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>
using namespace std;
vector<vector<pair<int, int>>> adj, p;
void dfs(int v, int& pi, int parent, int id) {
  p[pi][v] = {parent, id};
  for (auto& u : adj[v])
    if (u.first != parent) dfs(u.first, pi, v, u.second);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  adj.resize(n + 1);
  p.resize(n + 1, vector<pair<int, int>>(n + 1));
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    adj[u].push_back(make_pair(v, i));
    adj[v].push_back(make_pair(u, i));
  }
  int m;
  cin >> m;
  vector<vector<int>> q;
  vector<int> f(n, 1);
  for (int i = 0; i < m; i++) {
    int a, b, g;
    cin >> a >> b >> g;
    q.push_back({g, a, b});
  }
  for (int i = 1; i <= n; i++) dfs(i, i, 0, 0);
  sort(q.begin(), q.end());
  for (int i = 0; i < m; i++) {
    int a = q[i][1], b = q[i][2], g = q[i][0];
    int u = b;
    while (u != a) {
      int id = p[a][u].second;
      f[id] = max(g, f[id]);
      u = p[a][u].first;
    }
  }
  for (int i = 0; i < m; i++) {
    int a = q[i][1], b = q[i][2], g = q[i][0];
    int u = b, val = 1e6;
    while (u != a) {
      int id = p[a][u].second;
      val = min(val, f[id]);
      u = p[a][u].first;
    }
    if (val != g) {
      cout << -1;
      return 0;
    }
  }
  for (int i = 1; i < n; i++) cout << f[i] << " ";
}