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:
#!/usr/bin/python3
# @Author  : indiewar
import sys
sys.setrecursionlimit(5233)
n = int(input())
G = [[] for i in range(n+1)]
dep = [0 for i in range(n+1)]
par = [-1 for i in range(n+1)]
x = [0 for i in range(n+1)]
y = [0 for i in range(n+1)]

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

m = int(input())
a = [0 for i in range(m+1)]
b = [0 for i in range(m+1)]
g = [[]  for i in range(m+1)]
ans = [0 for i in range(n+1)]

def bfs():
    q = [1]
    par[1] = -2
    front = 0
    while front < len(q):
        u = q[front]
        front += 1
        for v in G[u]:
            if par[v] == -1:
                par[v] = u
                # print(v, par[v])
                dep[v] = dep[u] + 1
                # print(dep[v])
                q.append(v)
    # dep[x] = d
    # par[x] = fa
    # for v in G[x]:
    #     if v != fa:
    #         dfs(v,x,d+1)

def lca(u,v,w):
    while dep[u] > dep[v]:
        ans[u] = max(ans[u],w)
        u = par[u]

    while dep[v] > dep[u]:
        ans[v] = max(ans[v],w)
        v = par[v]

    while u != v:
        ans[u] = max(ans[u], w)
        ans[v] = max(ans[v], w)
        u = par[u]
        v = par[v]

def check(u,v,w):
    while dep[u] > dep[v]:
        if ans[u] == w: return True
        u = par[u]

    while dep[v] > dep[u]:
        if ans[v] == w: return True
        v = par[v]

    while u != v:
        if ans[u] == w: return True
        if ans[v] == w: return True
        u = par[u]
        v = par[v]

    return False

bfs()
for i in range(m):
    a[i],b[i],g[i] = map(int,input().split())
    lca(a[i],b[i],g[i])


f = True
for i in range(m):
    if check(a[i],b[i],g[i]) == False:
        f = False
        print(-1)
        break


if f == True:
    for i in range(n-1):
        if dep[x[i]] > dep[y[i]]:
            print(max(1,ans[x[i]]),end=" ")
        else:
            print(max(1, ans[y[i]]), end=" ")