You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Since Boboniu finished building his Jianghu, he has been doing Kungfu on these mountains every day.

Boboniu designs a map for his $$$n$$$ mountains. He uses $$$n-1$$$ roads to connect all $$$n$$$ mountains. Every pair of mountains is connected via roads.

For the $$$i$$$-th mountain, Boboniu estimated the tiredness of doing Kungfu on the top of it as $$$t_i$$$. He also estimated the height of each mountain as $$$h_i$$$.

A path is a sequence of mountains $$$M$$$ such that for each $$$i$$$ ($$$1 \le i < |M|$$$), there exists a road between $$$M_i$$$ and $$$M_{i+1}$$$. Boboniu would regard the path as a challenge if for each $$$i$$$ ($$$1\le i<|M|$$$), $$$h_{M_i}\le h_{M_{i+1}}$$$.

Boboniu wants to divide all $$$n-1$$$ roads into several challenges. Note that each road must appear in exactly one challenge, but a mountain may appear in several challenges.

Boboniu wants to minimize the total tiredness to do all the challenges. The tiredness of a challenge $$$M$$$ is the sum of tiredness of all mountains in it, i.e. $$$\sum_{i=1}^{|M|}t_{M_i}$$$.

He asked you to find the minimum total tiredness. As a reward for your work, you'll become a guardian in his Jianghu.

## Input Format
The first line contains a single integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$), denoting the number of the mountains.

The second line contains $$$n$$$ integers $$$t_1, t_2, \ldots, t_n$$$ ($$$1 \le t_i \le 10^6$$$), denoting the tiredness for Boboniu to do Kungfu on each mountain.

The third line contains $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ ($$$1 \le h_i \le 10^6$$$), denoting the height of each mountain.

Each of the following $$$n - 1$$$ lines contains two integers $$$u_i$$$, $$$v_i$$$ ($$$1 \le u_i, v_i \le n, u_i \neq v_i$$$), denoting the ends of the road. It's guaranteed that all mountains are connected via roads.

## Output Format
Print one integer: the smallest sum of tiredness of all challenges.

## Examples
```input
5
40 10 30 50 20
2 3 2 3 1
1 2
1 3
2 4
2 5
```
```output
160
```
-----
```input
5
1000000 1 1 1 1
1000000 1 1 1 1
1 2
1 3
1 4
1 5
```
```output
4000004
```
-----
```input
10
510916 760492 684704 32545 484888 933975 116895 77095 127679 989957
402815 705067 705067 705067 623759 103335 749243 138306 138306 844737
1 2
3 2
4 3
1 5
6 4
6 7
8 7
8 9
9 10
```
```output
6390572
```

## Note
For the first example:

In the picture, the lighter a point is, the higher the mountain it represents. One of the best divisions is:

- Challenge $$$1$$$: $$$3 \to 1 \to 2$$$
- Challenge $$$2$$$: $$$5 \to 2 \to 4$$$

The total tiredness of Boboniu is $$$(30 + 40 + 10) + (20 + 10 + 50) = 160$$$. It can be shown that this is the minimum total tiredness.

Now solve the problem and return the code.