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F. Berland Beauty

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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.

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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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