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.awt.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

public class Main {
    static int mod = (int) 1e9 + 7;
    static  ArrayList<Edge>[] adj;
    static int[][] p;
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int n = sc.nextInt();
        edges = new LinkedList[n];
        for(int i = 0; i < n; i++) edges[i] = new LinkedList<>();
        for(int i = 1; i < n; i++) {
            int a = sc.nextInt()-1;
            int b = sc.nextInt()-1;
            edges[a].add(new Edge(b, i-1));
            edges[b].add(new Edge(a, i-1));
        }
        par = new int[n];
        depth = new int[n];
        edgeid = new int[n];
        Arrays.fill(edgeid, -1);
        ret = new int[n-1];
        dfs(0, -1);
        Arrays.fill(ret, 1);
        int m = sc.nextInt();
        int[] lhs = new int[m];
        int[] rhs = new int[m];
        int[] w = new int[m];
        for(int i = 0; i < m; i++) {
            lhs[i] = sc.nextInt()-1;
            rhs[i] = sc.nextInt()-1;
            w[i] = sc.nextInt();
            int a = lhs[i];
            int b = rhs[i];
            while(a != b) {
                if(depth[a] > depth[b]) {
                    ret[edgeid[a]] = Math.max(ret[edgeid[a]], w[i]);
                    a = par[a];
                }
                else if(depth[b] > depth[a]) {
                    ret[edgeid[b]] = Math.max(ret[edgeid[b]], w[i]);
                    b = par[b];
                }
                else {
                    ret[edgeid[a]] = Math.max(ret[edgeid[a]], w[i]);
                    a = par[a];
                    ret[edgeid[b]] = Math.max(ret[edgeid[b]], w[i]);
                    b = par[b];
                }
            }
        }
        boolean good = true;
        for(int i = 0; good && i < m; i++) {
            int minw = (int)1e6;
            int a = lhs[i];
            int b = rhs[i];
            while(a != b) {
                if(depth[a] > depth[b]) {
                    minw = Math.min(minw, ret[edgeid[a]]);
                    a = par[a];
                }
                else if(depth[b] > depth[a]) {
                    minw = Math.min(minw, ret[edgeid[b]]);
                    b = par[b];
                }
                else {
                    minw = Math.min(minw, ret[edgeid[a]]);
                    a = par[a];
                    minw = Math.min(minw, ret[edgeid[b]]);
                    b = par[b];
                }
            }
            good = minw == w[i];
        }
        if(!good) System.out.println(-1);
        else {
            StringBuilder sb=new StringBuilder();
            for(int i = 0; i < ret.length; i++)sb.append(ret[i]+" ");
            System.out.println(sb);
        }
    }
    static LinkedList<Edge>[] edges;
    static int[] ret;
    static int[] par;
    static int[] depth;
    static int[] edgeid;

    public static void dfs(int curr, int p) {
        for(Edge out: edges[curr]) {
            if(out.d == p) continue;
            par[out.d] = curr;
            depth[out.d] = 1 + depth[curr];
            edgeid[out.d] = out.i;
            dfs(out.d, curr);
        }
    }
}
class Edge {
    public int d, i;
    public Edge(int a, int b) {
        d=a;
        i=b;
    }
}
class queries implements Comparable<queries>{
    int a,b,g;
    public queries(int a,int b,int g){
        this.a=a;this.b=b;this.g=g;
    }
    public int compareTo(queries o){
        return this.g-o.g;
    }
}
class FastReader {
    BufferedReader br;
    StringTokenizer st;

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

    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;
    }
}