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 sys
input = sys.stdin.readline
from operator import itemgetter

n=int(input())
EDGE=[sorted(map(int,input().split())) for i in range(n-1)]

E=[[] for i in range(n+1)]

D=dict()

for i in range(n-1):
    x,y=EDGE[i]
    D[(x<<13)+y]=i
    D[(y<<13)+x]=i
    E[x].append(y)
    E[y].append(x)

m=int(input())

Q=sorted([tuple(map(int,input().split())) for i in range(m)],key=itemgetter(2),reverse=True)
    
def dfs(x,y,n,w):
    USE=[-1]*(n+1)
    NOW=[x]
    
    while NOW:
        n=NOW.pop()
        if n==y:
            break

        for to in E[n]:
            if USE[to]==-1:
                USE[to]=n
                NOW.append(to)

    change=0
    while y!=x:
        p=D[(y<<13)+USE[y]]
        if ANS[p]<=w:
            change+=1
            ANS[p]=w
        y=USE[y]

    if change==0:
        print(-1)
        sys.exit()
        
ANS=[1]*(n-1)

for a,b,q in Q:
    dfs(a,b,n,q)
    flag=1

print(*ANS)