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F. Berland Beauty
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$f_1, f_2, \dots, f_{n-1}$$$, which the passengers' answer is consistent with or report that it doesn't exist.

Input

The first line contains a single integer $$$n$$$ ($$$2 \le n \le 5000$$$) — 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.

Output

If 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.

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