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 jdk.nashorn.internal.runtime.ListAdapter;
    import org.omg.PortableInterceptor.INACTIVE;

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

    public class Main {
        public static void main(String[] args) throws IOException {
            Scanner in = new Scanner(System.in);
            int n = in.nextInt();
            Map<Integer,List<Integer>> vertex=new HashMap<>();
            int [][]edge=new int[n+1][n+1];
            int [][]init=new int[n-1][2];
            for(int i=0;i<n-1;i++){
                int x=in.nextInt();
                int y=in.nextInt();
                init[i][0]=x;init[i][1]=y;
                List<Integer> integers = vertex.get(x);
                List<Integer> integers1 = vertex.get(y);
                if(integers==null){
                    integers=new ArrayList<>();
                    vertex.put(x,integers);
                }

                if(integers1==null){
                    integers1=new ArrayList<>();
                    vertex.put(y,integers1);
                }
                integers.add(y);
                integers1.add(x);
            }
            int m=in.nextInt();
            Integer [][]problem=new Integer[m][3];
            for(int i=0;i<m;i++){
                problem[i][0]=in.nextInt();
                problem[i][1]=in.nextInt();
                problem[i][2]=in.nextInt();
            }
            Arrays.sort(problem, new Comparator<Integer[]>() {
                @Override
                public int compare(Integer[] o1, Integer[] o2) {
                    return o2[2]-o1[2];
                }
            });
            int path[]=new int[n];
            boolean tag[]=new boolean[n+1];
            boolean flag=true;
            for(Integer []temp:problem){
                Arrays.fill(tag,false);
                dfs(temp[0],temp[1],vertex,0,path,tag);
                boolean visit=true;
                int num=0;
                for(int i=1;i<n&&visit;i++){
                    if(path[i]==temp[1])visit=false;
                    if(edge[path[i-1]][path[i]]==0||edge[path[i-1]][path[i]]<=temp[2]){
                            edge[path[i - 1]][path[i]] = temp[2];
                            edge[path[i]][path[i - 1]] = temp[2];
                            num++;
                    }
                }
                if(num==0){
                    flag=false;
                    break;
                }
            }
            if(flag){
               for(int i=0;i<n-1;i++)
                    System.out.print((edge[init[i][0]][init[i][1]]==0?1:edge[init[i][0]][init[i][1]])+" ");
            }else System.out.println(-1);
        }
        public  static boolean dfs(int root,int end,Map<Integer,List<Integer>> vertex,int index,int path[],boolean []tag){
            if(tag[root])
                return true;
            path[index]=root;
            tag[root]=true;
            if(root==end)
                return false;
            for(Integer integer:vertex.get(root))
                if(!dfs(integer,end,vertex,index+1,path,tag))return false;
            path[index]=0;
            return true;
        }
    }