#include <bits/stdc++.h>

#define f first
#define s second
#define pb push_back
#define mp make_pair

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;

const int N = 300500, inf = 1e9, mod = 998244353;
const ll INF = 1e18;

int sum(int a, int b) {
    a += b;
    if (a >= mod)
        a -= mod;
    return a;
}

int sub(int a, int b) {
    a -= b;
    if (a < 0)
        a += mod;
    return a;
}

int mult(int a, int b) {
    return 1ll * a * b % mod;
}

int bp(int a, int b) {
    int res = 1;
    while (b) {
        if (b & 1)
            res = mult(res, a);
        a = mult(a, a);
        b >>= 1;
    }
    return res;
}

int inv(int x) {
    return bp(x, mod - 2);
}

vector<pii> g[N];
int n;
ll v_cost[N], v_weight[N], e_weight[N];

ll conds_n, conds[N], val[N];

ll dp[N][2], ans;

// 0 v <= w[pe]
// 1 v >= w[pe]

void add(int l, int r, ll x){
    if(l > r)
        return;
    val[l] += x;
    val[r + 1] -= x;
}
void dfs(int v, int pe) {
    dp[v][0] = dp[v][1] = INF;
    for (auto it: g[v]) {
        int to = it.f;
        int e = it.s;
        if (e == pe)
            continue;
        dfs(to, e);
    }

    sort(g[v].begin(), g[v].end(), [](pii i, pii j) {
        return e_weight[i.s] < e_weight[j.s];
    });
    conds_n = 0;
    conds[conds_n++] = v_weight[v];
    for (auto it: g[v]) {
        int to = it.f;
        int e = it.s;
        if (e == pe)
            continue;
        conds[conds_n++] = e_weight[e];
    }
    if (pe != -1)
        conds[conds_n++] = e_weight[pe];
    sort(conds, conds + conds_n);
    conds_n = unique(conds, conds + conds_n) - conds;
    for(int i = 0; i < conds_n; i++)
        val[i] = 0;
    for (auto it: g[v]) {
        int to = it.f;
        int e = it.s;
        if (e == pe)
            continue;
        int pos = lower_bound(conds, conds + conds_n, e_weight[e]) - conds;
        add(0, pos - 1, dp[to][1]);
        add(pos, pos, min(dp[to][0], dp[to][1]));
        add(pos + 1, conds_n - 1, dp[to][0]);
    }
    ll x = 0;
    for(int i = 0; i < conds_n; i++){
        x += val[i];
        ll cur = x + abs(conds[i] - v_weight[v]) * v_cost[v];
        if(pe == -1){
            ans = min(ans, cur);
        }else{
            if(conds[i] <= e_weight[pe])
                dp[v][0] = min(dp[v][0], cur);
            if(conds[i] >= e_weight[pe])
                dp[v][1] = min(dp[v][1], cur);
        }
    }
//    cerr << v << " " << dp[v][0] << " " << dp[v][1] << endl;
}

void solve() {
    cin >> n;
    for (int i = 0; i < n; i++)
        cin >> v_cost[i];
    for (int i = 0; i < n; i++)
        cin >> v_weight[i];
    for (int i = 0; i < n - 1; i++) {
        int v, u;
        cin >> v >> u >> e_weight[i];
        v--, u--;
        g[v].pb({u, i});
        g[u].pb({v, i});
    }
    ans = INF;
    dfs(0, -1);
    cout << ans << "\n";
    for(int i = 0; i < n; i++)
        g[i].clear();
}

int main() {
#ifdef DEBUG
    freopen("input.txt", "r", stdin);
#endif
    ios_base::sync_with_stdio(false);
    int t = 1;
    cin >> t;
    for (int i = 1; i <= t; i++) {
//        cout << "Case #" << i << endl;
        solve();
    }
}