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:
import math
import sys
input = sys.stdin.readline
n = int(input())
g = [[] for _ in range(n)]
for i in range(n - 1):
    x, y = map(lambda i : int(i) - 1, input().split())
    g[x].append((y, i))
    g[y].append((x, i))
par = [-1] * n
parEdge = [-1] * n
dep = [0] * n
stack = [0]
par[0] = 0
while len(stack) > 0:
    cur = stack.pop()
    for node, edge in g[cur]:
        if par[node] == -1:
            dep[node] = 1 + dep[cur]
            par[node], parEdge[node] = cur, edge
            stack.append(node)
paths = []
m = int(input())
for i in range(m):
    a, b, f = map(int, input().split())
    paths.append((f, a - 1, b - 1))
paths.sort(reverse=True)


value = [-1] * (n - 1)
for f, a, b in paths:
    if dep[a] > dep[b]:
        a, b = b, a
    while dep[b] != dep[a]:
        if value[parEdge[b]] == -1:
            value[parEdge[b]] = f
        b = par[b]
    while a != b:
        if value[parEdge[a]] == -1:
            value[parEdge[a]] = f
        if value[parEdge[b]] == -1:
            value[parEdge[b]] = f
        a, b = par[a], par[b]
for i in range(n - 1):
    if value[i] == -1:
        value[i] = 1
for f, a, b in paths:
    if dep[a] > dep[b]:
        a, b = b, a
    ans = 100000000
    while dep[b] != dep[a]:
        ans = min(ans, value[parEdge[b]])
        b = par[b]
    while a != b:
        ans = min(ans, value[parEdge[a]], value[parEdge[b]])
        a, b = par[a], par[b]
    if ans != f:
        print(-1)
        exit(0)
print(' '.join(map(str, value)))