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 CPP):

Solution:
#include <bits/stdc++.h>
const int maxn = 5000 + 7;
const int inf = 1e8;
int n, m, aa, bb;
std::pair<int, int> x[maxn];
int val[maxn][maxn];
std::vector<int> t[maxn];
int a[maxn], b[maxn], g[maxn];
std::pair<bool, int> dfs1(int now, int fa, int end) {
  if (now == end) {
    return std::make_pair(1, val[now][fa]);
  }
  int minn = inf;
  bool check = 0;
  std::pair<bool, int> temp;
  for (auto it : t[now]) {
    if (it != fa) {
      temp = dfs1(it, now, end);
      if (temp.first) {
        check = 1;
        minn = std::min(temp.second, val[now][it]);
      }
    }
  }
  return std::make_pair(check, minn);
}
int query(int u, int v) { return dfs1(u, -1, v).second; }
bool dfs2(int now, int fa, int end, int gate) {
  if (now == end) {
    val[now][fa] = val[fa][now] = std::max(val[fa][now], gate);
    return 1;
  }
  bool check = 0;
  for (auto it : t[now]) {
    if (it != fa) {
      if (dfs2(it, now, end, gate)) {
        check = 1;
        val[now][it] = val[it][now] = std::max(val[now][it], gate);
      }
    }
  }
  return check;
}
void modify(int u, int v, int x) { dfs2(u, -1, v, x); }
int main(int argc, char *argval[]) {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  std::cin >> n;
  for (int i = 0; i < n - 1; i++) {
    std::cin >> aa >> bb;
    x[i] = std::make_pair(aa, bb);
    val[aa][bb] = val[bb][aa] = 1;
    t[aa].push_back(bb);
    t[bb].push_back(aa);
  }
  std::cin >> m;
  bool yes = 1;
  for (int i = 0; i < m; i++) {
    std::cin >> a[i] >> b[i] >> g[i];
    modify(a[i], b[i], g[i]);
  }
  for (int i = 0; i < m; i++) {
    if (query(a[i], b[i]) > g[i]) {
      yes = 0;
    }
  }
  if (yes) {
    for (int i = 0; i < n - 1; i++) {
      std::cout << val[x[i].first][x[i].second] << ' ';
    }
    std::cout << '\n';
  } else {
    std::cout << "-1\n";
  }
}