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.util.*;

public class Bestland{
    static int a,b,g,ans;
    static int[] aa=new int[5005],bb=new int[5005],gg=new int[5005],A=new int[5005];
    static ArrayList<ArrayList<int[]>> e = new ArrayList<>(5005);
    public static boolean dfs(int id,int p){
        if(id==b)return true;
        for (int j = 0; j < e.get(id).size(); j++) {
            int[] i=e.get(id).get(j);
            int to=i[0];
            if(to!=p)if(dfs(to,id)){A[i[1]]=Math.max(A[i[1]],g);return true;}
        }
        return false;
    }
    public static boolean Qdfs(int id,int p){
        if(id==b)return true;
        for (int j = 0; j < e.get(id).size(); j++) {
            int[] i=e.get(id).get(j);
            int to=i[0];
            if(to!=p)if(Qdfs(to,id)){ans=Math.min(ans,A[i[1]]);return true;}
        }
        return false;
    }
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(); 
        for (int i = 0; i <= n; i++) {e.add(new ArrayList<>());A[i]=1;}    
        for (int i = 1; i < n; i++) {
            int a =in.nextInt();int b =in.nextInt();
            int[] aye={b,i};
            int[] bee={a,i};
            e.get(a).add(aye);
            e.get(b).add(bee);
        }
        int m=in.nextInt();
        for (int i = 0; i < m; i++) {
            a =in.nextInt();b =in.nextInt();g =in.nextInt();
            aa[i]=a;bb[i]=b;gg[i]=g;
            dfs(a, 0);
        }
        for (int i = 0; i < m; i++) {          
            a=aa[i];b=bb[i];g=gg[i];
            ans=(1<<30);
            Qdfs(a, 0);
            if(ans!=g){System.out.println("-1");in.close();return;}
        }
        for (int i = 1; i < n; i++)System.out.print(A[i]+" ");
        in.close();
    }
}