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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Collection;
import java.util.Map;
import java.util.Map.Entry;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Queue;
import java.util.LinkedList;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sparsh Sanchorawala
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ESnukesSubwayTrip solver = new ESnukesSubwayTrip();
        solver.solve(1, in, out);
        out.close();
    }

    static class ESnukesSubwayTrip {
        public void solve(int testNumber, InputReader s, PrintWriter w) {
            int n = s.nextInt(), m = s.nextInt();
            HashMap<Integer, ArrayList<Integer>>[] hm = new HashMap[n];
            for (int i = 0; i < n; i++) {
                hm[i] = new HashMap<>();
            }
            for (int i = 0; i < m; i++) {
                int u = s.nextInt() - 1, v = s.nextInt() - 1, c = s.nextInt() - 1;
                hm[u].putIfAbsent(c, new ArrayList<>());
                hm[u].get(c).add(v);
                hm[v].putIfAbsent(c, new ArrayList<>());
                hm[v].get(c).add(u);
            }

            int res = (int) 1e6;

            HashMap<Integer, Integer>[] level = new HashMap[n];
            for (int i = 0; i < n; i++) {
                level[i] = new HashMap<>();
            }
            int[] vc = new int[n];
            level[0].put(-1, 0);
            Queue<Pair> q0 = new LinkedList<>();
            q0.add(new Pair(0, -1));
            while (!q0.isEmpty()) {
                Queue<Pair> q1 = new LinkedList<>();
                while (!q0.isEmpty()) {
                    Pair p = q0.poll();
                    int x = p.i;
                    int xw = p.w;
                    int xd = level[x].get(xw);
                    if (xd == -1)
                        continue;
                    if (x == n - 1 && xd < res)
                        res = xd;
                    level[x].put(xw, -1);
                    vc[x]++;
                    if (vc[x] == 1) {
                        for (Map.Entry<Integer, ArrayList<Integer>> e : hm[x].entrySet()) {
                            int yw = e.getKey();
                            for (int y : e.getValue()) {
                                int yd = level[y].getOrDefault(yw, (int) 1e6);
                                if (yd > xd + 1) {
                                    q1.add(new Pair(y, yw));
                                    level[y].put(yw, xd + 1);
                                }
                            }
                        }
                    }
                    if (hm[x].get(xw) != null) {
                        ArrayList<Integer> hs = hm[x].get(xw);
                        for (int y : hs) {
                            int yd = level[y].getOrDefault(xw, (int) 1e6);
                            if (yd > xd) {
                                q0.add(new Pair(y, xw));
                                level[y].put(xw, xd);
                            }
                        }
                    }
                }
                q0 = q1;
            }

            if (res != (int) 1e6)
                w.println(res);
            else
                w.println(-1);
        }

        class Pair {
            int i;
            int w;

            Pair(int i, int w) {
                this.i = i;
                this.w = w;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}