1296_F. Berland Beauty
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
```python
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__

from collections import deque

n = int(input())
G = [[] for i in range(n)]
edges = []
for i in range(n-1):
    a,b = map(int, input().split())
    a,b = a-1,b-1
    G[a].append(b)
    G[b].append(a)
    edges.append((a,b))

dep = [0]*n
par = [0]*n

def bfs(root):
    que = deque()
    que.append((-1,root,0))
    while que:
        p,v,d = que.pop()
        dep[v]=d
        par[v]=p
        for to in G[v]:
            if to != p:
                que.append((v,to,d+1))

bfs(0)

num = [1]*n
def lca(a,b,g):
    cnt = 0
    if dep[a] < dep[b]:
        a,b = b,a
    while dep[a] > dep[b]:
        if num[a] <= g:
            num[a] = g
            cnt += 1
        a = par[a]
    while a!=b:
        if num[a] <= g:
            num[a] = g
            cnt += 1
        if num[b] <= g:
            num[b] = g
            cnt += 1
        a = par[a]
        b = par[b]
    return cnt > 0

q = int(input())
query = []
for i in range(q):
    a,b,g = map(int, input().split())
    a,b = a-1,b-1
    query.append((g,a,b))
query.sort(reverse=True)

for g,a,b in query:
    if not lca(a,b,g):
        print(-1)
        exit()

ans = []
for a,b in edges:
    if dep[a] < dep[b]:
        a,b = b,a
    ans.append(num[a])

print(*ans)

```