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;
const int N = 5e3 + 5;
int n, m, a, b, g, aa[N], bb[N], gg[N], val[N], ans;
struct edge {
  int v, id;
};
vector<edge> e[N];
bool dfs(int id, int f) {
  if (id == b) return 1;
  bool p = 0;
  for (auto i : e[id]) {
    int to = i.v;
    if (to != f)
      if (dfs(to, id)) val[i.id] = max(val[i.id], g), p = 1;
  }
  return p;
}
int query(int id, int f) {
  if (id == b) return 1;
  bool p = 0;
  for (auto i : e[id]) {
    int to = i.v;
    if (to != f)
      if (query(to, id)) ans = min(ans, val[i.id]), p = 1;
  }
  return p;
}
int main() {
  cin >> n;
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    e[u].push_back({v, i});
    e[v].push_back({u, i});
  }
  cin >> m;
  for (int i = 1; i <= m; i++) {
    cin >> a >> b >> g;
    aa[i] = a, bb[i] = b, gg[i] = g;
    dfs(a, 0);
  }
  for (int i = 1; i <= m; i++) {
    a = aa[i], b = bb[i], g = gg[i];
    ans = 1e7;
    query(a, 0);
    if (ans != g) puts("-1"), exit(0);
  }
  for (int i = 1; i < n; i++) cout << (val[i] == 0 ? 1000000 : val[i]) << " ";
  return 0;
}