#include <bits/stdc++.h>
using namespace std;
const int N = 5010;
inline int read() {
  int s = 0, w = 1;
  register char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') w = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9')
    s = (s << 3) + (s << 1) + (ch ^ 48), ch = getchar();
  return s * w;
}
int n, m, dis[N], flg, f[N], q[N], cnt, book[N][N];
int head[N], maxE;
struct Edge {
  int nxt, to;
} e[N << 1];
struct Node {
  int u, v, w;
} g[N << 1];
struct TE {
  int u, v;
} T[N << 1];
inline bool cp(Node x, Node y) { return x.w > y.w; }
inline void Add(int u, int v) {
  e[++maxE].nxt = head[u];
  head[u] = maxE;
  e[maxE].to = v;
}
void DFS(int x, int fa, int gl) {
  if (flg) {
    return;
  }
  for (int i = head[x]; i; i = e[i].nxt) {
    int v = e[i].to;
    if (v == gl) {
      q[++cnt] = v;
      flg = 1;
      return;
    }
    if (v == fa) continue;
    cnt++;
    q[cnt] = v;
    DFS(v, x, gl);
    if (flg) {
      return;
    }
    cnt--;
  }
}
signed main() {
  n = read();
  for (register int i = 1; i < n; i++) {
    int x, y;
    x = read(), y = read();
    Add(x, y), Add(y, x);
    T[i].u = x, T[i].v = y;
  }
  m = read();
  for (register int i = 1; i <= m; i++)
    g[i].u = read(), g[i].v = read(), g[i].w = read();
  sort(g + 1, g + 1 + m, cp);
  for (register int i = 1; i <= m; i++) {
    flg = cnt = 0;
    DFS(g[i].u, 0, g[i].v);
    q[0] = g[i].u;
    flg = 0;
    for (register int j = 1; j <= cnt; j++) {
      if (book[q[j - 1]][q[j]] > g[i].w) continue;
      flg = 1;
      book[q[j - 1]][q[j]] = book[q[j]][q[j - 1]] = g[i].w;
    }
    if (!flg) {
      puts("-1");
      return 0;
    }
  }
  for (register int i = 1; i < n; i++)
    printf("%d ", max(book[T[i].u][T[i].v], 1));
  puts("");
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 5010;
inline int read() {
  int s = 0, w = 1;
  register char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') w = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9')
    s = (s << 3) + (s << 1) + (ch ^ 48), ch = getchar();
  return s * w;
}
int n, m, dis[N], flg, f[N], q[N], cnt, book[N][N];
int head[N], maxE;
struct Edge {
  int nxt, to;
} e[N << 1];
struct Node {
  int u, v, w;
} g[N << 1];
struct TE {
  int u, v;
} T[N << 1];
inline bool cp(Node x, Node y) { return x.w > y.w; }
inline void Add(int u, int v) {
  e[++maxE].nxt = head[u];
  head[u] = maxE;
  e[maxE].to = v;
}
void DFS(int x, int fa, int gl) {
  if (flg) {
    return;
  }
  for (int i = head[x]; i; i = e[i].nxt) {
    int v = e[i].to;
    if (v == gl) {
      q[++cnt] = v;
      flg = 1;
      return;
    }
    if (v == fa) continue;
    cnt++;
    q[cnt] = v;
    DFS(v, x, gl);
    if (flg) {
      return;
    }
    cnt--;
  }
}
signed main() {
  n = read();
  for (register int i = 1; i < n; i++) {
    int x, y;
    x = read(), y = read();
    Add(x, y), Add(y, x);
    T[i].u = x, T[i].v = y;
  }
  m = read();
  for (register int i = 1; i <= m; i++)
    g[i].u = read(), g[i].v = read(), g[i].w = read();
  sort(g + 1, g + 1 + m, cp);
  for (register int i = 1; i <= m; i++) {
    flg = cnt = 0;
    DFS(g[i].u, 0, g[i].v);
    q[0] = g[i].u;
    flg = 0;
    for (register int j = 1; j <= cnt; j++) {
      if (book[q[j - 1]][q[j]] > g[i].w) continue;
      flg = 1;
      book[q[j - 1]][q[j]] = book[q[j]][q[j - 1]] = g[i].w;
    }
    if (!flg) {
      puts("-1");
      return 0;
    }
  }
  for (register int i = 1; i < n; i++)
    printf("%d ", max(book[T[i].u][T[i].v], 1));
  puts("");
  return 0;
}

```