The city Valera lives in is going to hold elections to the city Parliament.

The city has n districts and n - 1 bidirectional roads. We know that from any district there is a path along the roads to any other district. Let's enumerate all districts in some way by integers from 1 to n, inclusive. Furthermore, for each road the residents decided if it is the problem road or not. A problem road is a road that needs to be repaired.

There are n candidates running the elections. Let's enumerate all candidates in some way by integers from 1 to n, inclusive. If the candidate number i will be elected in the city Parliament, he will perform exactly one promise — to repair all problem roads on the way from the i-th district to the district 1, where the city Parliament is located.

Help Valera and determine the subset of candidates such that if all candidates from the subset will be elected to the city Parliament, all problem roads in the city will be repaired. If there are several such subsets, you should choose the subset consisting of the minimum number of candidates.

Input

The first line contains a single integer n (2 ≤ n ≤ 105) — the number of districts in the city.

Then n - 1 lines follow. Each line contains the description of a city road as three positive integers xi, yi, ti (1 ≤ xi, yi ≤ n, 1 ≤ ti ≤ 2) — the districts connected by the i-th bidirectional road and the road type. If ti equals to one, then the i-th road isn't the problem road; if ti equals to two, then the i-th road is the problem road.

It's guaranteed that the graph structure of the city is a tree.

Output

In the first line print a single non-negative number k — the minimum size of the required subset of candidates. Then on the second line print k space-separated integers a1, a2, ... ak — the numbers of the candidates that form the required subset. If there are multiple solutions, you are allowed to print any of them.

Examples

Input

5
1 2 2
2 3 2
3 4 2
4 5 2


Output

1
5 


Input

5
1 2 1
2 3 2
2 4 1
4 5 1


Output

1
3 


Input

5
1 2 2
1 3 2
1 4 2
1 5 2


Output

4
5 4 3 2 
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.*;
import java.io.IOException;
import java.io.InputStream;
import java.io.UnsupportedEncodingException;
import java.math.BigInteger;

/**
 * Ashesh Vidyut (Drift King) *
 */
public class C {
    public static HashSet<Integer> ans = new HashSet<Integer>();
    public static void main(String[] args) {
        try {
            InputReader in = new InputReader(System.in);
            BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
            int n = in.readInt();
            List<Road> graph[] = new Vector[n];
            for (int i = 0; i < n; i++) {
                graph[i] = new Vector<Road>();
            }
            for (int i = 1; i < n; i++) {
                int fc = in.readInt() - 1;
                int sc = in.readInt() - 1;
                int problem = in.readInt();
                graph[fc].add(new Road(sc, problem != 1));
                graph[sc].add(new Road(fc, problem != 1));
            }
            dfs(n, graph);
            out.write(Integer.toString(ans.size()));
            out.newLine();
            for(int c : ans){
                out.write(Integer.toString(c + 1)+" ");
            }
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
    public static void dfs(int n, List<Road> g[]){
        boolean vis[] = new boolean[n];
        dfs_visit(0, n, g, vis, 0);
    }
    public static void dfs_visit(int i, int n, List<Road> g[], boolean v[], int lastaddedparent){
        v[i] = true;
        for(Road ch : g[i]){
            if(!v[ch.tocity]){
                if(ch.damaged){
                    if(ans.contains(lastaddedparent)){
                        ans.remove(lastaddedparent);
                    }
                    ans.add(ch.tocity);
                    dfs_visit(ch.tocity, n, g, v, ch.tocity);
                }
                else{
                    dfs_visit(ch.tocity, n, g, v, lastaddedparent);
                }
            }
        }
    }
}
class Road{
    int tocity;
    boolean damaged;
    public Road(int tocity, boolean d){
        this.tocity = tocity;
        this.damaged = d;
    }
}
class InputReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    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 peek() {
        if (numChars == -1)
            return -1;
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                return -1;
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar];
    }

    public int readInt() {
        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 long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long 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 String readString() {
        int length = readInt();
        if (length < 0)
            return null;
        byte[] bytes = new byte[length];
        for (int i = 0; i < length; i++)
            bytes[i] = (byte) read();
        try {
            return new String(bytes, "UTF-8");
        } catch (UnsupportedEncodingException e) {
            return new String(bytes);
        }
    }

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

    private String readLine0() {
        StringBuffer buf = new StringBuffer();
        int c = read();
        while (c != '\n' && c != -1) {
            if (c != '\r')
                buf.appendCodePoint(c);
            c = read();
        }
        return buf.toString();
    }

    public String readLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines)
            return readLine();
        else
            return readLine0();
    }

    public BigInteger readBigInteger() {
        try {
            return new BigInteger(readString());
        } catch (NumberFormatException e) {
            throw new InputMismatchException();
        }
    }

    public char readCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    public double readDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, readInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }

    public boolean isExhausted() {
        int value;
        while (isSpaceChar(value = peek()) && value != -1)
            read();
        return value == -1;
    }

    public String next() {
        return readString();
    }

    public boolean readBoolean() {
        return readInt() == 1;
    }
}

