}
	
	public void addBidirectionalEdge(int from,int to,int cost) {
		addEdge(from,to,cost);
		addEdge(to,from,cost);
	}
	public void addEdge(int from,int to,int cost) {
//		System.out.println(from + "," + to + "," + cost);
		graph[from].add(new Edge(to, cost));
	}

	//O(E) all cost is 0 or 1
	public int[] minDistQueue(int s) {
		int[] d = new int[n];
		Arrays.fill(d, INF);
		ArrayDeque<Integer> q = new ArrayDeque<Integer>();
		q.add(s);
		d[s] = 0;
		while(!q.isEmpty()) {
			int v = q.pollFirst();
			for(Edge e:graph[v]) {
				int u = e.to;
				if (d[v] + e.cost < d[u]) {
					d[u] = d[v] + e.cost;
					if (e.cost == 0) {
						q.addFirst(u);
					}else{
						q.addLast(u);
					}
				}
			}
		}
		return d;
	}

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

class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	
	public IO() { this(System.in);}
	public IO(InputStream source) { super(System.out); this.in = source;}
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	private static boolean isNewLine(int c) { return c == '\n' || c == '\r';}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public boolean hasNextLine() { while(hasNextByte() && isNewLine(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while(isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}
	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}
	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}
	public double nextDouble() { return Double.parseDouble(next());}
	public int[] nextIntArray(int n) { int[] a = new int[n]; for(int i=0;i<n;i++) a[i] = nextInt(); return a;}
	public long[] nextLongArray(int n) { long[] a = new long[n]; for(int i=0;i<n;i++) a[i] = nextLong(); return a;}
	public double[] nextDoubleArray(int n) { double[] a = new double[n]; for(int i=0;i<n;i++) a[i] = nextDouble(); return a;}
	public void nextIntArrays(int[]... a) { for(int i=0;i<a[0].length;i++) for(int j=0;j<a.length;j++) a[j][i] = nextInt();}
	public int[][] nextIntMatrix(int n,int m) { int[][] a = new int[n][]; for(int i=0;i<n;i++) a[i] = nextIntArray(m); return a;}
	public char[][] nextCharMap(int n,int m) { char[][] a = new char[n][]; for(int i=0;i<n;i++) a[i] = nextCharArray(m); return a;}
	public void close() { super.close(); try {in.close();} catch (IOException e) {}}
}