问题 A: Tree

For a rootless tree with $n$ vertices and $n-1$ edges, each edge has edge weights. In the beginning, each vertex has a color (black or white), you can choose to reverse the color of some vertex, but this will pay the $\text{cost}$.

For a tree, we define its $\text{earnings}$ as ∑x∈V1∑y∈V2val(x,y)\sum\limits_{x\in V_1}\sum\limits_{y\in V_2}val(x,y)x∈V1∑y∈V2∑val(x,y), where V1V_1V1 is the set of white vertices and V2V_2V2 is the set of black vertices.

Where val(x,y)val(x,y)val(x,y) is the maximum edge weight in the shortest path from $x$ to $y$.

You need to reverse some vertices (or not) so that the $\text{earnings-cost}$ is maximum? You need to calculate the answer.

The first line contains a positive integer $n(1\le n\le 3000)$, representing the number of vertices in the tree.
The second line contains a row of $n$ integers ai (0≤ai≤1)a_i \ (0\le a_i\le 1)ai (0≤ai≤1), representing the initial color of the $i$-th vertex ($0$ for white, $1$ for black).
The third line contains a row of $n$ integers costi (1≤costi≤109)cost_i\ (1\leq cost_i\leq 10^9)costi (1≤costi≤109), representing the cost of changing the $i$-th vertex.
The next $n-1$ line, each line contains three positive integers uj,vj,wj (1≤uj,vj,wj≤n)u_j,v_j,w_j\ (1\leq u_j,v_j,w_j\le n)uj,vj,wj (1≤uj,vj,wj≤n) represents an undirected edge and edge weight. It is guaranteed that the input is a tree.

A line of output with an integer represents the maximum $\text{earnings-cost}$.

3
0 0 0
1 2 3
1 2 1
2 3 2

2