D. Boboniu and Jianghutime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputSince 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.InputThe 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.OutputPrint one integer: the smallest sum of tiredness of all challenges.ExamplesInput
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
NoteFor 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.
5
40 10 30 50 20
2 3 2 3 1
1 2
1 3
2 4
2 5

160 
['dp', 'greedy', 'sortings', 'trees', '*2800']