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:
/**
 * @author derrick20
 */

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

public class BerlandBeauty {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        int N = sc.nextInt();
        adjList = new ArrayList[N];
        Arrays.setAll(adjList, i -> new ArrayList<>());
        ArrayDeque<Integer> edges = new ArrayDeque();
        for (int i = 0; i < N - 1; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            adjList[u].add(v);
            adjList[v].add(u);
            edges.add(u);
            edges.add(v);
        }
        parent = new int[N];
        depth = new int[N];
        dfs(0, -1, 0);
        int M = sc.nextInt();
        Data[] data = new Data[M];
        for (int i = 0; i < M; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            int val = sc.nextInt();
            data[i] = new Data(u, v, val);
        }
        Arrays.sort(data, Comparator.comparingInt(d -> -d.val));
        // want high values first
        int[] color = new int[N];
        Arrays.fill(color, 1);
        boolean poss = true;
//        System.out.println(Arrays.toString(data));
        painting: for (int i = 0; i < M; i++) {
            int u = data[i].u;
            int v = data[i].v;
            int col = data[i].val;
            int r = lca(u, v);
            boolean allBigger = true;
            if (u != r) {
                int curr = u;
                while (curr != r) {
                    // Either it's bigger than us, or it's 1, since we
                    // are moving monotonically! So, as long as we get
                    // one color down, we're good
                    if (color[curr] <= col) {
                        allBigger = false;
                        color[curr] = col;
                    }
                    curr = parent[curr];
                }
            }
            if (v != r) {
                int curr = v;
                while (curr != r) {
                    if (color[curr] <= col) {
                        allBigger = false;
                        color[curr] = col;
                    }
                    curr = parent[curr];
                }
            }
            if (allBigger) {
                poss = false;
                break painting;
            }
        }
        if (poss) {
            StringJoiner sj = new StringJoiner(" ");
            for (int k = 1; k < N; k++) {
                int u = edges.pollFirst();
                int v = edges.pollFirst();
                int e = u == parent[v] ? v : u;
                sj.add(Integer.toString(color[e]));
            }
            out.println(sj);
        }
        else {
            out.println(-1);
        }
        out.close();
    }

    static ArrayList<Integer>[] adjList;
    static int[] parent, depth;

    static int lca(int a, int b) {
        if (depth[b] < depth[a]) {
            int temp = b;
            b = a;
            a = temp;
        }
        while (depth[a] < depth[b]) {
            b = parent[b];
        }
        while (a != b) {
            a = parent[a];
            b = parent[b];
        }
        return a;
    }

    static void dfs(int node, int par, int d) {
        depth[node] = d;
        for (int adj : adjList[node]) {
            if (adj != par) {
                parent[adj] = node;
                dfs(adj, node, d + 1);
            }
        }
    }

    static class Data {
        int u, v, val;
        public Data(int uu, int vv, int value) {
            u = uu; v = vv; val = value;
        }
        public String toString() {
            return u + " " + v + ": " + val;
        }
    }

    static class FastScanner {
        private int BS = 1 << 16;
        private char NC = (char) 0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;

        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }

        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            } catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }

        private char getChar() {
            while (bId == size) {
                try {
                    size = in.read(buf);
                } catch (Exception e) {
                    return NC;
                }
                if (size == -1) return NC;
                bId = 0;
            }
            return (char) buf[bId++];
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public int[] nextInts(int N) {
            int[] res = new int[N];
            for (int i = 0; i < N; i++) {
                res[i] = (int) nextLong();
            }
            return res;
        }

        public long[] nextLongs(int N) {
            long[] res = new long[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextLong();
            }
            return res;
        }

        public long nextLong() {
            cnt = 1;
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            long res = 0;
            for (; c >= '0' && c <= '9'; c = getChar()) {
                res = (res << 3) + (res << 1) + c - '0';
                cnt *= 10;
            }
            return neg ? -res : res;
        }

        public double nextDouble() {
            double cur = nextLong();
            return c != '.' ? cur : cur + nextLong() / cnt;
        }

        public double[] nextDoubles(int N) {
            double[] res = new double[N];
            for (int i = 0; i < N; i++) {
                res[i] = nextDouble();
            }
            return res;
        }

        public String next() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c > 32) {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }

        public String nextLine() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c != '\n') {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }

        public boolean hasNext() {
            if (c > 32) return true;
            while (true) {
                c = getChar();
                if (c == NC) return false;
                else if (c > 32) return true;
            }
        }
    }

    static void ASSERT(boolean assertion, String message) {
        if (!assertion) throw new AssertionError(message);
    }
}