F. Berland Beautytime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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, \dots, f_{n-1}, which the passengers' answer is consistent with or report that it doesn't exist.InputThe first line contains a single integer n (2 \le n \le 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 \le x_i, y_i \le n, x_i \ne 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 \le m \le 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 \le a_j, b_j \le n; a_j \ne b_j; 1 \le g_j \le 10^6) — the departure station, the arrival station and the minimum scenery beauty along his path.OutputIf there is no answer then print a single integer -1.Otherwise, print n-1 integers f_1, f_2, \dots, f_{n-1} (1 \le f_i \le 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.ExamplesInput
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

4
1 2
3 2
3 4
2
1 2 5
1 3 3

5 3 5 
['constructive algorithms', 'dfs and similar', 'greedy', 'sortings', 'trees', '*2100']