Problem: There are n railway stations in Berland. They are connected to each other by n-1 railway sections. The railway network is connected, i.e. can be represented as an undirected tree.

You have a map of that network, so for each railway section you know which stations it connects.

Each of the n-1 sections has some integer value of the scenery beauty. However, these values are not marked on the map and you don't know them. All these values are from 1 to 10^6 inclusive.

You asked m passengers some questions: the j-th one told you three values:

  * his departure station a_j; 
  * his arrival station b_j; 
  * minimum scenery beauty along the path from a_j to b_j (the train is moving along the shortest path from a_j to b_j). 



You are planning to update the map and set some value f_i on each railway section — the scenery beauty. The passengers' answers should be consistent with these values.

Print any valid set of values f_1, f_2, ..., f_{n-1}, which the passengers' answer is consistent with or report that it doesn't exist.

Input

The first line contains a single integer n (2 ≤ n ≤ 5000) — the number of railway stations in Berland.

The next n-1 lines contain descriptions of the railway sections: the i-th section description is two integers x_i and y_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i), where x_i and y_i are the indices of the stations which are connected by the i-th railway section. All the railway sections are bidirected. Each station can be reached from any other station by the railway.

The next line contains a single integer m (1 ≤ m ≤ 5000) — the number of passengers which were asked questions. Then m lines follow, the j-th line contains three integers a_j, b_j and g_j (1 ≤ a_j, b_j ≤ n; a_j ≠ b_j; 1 ≤ g_j ≤ 10^6) — the departure station, the arrival station and the minimum scenery beauty along his path.

Output

If there is no answer then print a single integer -1.

Otherwise, print n-1 integers f_1, f_2, ..., f_{n-1} (1 ≤ f_i ≤ 10^6), where f_i is some valid scenery beauty along the i-th railway section.

If there are multiple answers, you can print any of them.

