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.util.*;
import java.io.*;
import java.math.BigInteger;
import java.text.*;
public class Main implements Runnable {
    static int mod = 1000_000_007;
    static long lim = (long)1e9 + 6;
    static long mod1 = 998244353;
    static boolean fileIO = false;
    static FastScanner f;
    static int inf = 2000_000_000;
    static PrintWriter pw = new PrintWriter(System.out);
    static Scanner S = new Scanner(System.in);
    static long x0; static long y0;
    static long iinf = Long.MAX_VALUE;
    static double eps = (double)1e-6;
    public static HashMap<Integer , ArrayList<Integer>> g;
    static int color[] , dp[];
    static void dfs(int src , int par) {
        dp[src] = 0;
        if (color[src] == 1) ++dp[src];

        for (Integer node : g.get(src)) {
            if (node != par) {
                dfs(node , src);
                dp[src] += dp[node];
            }
        }
    }
    public static void solve() {
        int n = f.ni();
        g = new HashMap<>();
        color = new int[n + 1];
        dp = new int[n + 1];
        for (int i = 1; i <= n; ++i) g.put(i , new ArrayList<Integer>());
        for (int i = 0; i + 1 < n; ++i) {
            int u = f.ni(); int v = f.ni();
            g.get(u).add(v);
            g.get(v).add(u);
            if (f.ni() == 2) {
                color[u] = 1;
                color[v] = 1;
            }
        }

        dfs(1 , 0);
        HashSet<Integer> ans = new HashSet<>();
        int cnt = 0;
        for (int i = 1; i <= n; ++i) {
            if (dp[i] == 1) {
                ans.add(i);
                ++cnt;
            }
        }
        pn(cnt);
        for (Integer node : ans) p(node + " ");
    }      
    public static void main(String[] args)throws IOException , InterruptedException {
        Thread thread = new Thread(null , new Main() , "F*uckit" , 1 << 28);
        thread.start();
        thread.join();  
    }
        
/******************************END OF MAIN PROGRAM*******************************************/
    public void run() {
        f = new FastScanner(System.in);
        //pre();
        int t = 1;
        int tt = 1;
        //fw = new FileWriter("!out.txt");
        while(t --> 0) {
            //fw.write("Case #" + (tt++) + ": ");
            //fw.write("\n");
            solve();
        }
        pw.flush(); 
        pw.close();
        //fw.close();  
    }
    public static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastScanner.SpaceCharFilter filter;
 
        public FastScanner(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 ni() {
            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 nl() {
            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 next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void pn(Object o){pw.println(o);}
    public static void pi(Object o){pw.print(o);pw.flush();}
    public static void p(Object o){pw.print(o);}
    public static void pni(Object o){pw.println(o);pw.flush();}
    static int gcd(int a,int b){if(b==0)return a;else{return gcd(b,a%b);}}
    static long gcd(long a,long b){if(b==0l)return a;else{return gcd(b,a%b);}}
    static long lcm(long a,long b){return (a*b/gcd(a,b));}
    static long exgcd(long a,long b){if(b==0){x0=1;y0=0;return a;}long temp=exgcd(b,a%b);long t=x0;x0=y0;y0=t-a/b*y0;return temp;}
    static long pow(long a,long b){long res=1;while(b>0){if((b&1)==1)res=res*a;b>>=1;a=a*a;}return res;}
    static long mpow(long a,long b, long m){long res=1;while(b>0){if((b&1)==1)res=((res%m)*(a%m))%m;b>>=1;a=((a%m)*(a%m))%m;}return res;}
    static long mul(long a , long b){return ((a%mod)*(b%mod)%mod);}
    static long adp(long a , long b){return ((a%mod)+(b%mod)%mod);}
    static boolean isPrime(long n){if(n<=1)return false;if(n<=3)return true;if(n%2==0||n%3==0)return false;for(long i=5;i*i<=n;i=i+6)if(n%i==0||n%(i+2)==0)return false;return true;}
    static boolean isPrime(int n){if(n<=1)return false;if(n<=3)return true;if(n%2==0||n%3==0)return false;for(int i=5;i*i<=n;i=i+6)if(n%i==0||n%(i+2)==0)return false;return true;}
    static HashSet<Long> factors(long n){HashSet<Long> hs=new HashSet<Long>();for(long i=1;i<=(long)Math.sqrt(n);i++){if(n%i==0){hs.add(i);hs.add(n/i);}}return hs;}
    static HashSet<Integer> factors(int n){HashSet<Integer> hs=new HashSet<Integer>();for(int i=1;i<=(int)Math.sqrt(n);i++){if(n%i==0){hs.add(i);hs.add(n/i);}}return hs;}
    static HashSet<Long> pf(long n){HashSet<Long> ff=factors(n);HashSet<Long> ans=new HashSet<Long>();for(Long i:ff)if(isPrime(i))ans.add(i);return ans;}
    static HashSet<Integer> pf(int n){HashSet<Integer> ff=factors(n);HashSet<Integer> ans=new HashSet<Integer>();for(Integer i:ff)if(isPrime(i))ans.add(i);return ans;}
    static int[] inpint(int n){int arr[]=new int[n+1];for(int i=1;i<=n;++i){arr[i]=f.ni();}return arr;}
    static long[] inplong(int n){long arr[] = new long[n+1];for(int i=1;i<=n;++i){arr[i]=f.nl();}return arr;}
    static boolean ise(int x){return ((x&1)==0);}static boolean ise(long x){return ((x&1)==0);}
    static int gnv(char c){return Character.getNumericValue(c);} // Credits - KharYusuf for Multiset Class
    static class MultiSet<T extends Comparable<T>>{
        public int size=0;
        public TreeMap<T,Integer> tr;
        public MultiSet(){tr=new TreeMap<>();}
        public void add(T u){tr.put(u,tr.getOrDefault(u,0)+1);++size;}
        public boolean contains(T u){return tr.containsKey(u);}
        public void clear(){tr.clear();}
        public void remove(T x){tr.remove(x);}
        public T last(){return tr.lastKey();}
    }
    static int log(long x){return x==1?0:(1+log(x/2));} static int log(int x){return x==1?0:(1+log(x/2));}
    static void sort(int[] a){ArrayList<Integer> l=new ArrayList<>();for(int i:a)l.add(i);Collections.sort(l);for(int i=0;i<a.length;++i)a[i]=l.get(i);}
    static void sort(long[] a){ArrayList<Long> l=new ArrayList<>();for(long i:a)l.add(i);Collections.sort(l);for(int i=0;i<a.length;++i)a[i]=l.get(i);}
    static void sort(ArrayList<Integer> a){Collections.sort(a);}
}