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 copy
n = int(input())

g = [[] for i in range(n)]
depth = [0 for i in range(n)]
parent = [-2 for i in range(n)]
parent[0] = -1
beauty = [1 for i in range(n)]
Edges = []



def chk(f,t):
    _min = 1145141919810
    while f!=t:
        if depth[f] < depth[t]:
            f,t = t,f
        _min = min(beauty[f],_min)
        f = parent[f]
    return _min

def dfs():
    callstack = [0]
    while len(callstack):
        c = callstack.pop()
        for i in g[c]:
            if parent[c] == i:
                continue
            parent[i] = c
            depth[i] = depth[c] + 1
            callstack.append(i)

def update(f,t,w):
    while f!=t:
        if depth[f] < depth[t]:
            f,t = t,f
        beauty[f] = max(beauty[f],w)
        f = parent[f]

for i in range(n-1):
    fr,to = (int(i)-1 for i in input().split(' '))
    g[fr].append(to)
    g[to].append(fr)
    Edges.append((fr,to))

dfs()
g = []
m = int(input())

for i in range(m):
    fr,to,we = (int(i) for i in input().split(' '))
    fr -= 1
    to -= 1
    g.append((fr,to,we))
    update(fr,to,we)

for a,b,c in g:
    if chk(a,b) != c:
        print(-1)
        exit(0)

for a,b in Edges:
    if parent[a] == b:
        print(beauty[a],end=' ')
    else:
        print(beauty[b],end=' ')