Examples

Input


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


Output


5 3 5


Input


6
1 2
1 6
3 1
1 5
4 1
4
6 1 3
3 4 1
6 5 2
1 2 5


Output


5 3 1 2 1 


Input


6
1 2
1 6
3 1
1 5
4 1
4
6 1 1
3 4 3
6 5 3
1 2 4


Output


-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastReader scan = new FastReader();
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("outofplace.out")));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        Task solver = new Task();
        //int t = scan.nextInt();
        int t = 1;
        for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
        out.close();
    }
    static class Task {
        public void solve(int testNumber, FastReader sc, PrintWriter pw) {
            int n = sc.nextInt();
            ArrayList<Integer>[] adjl = new ArrayList[n+1];
            for(int i =0 ;i<=n;i++){
                adjl[i]=new ArrayList<>();
            }
            int[] ind = new int[25020000];
            for(int i=1;i<n;i++){
                int a = sc.nextInt();int b = sc.nextInt();adjl[a].add(b);adjl[b].add(a);
                ind[a*5001+b]=i-1;
            }
            lcaq l = new lcaq(n+1,1,adjl);
            int[] bfs = new int[n+1];
            Queue<Integer > q = new LinkedList<>();
            q.add(1);
            Arrays.fill(bfs,Integer.MAX_VALUE);
            bfs[1]=0;
            while(!q.isEmpty()){
                int x = q.poll();
                for(int a : adjl[x]){
                    if(bfs[a]== Integer.MAX_VALUE){
                        bfs[a]=bfs[x]+1;
                        q.add(a);
                    }
                }
            }
            int s = sc.nextInt();
            int[]qs[]=new int[s][3];
            int[] mins = new int[n-1];
            Arrays.fill(mins,1);
            for(int i=0;i<s;i++){
                int a = sc.nextInt();
                int b =sc.nextInt();
                int c = sc.nextInt();
                int x = l.lca(a,b);
                qs[i][0]=a;
                qs[i][1]=b;
                qs[i][2]=c;
                q.add(a);
                while (!q.isEmpty()){
                    int t = q.poll();
                    if(t==x){
                        break;
                    }
                    for(int asd : adjl[t]){
                        if(bfs[asd]+1==bfs[t]){
                            int in = Math.max(ind[t*5001+asd],ind[asd*5001+t]);
                            mins[in]=Math.max(mins[in],c);
                            q.add(asd);
                            break;
                        }
                    }
                }
                q.add(b);
                while (!q.isEmpty()){
                    int t = q.poll();
                    if(t==x){
                        break;
                    }
                    for(int asd : adjl[t]){
                        if(bfs[asd]+1==bfs[t]){
                            int in = Math.max(ind[t*5001+asd],ind[asd*5001+t]);
                            mins[in]=Math.max(mins[in],c);
                            q.add(asd);
                            break;
                        }
                    }
                }
            }
            for(int[] x : qs){
                q.add(x[0]);
                int ct = 0;
                int z = l.lca(x[0],x[1]);
                while (!q.isEmpty()){
                    if(ct>0)break;
                    int t = q.poll();
                    if(t==z){
                        break;
                    }
                    for(int asd : adjl[t]){
                        if(bfs[asd]+1==bfs[t]){
                            int in = Math.max(ind[t*5001+asd],ind[asd*5001+t]);
                            if(mins[in]==x[2]){
                                ct++;
                            }
                            q.add(asd);
                            break;
                        }
                    }
                }
                q=new LinkedList<>();
                q.add(x[1]);
                while (!q.isEmpty()){
                    if(ct>0)break;
                    int t = q.poll();
                    if(t==z){
                        break;
                    }
                    for(int asd : adjl[t]){
                        if(bfs[asd]+1==bfs[t]){
                            int in = Math.max(ind[t*5001+asd],ind[asd*5001+t]);
                            if(mins[in]==x[2]){
                                ct++;
                            }
                            q.add(asd);
                            break;
                        }
                    }
                }
                q=new LinkedList<>();
                if(ct==0){
                    pw.println(-1);
                    return;
                }
            }
            for(int i=0;i<n-1;i++){
                pw.print(mins[i]+" ");
            }
        }
    }
    static class lcaq{
        int n, l;
        int timer;
        int[] in;
        int[] out;
        ArrayList<Integer>[] adjl;
        ArrayList<ArrayList<Integer>> up;
        lcaq(int n,int root,ArrayList<Integer>[] adjl){
            this.n=n;
            in= new int[n];
            out = new int[n];
            this.adjl=adjl;
            timer = 0;
            l=(int)Math.ceil(Math.log(n)/Math.log(2));
            up=new ArrayList<ArrayList<Integer>>();
            for(int i=0;i<=n;i++){
                up.add(new ArrayList<Integer>());
            }
            dfs(root,root);
        }
        void dfs(int v, int p){
            in[v]=timer+=1;
            up.get(v).add(p);
            for(int i=1;i<=l;i++){
                up.get(v).add(up.get(up.get(v).get(i-1)).get(i-1));
            }
            for(int x : adjl[v]){
                if(x!=p)
                    dfs(x,v);
            }
            out[v]=timer+=1;
        }
        boolean is_ancestor(int u, int v)
        {
            return in[u] <= in[v] && out[u] >= out[v];
        }

        int lca(int u, int v)
        {
            if (is_ancestor(u, v))
                return u;
            if (is_ancestor(v, u))
                return v;
            for (int i = l; i >= 0; --i) {
                if (!is_ancestor(up.get(u).get(i), v))
                    u = up.get(u).get(i);
            }
            return up.get(u).get(0);
        }
    }
    static class tup implements Comparable<tup>,Comparator<tup>{
        int a, b,c,d;
        tup(){};
        tup(int a, int b,int c, int d){
            this.a=a;
            this.b=b;
            this.c=c;
            this.d=d;
        }

        @Override
        public int compareTo(tup o) {
            return a!=o.a?Integer.compare(o.a,a):Integer.compare(o.b,b);
        }

        @Override
        public int compare(tup o1, tup o2) {
            return o2.b!=o1.b?Integer.compare(o2.b,o1.b):Integer.compare(o2.a,o1.a);
        }
    }
    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}