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 PYTHON):

Solution:
import sys

__author__ = 'ratmir'

from collections import deque


def solve(n, a, graph):
    return 1


def execute():
    [n] = [int(x1) for x1 in sys.stdin.readline().split()]

    graph = dict()
    paths_m = dict()
    for i in range(0, n - 1):
        # read graph
        [v1, v2] = [int(x1) for x1 in sys.stdin.readline().split()]
        if v1 not in graph:
            graph[v1] = []
        if v2 not in graph:
            graph[v2] = []
        graph[v1].append(v2)
        graph[v2].append(v1)
        paths_m[(v1, v2)] = i
        paths_m[(v2, v1)] = i

    [m] = [int(x1) for x1 in sys.stdin.readline().split()]
    paths = set()
    for i in range(0, m):
        a, b, g = [int(x1) for x1 in sys.stdin.readline().split()]
        xab = max(a, b)
        nab = min(a, b)
        paths.add((g, nab, xab))

    paths = sorted(list(paths))[::-1]

    # print graph
    # bfs with sqrt decomposition of parent for trees
    visited = {1}
    dq = deque()
    dq.append((1, 1))
    levels = [-1] * (n + 1)
    parents = [-1] * (n + 1)
    while len(dq) > 0:
        v, level = dq.popleft()
        levels[v] = level
        for vn in graph[v]:
            if vn not in visited:
                visited.add(vn)
                parents[vn] = v
                dq.append((vn, level + 1))
    # print paths_m
    bad = False
    values = [None] * (n - 1)
    for path in paths:
        g, a, b = path
        level_a = levels[a]
        level_b = levels[b]
        va = a
        vb = b
        cnt = 0
        if level_a > level_b:
            for k in range(level_b, level_a):
                vv = va, parents[va]
                pm = paths_m[vv]
                if values[pm] is None or values[pm] == g:
                    values[pm] = g
                    cnt += 1
                va = parents[va]
        if level_a < level_b:
            for k in range(level_a, level_b):
                vv = vb, parents[vb]
                pm = paths_m[vv]
                if values[pm] is None or values[pm] == g:
                    values[pm] = g
                    cnt += 1
                vb = parents[vb]
        k = min(level_a, level_b) - 1
        while k > 0:
            if va == vb:
                break
            vv = va, parents[va]
            pm = paths_m[vv]
            if values[pm] is None or values[pm] == g:
                values[pm] = g
                cnt += 1
            vv = vb, parents[vb]
            pm = paths_m[vv]
            if values[pm] is None or values[pm] == g:
                values[pm] = g
                cnt += 1
            va = parents[va]
            vb = parents[vb]
            k -= 1
        if cnt == 0:
            bad = True
            break
        # print path_a, path_b, values

    for i in range(0, n - 1):
        if values[i] is None:
            values[i] = 1
    if bad:
        print -1
    if not bad:
        print(''.join(' {}'.format(k) for k in values)[1:])


execute()