write a go solution for Description:
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<=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<=i<|M|), h_M_i<=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<=n<=2*10^5), denoting the number of the mountains.

The second line contains n integers t_1,t_2,ldots,t_n (1<=t_i<=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<=h_i<=10^6), denoting the height of each mountain.

Each of the following n-1 lines contains two integers u_i, v_i (1<=u_i,v_i<=n,u_ineqv_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.

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: 3to1to2
- Challenge 2: 5to2to4

The total tiredness of Boboniu is (30+40+10)+(20+10+50)=160. It can be shown that this is the minimum total tiredness.. Output only the code with no comments, explanation, or additional text.