#include <cstdio>
#include <vector>
#include <algorithm>
#include <set>
#define X first
#define Y second
#define PB push_back
using namespace std;
typedef vector < int > vi;
typedef long long ll;
typedef pair < ll, ll > pii;
typedef vector < pii > vp;
const int N = 3e5 + 50;
const ll INF = (ll)1e18;
int n, cst[N], a[N], naj[N], tko[N], min_cst[N], pos = 0;
vector < int > v[N];
ll dp_nula[N], off[N];
vector < ll > dp_am[N], dp_od[N];
set < pii > miin[N];
set < pii > govna[N];
inline ll get_dp(int v, int k) {
if(a[v] >= k) return dp_nula[v];
return dp_am[v][max(0, (int)dp_am[v].size() - (k - a[v]))] + off[v];
}
void minaj(ll &x, ll y) {
x = min(x, y);
}
void ocisti_od_sranja(int v, int dokle) {
if(miin[v].size() == 0) return;
int j = a[v] + 1; ll dos = INF;
for(auto it = miin[v].begin();it != miin[v].end() && it -> X <= dokle;) {
while(j < it -> X) {
minaj(dp_am[v][(int)dp_am[v].size() - (j - a[v] - 1) - 1], dos);
j++;
}
dos = min(dos, it -> Y);
it = miin[v].erase(it);
govna[v].erase({it -> Y + min_cst[it -> X], it -> X});
}
if(dokle < a[v] + (int)dp_am[v].size()) {
miin[v].insert({dokle + 1, dos});
govna[v].insert({dos + min_cst[dokle + 1], dokle + 1});
}
while(j <= dokle) minaj(dp_am[v][(int)dp_am[v].size() - (j - a[v] - 1) - 1], dos), j++;
for(int j = a[v] + dp_am[v].size() - dokle;j < (int)dp_am[v].size();j++) {
dp_od[v][j] = dp_am[v][j] + cst[a[v] + (int)dp_am[v].size() - j];
if(j) dp_od[v][j] = min(dp_od[v][j], dp_od[v][j - 1]);
}
}
void f(int x, int lst) {
for(int y : v[x]) if(y != lst) f(y, x);
if(tko[x] != -1) {
swap(dp_am[x], dp_am[tko[x]]);
swap(dp_od[x], dp_od[tko[x]]);
swap(miin[x], miin[tko[x]]);
swap(govna[x], govna[tko[x]]);
off[x] = off[tko[x]];
dp_am[x].PB(dp_nula[tko[x]] - off[x]);
dp_od[x].PB(min(dp_od[x].back(), dp_am[x].back() + cst[a[x] + 1]));
} else {
off[x] = 0;
dp_am[x] = {0, 0};
dp_od[x] = {cst[a[x] + 2], min(cst[a[x] + 2], cst[a[x] + 1])};
}
for(int y : v[x]) {
if(y == lst || y == tko[x]) continue;
if(a[y] != a[x] + 1) {
off[x] += dp_nula[y];
if(!a[y]) {
dp_am[x].back() += min(0LL, get_dp(y, a[x] + 1) - dp_nula[y]);
dp_od[x].back() = min(dp_am[x].back() + cst[a[x] + 1], dp_od[x][(int)dp_od[x].size() - 2]);
}
} else {
ocisti_od_sranja(y, a[y] + dp_am[y].size());
ocisti_od_sranja(x, a[y] + dp_am[y].size());
ll y_poc = get_dp(y, a[y] + dp_am[y].size());
off[x] += y_poc;
for(int k = 0;k < (int)dp_am[y].size();k++) {
dp_am[x][(int)dp_am[x].size() - k - 2] += get_dp(y, a[y] + k + 1) - y_poc;
}
dp_am[x].back() += dp_nula[y] - y_poc;
for(int k = (int)dp_am[y].size(); k >= 0; k--) {
int ind_x = (int)dp_am[x].size() - k - 1;
dp_od[x][ind_x] = dp_am[x][ind_x] + cst[a[x] + k + 1];
if(ind_x) dp_od[x][ind_x] = min(dp_od[x][ind_x], dp_od[x][ind_x - 1]);
}
}
}
dp_nula[x] = dp_od[x].back() + off[x];
dp_nula[x] = min(dp_nula[x], off[x] + dp_am[x][0] + min_cst[a[x] + dp_am[x].size()]);
if((int)govna[x].size() > 0)
dp_nula[x] = min(dp_nula[x], off[x] + govna[x].begin()->X);
miin[x].insert({a[x] + 2, dp_nula[x] - off[x]});
govna[x].insert({dp_nula[x] - off[x] + min_cst[a[x] + 2], a[x] + 2});
dp_am[x].back() = min(dp_am[x].back(), dp_nula[x] - off[x]);
dp_od[x].back() = min(dp_od[x][(int)dp_od[x].size() - 2], dp_am[x].back() + cst[a[x] + 1]);
}
void dfs_priprema(int x, int lst) {
tko[x] = -1; naj[x] = 2; pos++;
for(int y : v[x]) {
if(y == lst) continue;
dfs_priprema(y, x);
if(a[y] == a[x] + 1) {
if(tko[x] == -1 || naj[y] > naj[tko[x]]) {
naj[x] = naj[y] + 1; tko[x] = y;
}
}
}
}
int main(){
scanf("%d", &n);
for(int i = 1;i <= n;i++) scanf("%d", a + i);
for(int i = 1;i <= n;i++) scanf("%d", cst + i);
cst[n + 1] = cst[n]; min_cst[n + 1] = cst[n + 1];
min_cst[n] = cst[n];
for(int i = n - 1;i >= 1;i--) min_cst[i] = min(cst[i], min_cst[i + 1]);
for(int i = 1;i < n;i++) {
int x, y; scanf("%d%d", &x, &y);
v[x].PB(y), v[y].PB(x);
}
dfs_priprema(1, 1);
if(pos != n) return 0;
f(1, 1);
printf("%lld\n", dp_nula[1]);
return 0;
}
