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 com.sun.javafx.geom.Edge;

import java.io.*;
import java.util.*;

public class a {

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        int t = 1;
        for(int tt = 1; tt <= t; tt++) solver.solve(tt, scan, out);
        out.close();
    }

    static class Task {
        static int n, m;
        static ArrayList<Integer>[] adj;
        static int[][] parent;
        static int[][] minEdgeBeauty;
        static Item[] query;
        static ArrayDeque<Integer> edges = new ArrayDeque<>();

        public void solve(int testNumber, FastReader scan, PrintWriter out) {
            n = scan.nextInt();
            adj = new ArrayList[n];
            parent = new int[n][n];
            minEdgeBeauty = new int[n][n];

            for(int i = 0; i < n; i++) adj[i] = new ArrayList<>();
            for(int i = 0; i < n-1; i++) {
                int a = scan.nextInt()-1, b = scan.nextInt()-1;
                edges.addLast(a);
                edges.addLast(b);
                adj[a].add(b);
                adj[b].add(a);
            }
            m = scan.nextInt();
            query = new Item[m];
            for(int i = 0; i < n; i++) findParents(i, -1, i);
            for(int i = 0; i < m; i++) query[i] = new Item(scan.nextInt()-1, scan.nextInt()-1, scan.nextInt());
            Arrays.sort(query);
            for(Item Q : query) fillPath(Q.a, Q.b, Q.c);
            for(int i = 0; i < n; i++) {
                for(int j = i+1; j < n; j++) {
                    if(minEdgeBeauty[i][j] == 0) {
                        minEdgeBeauty[i][j] = minEdgeBeauty[j][i] = 1000000;
                    }
                }
            }
            for(Item Q : query) {
                if(!verify(Q.a, Q.b, Q.c)) {
                    out.println(-1);
                    return;
                }
            }
            while(!edges.isEmpty()) {
                int a = edges.pollFirst(), b = edges.pollFirst();
                out.print(minEdgeBeauty[a][b] + " ");
            }
        }

        static void findParents(int start, int prev, int at) {
            parent[start][at] = prev;
            for(int i : adj[at]) {
                if(i != prev) findParents(start, at, i);
            }
        }

        static void fillPath(int start, int at, int currVal) {
            while(at != start) {
                minEdgeBeauty[at][parent[start][at]] = minEdgeBeauty[parent[start][at]][at] = currVal;
                at = parent[start][at];
            }
        }

        static boolean verify(int start, int at, int minVal) {
            int ans = Integer.MAX_VALUE;
            while(at != start) {
                ans = Math.min(ans, minEdgeBeauty[at][parent[start][at]]);
                at = parent[start][at];
            }
            return ans == minVal;
        }

        static class Item implements Comparable<Item> {
            int a, b, c;
            public Item(int aa, int bb, int cc) {
                a = aa;
                b = bb;
                c = cc;
            }
            @Override
            public int compareTo(Item o) {
                return Integer.compare(c, o.c);
            }

        }

    }

    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 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 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;
        }
    }

}