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:
from collections import deque

def main():
    n = int(input())
    neighbours = [set() for _ in range(n+1)]
    sections = []
    for i in range(n-1):
        x, y = map(int, input().split())
        sections.append((x, y))
        neighbours[x].add((y,i))
        neighbours[y].add((x,i))
    rootpaths = [[] for _ in range(n+1)]

    q = deque()
    q.append(1)
    parents = [None] * (n+1)
    depth = [0] * (n+1)
    while q:
        i = q.popleft()
        for s,j in neighbours[i]:
            if s !=1 and not parents[s]:
                depth[s] = depth[i] + 1
                parents[s] = (i, j)
                q.append(s)

    def path(x, y):
        if depth[x] < depth[y]:
            x,y = y,x
        res = []
        while depth[x] > depth[y]:
            x, s = parents[x]
            res.append(s)
        while x != y:
            x, s = parents[x]
            res.append(s)
            y, s = parents[y]
            res.append(s)
        return res

    m = int(input())
    routes = []
    secset = [False] * (n -1)
    secval = [int(1E6)] * (n-1)
    for _ in range(m):
        a, b, g = map(int, input().split())
        routes.append((g, path(a,b)))
    routes.sort(reverse=True)
    for v, pp in routes:
        valid = False
        for p in pp:
            if not secset[p] or secval[p] == v:
                valid = True
                secset[p] = True
                secval[p] = v
        if not valid:
            print(-1)
            return
    print(' '.join(map(str, secval)))


if __name__ == "__main__":
    main()