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.awt.event.*;
import java.awt.geom.*;
import java.io.*;
import java.math.*;
import java.text.*;
import java.util.*;

/*
br = new BufferedReader(new FileReader("input.txt"));
pw = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
br = new BufferedReader(new InputStreamReader(System.in));
pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
 */

public class Main {
  private static BufferedReader br;
  private static StringTokenizer st;
  private static PrintWriter pw;

  public static void main(String[] args) throws IOException	{
    br = new BufferedReader(new InputStreamReader(System.in));
    pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    int qq = 1;
    //int qq = Integer.MAX_VALUE;
    //int qq = readInt();
    for(int casenum = 1; casenum <= qq; casenum++)	{
      int n = readInt();
      edges = new LinkedList[n];
      for(int i = 0; i < n; i++) edges[i] = new LinkedList<>();
      for(int i = 1; i < n; i++) {
        int a = readInt()-1;
        int b = readInt()-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 = readInt();
      int[] lhs = new int[m];
      int[] rhs = new int[m];
      int[] w = new int[m];
      for(int i = 0; i < m; i++) {
        lhs[i] = readInt()-1;
        rhs[i] = readInt()-1;
        w[i] = readInt();
        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) {
        pw.println(-1);
      }
      else {
        for(int i = 0; i < ret.length; i++) {
          if(i > 0) pw.print(" ");
          pw.print(ret[i]);
        }
        pw.println();
      }
    }
    pw.close();
  }

  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);
    }
  }

  static class Edge {
    public int d, i;
    public Edge(int a, int b) {
      d=a;
      i=b;
    }
  }

  private static void exitImmediately()	{
    pw.close();
    System.exit(0);
  }

  private static long readLong() throws IOException	{
    return Long.parseLong(nextToken());
  }

  private static double readDouble() throws IOException	{
    return Double.parseDouble(nextToken());
  }

  private static int readInt() throws IOException	{
    return Integer.parseInt(nextToken());
  }

  private static String nextToken() throws IOException	{
    while(st == null || !st.hasMoreTokens())	{
      if(!br.ready())	{
        exitImmediately();
      }
      st = new StringTokenizer(br.readLine().trim());
    }
    return st.nextToken();
  }
}