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 javafx.util.Pair;

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

import static java.lang.System.exit;

public class Main {
    static Scanner sc;
    static PrintWriter out;

    static final int N = (int) 5e3 + 5;
    static int n, x, y, q, z, par[], lvl[], val[], idx[][], values[];
    static ArrayList<Integer>[] v;
    static ArrayList<Pair<Integer, Pair<Integer, Integer>>> qry;

    static void init() {
        sc = new Scanner(System.in);
        out = new PrintWriter(System.out);

        par = new int[N];
        lvl = new int[N];
        val = new int[N];
        idx = new int[N][N];
        v = new ArrayList[N];
        qry = new ArrayList<>();
        values = new int[N];

        Arrays.fill(val, (int) -1);
        Arrays.fill(val, (int) 1e6);
        for (int i = 0; i < N; i++) {
            v[i] = new ArrayList<>();
        }
    }

    static void dfs(int u, int p) {
        for (Integer i : v[u])
            if (i != p) {
                lvl[i] = lvl[u] + 1;
                par[i] = u;
                dfs(i, u);
            }
    }

    static void udt(int x, int y, int z) {
        while (x != y) {
            if (lvl[x] < lvl[y]) {
                x = x + y;
                y = x - y;
                x = x - y;
            }

            values[idx[x][par[x]]] = Math.max(values[idx[x][par[x]]], z);
            x = par[x];
        }
    }

    static boolean can(int _z, int _x, int _y) {
        z = _z;
        x = _x;
        y = _y;

        boolean ok = false;
        while (x != y) {
            if (lvl[x] < lvl[y]) {
                x = x + y;
                y = x - y;
                x = x - y;
            }

            if (values[idx[x][par[x]]] == -1 || values[idx[x][par[x]]] == z || val[idx[x][par[x]]] == z) {
                ok = true;
                val[idx[x][par[x]]] = z;
                break;
            }
            x = par[x];
        }

        if (!ok) return ok;

        while (x != y) {
            if (lvl[x] < lvl[y]) {
                x = x + y;
                y = x - y;
                x = x - y;
            }
            if(values[idx[x][par[x]]] == z) {
                values[idx[x][par[x]]] = -1;
            }
            x = par[x];
        }

        return true;
    }

    public static void main(String[] args) throws IOException {
        init();

        n = sc.nextInt();
        for (int i = 0; i < n - 1; i++) {
            x = sc.nextInt();
            y = sc.nextInt();
            idx[x][y] = idx[y][x] = i;
            v[x].add(y);
            v[y].add(x);
        }

        dfs(1, 0);

        q = sc.nextInt();
        for (int i = 0; i < q; i++) {
            x = sc.nextInt();
            y = sc.nextInt();
            z = sc.nextInt();
            qry.add(new Pair<>(z, new Pair<>(x, y)));
            udt(x, y, z);
        }

        Collections.sort(qry, (p1, p2) -> {
            if (p1.getKey().equals(p2.getKey())) return 0;
            if (p1.getKey() > p2.getKey()) return 1;
            return -1;
        });

        for (int i = 0; i < qry.size(); i++) {
            if (!can(qry.get(i).getKey(), qry.get(i).getValue().getKey(), qry.get(i).getValue().getValue())) {
                System.out.println(-1);
                exit(0);
            }
        }

        for (int i = 0; i < n - 1; i++) out.print(val[i] + " ");

        out.close();
    }


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}