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

public class GFG {
	private static int max=100000000;
	private static void dfs(int s,int u,int p[][],ArrayList<ArrayList<Integer>> G){
		for(int i:G.get(u)){
			if(p[s][u]==i)
				continue;
			p[s][i]=u;
			dfs(s,i,p,G);
		}
	}
    public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int n=Integer.parseInt(br.readLine().trim());
		ArrayList<ArrayList<Integer>> G=new ArrayList<ArrayList<Integer>>(); 
		Map<Integer,Integer> m=new HashMap<>();
		for(int i=0;i<n;i++)
    		G.add(new ArrayList<Integer>());
		for(int i=0;i<n-1;i++){
			String s=br.readLine().trim();
			String ss[]=s.split("\\s+");
			int u=Integer.parseInt(ss[0])-1;
			int v=Integer.parseInt(ss[1])-1;
			int key=Math.min(u,v)*n+Math.max(u,v);
			m.put(key,i);
			G.get(v).add(u);
			G.get(u).add(v);
		}
		int p[][]=new int[n][];	
		
		int mm=Integer.parseInt(br.readLine().trim());
		Map<Integer,Integer> map=new HashMap<>();
		int [][]q=new int[mm][3];
		for(int i=0;i<mm;i++){
			String s=br.readLine().trim();
			String ss[]=s.split("\\s+");
			q[i][0]=Integer.parseInt(ss[0])-1;
			q[i][1]=Integer.parseInt(ss[1])-1;
			q[i][2]=Integer.parseInt(ss[2]);	
		}
		Arrays.sort(q,(q1,q2)->{
		    return q1[2]-q2[2];
		});
		for(int[] i:q){
			int u=i[0];
			int v=i[1];
			if(p[u]==null){
				p[u]=new int[n];
				p[u][u]=-1;
				dfs(u,u,p,G);
			}
			while(v!=u){
				int t=p[u][v];
				int key=Math.min(t,v)*n+Math.max(t,v);
				map.put(key,i[2]);
				v=t;
			}
		}
		for(int[] i:q){
			int u=i[0];
			int v=i[1];
			int min=Integer.MAX_VALUE;
			while(v!=u){
				int t=p[u][v];
				int key=Math.min(t,v)*n+Math.max(t,v);
				min=Math.min(min,map.get(key));
				v=t;
			}
			if(min!=i[2]){
				System.out.println("-1");
				return;
			}
		}
		int a[]=new int[n-1];
		for(int i:map.keySet()){
			a[m.get(i)]=map.get(i);
		}
		for(int i=0;i<n-1;i++){
		    if(a[i]==0)
		        a[i]=1000000;
			System.out.print(a[i]+" ");
		}
		System.out.println();
	}
}