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 PYTHON3):

Solution:
n = int(input())
e = [[] for _ in range(n + 1)]

for i in range(n - 1):
    u, v = map(int, input().split())
    e[u].append((v, i))
    e[v].append((u, i))

p = [(-1, -1) for _ in range(n + 1)]
p[1] = (-2, -1)
h = [0 for _ in range(n + 1)]
q = [1]
front = 0
while front < len(q):
    u = q[front]
    front += 1
    for v in e[u]:
        if p[v[0]][0] == -1:
            p[v[0]] = (u, v[1])
            h[v[0]] = h[u] + 1
            q.append(v[0])

m = int(input())
q = [() for _ in range(m)]
for i in range(m):
    q[i] = tuple(list(map(int, input().split())))
q.sort(key = lambda u: u[2], reverse = True)

f = [0 for _ in range(n)]
for i in range(m):
    u, v, c = q[i][0], q[i][1], q[i][2]
    ok = False
    
    while h[u] > h[v]:
        if not f[p[u][1]] > c:
            ok = True
            f[p[u][1]] = c;
        u = p[u][0]
        
    while h[v] > h[u]:
        if not f[p[v][1]] > c:
            ok = True
            f[p[v][1]] = c;
        v = p[v][0]
    
    while u != v:
        if not f[p[u][1]] > c:
            ok = True
            f[p[u][1]] = c;
        if not f[p[v][1]] > c:
            ok = True
            f[p[v][1]] = c;
        u = p[u][0]
        v = p[v][0]
        
    if not ok:
        print(-1)
        exit()

for i in range(n - 1):
    print(max(f[i], 1), end = ' ')