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 MAXN = 5000;
vector<tuple<int, int, int>> adjList[MAXN + 1];
tuple<int, int, int> edges[MAXN];
int ans[MAXN];
bool dfs(int v, int p, int target, int bt, int &minW) {
  if (v == target) return true;
  for (int i = 0; i < (int)adjList[v].size(); i++) {
    tuple<int, int, int> e = adjList[v][i];
    int u = get<0>(e);
    int ind = get<2>(e);
    int w = ans[ind];
    if (u != p) {
      if (dfs(u, v, target, bt, minW)) {
        minW = min(minW, w);
        adjList[v][i] = make_tuple(u, max(bt, w), ind);
        ans[ind] = max(bt, w);
        return true;
      }
    }
  }
  return false;
}
int main() {
  int n;
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    adjList[a].push_back(make_tuple(b, 0, i));
    adjList[b].push_back(make_tuple(a, 0, i));
  }
  int m;
  cin >> m;
  for (int i = 0; i < m; i++) {
    int a, b, g;
    cin >> a >> b >> g;
    edges[i] = make_tuple(g, a, b);
  }
  sort(edges, edges + m);
  bool valid = true;
  for (int i = m - 1; i >= 0; i--) {
    int a, b, g;
    g = get<0>(edges[i]);
    a = get<1>(edges[i]);
    b = get<2>(edges[i]);
    int minn = 2E6;
    dfs(a, a, b, g, minn);
    if (minn > g) valid = false;
  }
  if (valid) {
    for (int i = 0; i < n - 1; i++) {
      if (i > 0) cout << " ";
      cout << (ans[i] == 0 ? 1 : ans[i]);
    }
    cout << endl;
  } else
    cout << -1 << endl;
  return 0;
}