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
range = xrange
input = raw_input

inp = [int(x) for x in sys.stdin.read().split()]; ii = 0

n = inp[ii]; ii += 1

coupl = [[] for _ in range(n)]
U = []

for eind in range(n - 1):
    u = inp[ii] - 1; ii += 1
    v = inp[ii] - 1; ii += 1

    coupl[u].append(2*eind)
    coupl[v].append(2*eind + 1)

    U.append(u)
    U.append(v)

root = 0
bfs = [root]
P = [-1]*n
for node in bfs:
    for eind in coupl[node]:
        nei = U[eind ^ 1]
        P[nei] = eind ^ 1
        coupl[nei].remove(eind ^ 1)
        bfs.append(nei)

order = [0]*n
for i in range(n):
    order[bfs[i]] = i

class DisjointSetUnion:
    def __init__(self, n):
        self.parent = list(range(n))
        self.size = [1] * n
        self.num_sets = n
        self.true = list(range(n))

    def find(self, a):
        acopy = a
        while a != self.parent[a]:
            a = self.parent[a]
        while acopy != a:
            self.parent[acopy], acopy = a, self.parent[acopy]
        return a

    def merge(self, a, b):
        a, b = self.find(a), self.find(b)
        if a != b:
            if self.size[a] < self.size[b]:
                a, b = b, a

            self.num_sets -= 1
            self.parent[b] = a
            self.size[a] += self.size[b]
            if order[self.true[b]] < order[self.true[a]]:
                self.true[a] = self.true[b]

dsu = DisjointSetUnion(n)

m = inp[ii]; ii += 1
paths = []
for _ in range(m):
    u = inp[ii] - 1; ii += 1
    v = inp[ii] - 1; ii += 1
    w = inp[ii]; ii += 1
    paths.append((w,u,v))

F = [1]*(n - 1)

paths.sort()

while paths:
    w = paths[-1][0]
    tmp = []
    while paths and paths[-1][0] == w:
        w,u,v = paths.pop()
        
        u = dsu.true[dsu.find(u)]
        v = dsu.true[dsu.find(v)]
        
        if u == v:
            print -1
            sys.exit()
        
        tmp.append((u,v))
    
    for u,v in tmp:
        u = dsu.true[dsu.find(u)]
        v = dsu.true[dsu.find(v)]
        
        while u != v:
            if order[u] < order[v]:
                eind = P[v]
                F[eind >> 1] = w
                dsu.merge(v, U[eind ^ 1])

                v = dsu.true[dsu.find(v)]
            else:
                eind = P[u]
                F[eind >> 1] = w
                dsu.merge(u, U[eind ^ 1])
                
                u = dsu.true[dsu.find(u)]
print ' '.join(str(f) for f in F)