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,math,itertools
from collections import Counter,deque,defaultdict
from bisect import bisect_left,bisect_right 
from heapq import heappop,heappush,heapify
mod = 10**9+7
INF = float('inf')
def inp(): return int(sys.stdin.readline())
def inpl(): return list(map(int, sys.stdin.readline().split()))

def err():
    print('-1'); exit()
n = inp()
g = [[] for _ in range(n)]
d = []
for i in range(n-1):
    a,b = inpl()
    a,b = a-1,b-1
    g[a].append(b)
    g[b].append(a)
    if a>b: a,b = b,a
    d.append([a,b])
bea = [[-1]*n for _ in range(n)]
cnt = [0] * (10**6+10)
m = inp()
pas = [inpl() for _ in range(m)]
pas.sort(key = lambda x:x[2])
root = []
for i,(a,b,c) in enumerate(pas):
    a,b = a-1,b-1
    pre = [-1] * n
    q = deque([a])
    f = True
    while q and f:
        nv = q.popleft()
        for v in g[nv]:
            if v == pre[nv]: continue
            pre[v] = nv
            if v == b:
                ro = [v]
                while v != a:
                    s,t = v,pre[v]
                    if s>t: s,t = t,s
                    bea[s][t] = c
                    ro.append(pre[v])
                    v = pre[v]
                root.append(ro[::-1])
                f = False
            q.append(v)
for i,(a,b,c) in enumerate(pas):
    a,b = a-1,b-1
    bad = True
    for j in range(len(root[i])-1):
        s,t = root[i][j], root[i][j+1]
        if s>t: s,t = t,s
        if bea[s][t] == c: bad = False; break
    if bad: err()

res = []
for i in range(n-1):
    a,b = d[i]
    now = bea[a][b]
    if now == -1:
        now = 1
    res.append(now)
print(*res)