#include<bits/stdc++.h>
#define rep(i, a, b) for(int i = (a); i < (b); i++)
#define _for(i, a, b) for(int i = (a); i <= (b); i++)
using namespace std;

typedef long long ll;
const int N = 1e5 + 10;
int c[N], a[N], n;
vector<ll> val[N], dp[N], pre[N], suf[N];
unordered_map<int, int> mp[N];
vector<pair<int, int>> g[N];

void dfs(int u, int fa)
{
	dp[u].resize(val[u].size() + 1);

	for(auto [v, w]: g[u])
	{
		if(v == fa) continue;
		dfs(v, u);

		int pv = mp[v][w];
		ll cur = pre[v][pv];

		int pu = mp[u][w];
		dp[u][pu + 1] += cur;

		cur = suf[v][pv];
		dp[u][0] += cur;
		dp[u][pu] -= cur;

		dp[u][pu] += pre[v][val[v].size() - 1];
		dp[u][pu + 1] -= pre[v][val[v].size() - 1];
	}

//	puts("!!");
//	for(auto x: dp[u]) printf("%lld ", x); puts("");

	rep(i, 1, val[u].size()) dp[u][i] += dp[u][i - 1];
	rep(i, 0, val[u].size()) dp[u][i] += 1LL * c[u] * abs(val[u][i] - a[u]);

	pre[u].resize(val[u].size());
	suf[u].resize(val[u].size());
	pre[u][0] = dp[u][0];
	rep(i, 1, val[u].size()) pre[u][i] = min(dp[u][i], pre[u][i - 1]);

	suf[u][val[u].size() - 1] = dp[u][val[u].size() - 1];
	for(int i = val[u].size() - 2; i >= 0; i--)
	 	suf[u][i] = min(dp[u][i], suf[u][i + 1]);

//	puts("##!");
//	for(auto x: dp[u]) printf("%lld ", x); puts("");
}

int main()
{
	int T; scanf("%d", &T);
	while(T--)
	{
		scanf("%d", &n);
		_for(i, 1, n) scanf("%d", &c[i]), g[i].clear(), val[i].clear(), mp[i].clear(), dp[i].clear(), pre[i].clear(), suf[i].clear();
		_for(i, 1, n) scanf("%d", &a[i]), val[i].push_back(a[i]);
		_for(i, 1, n - 1)
		{
			int u, v, w;
			scanf("%d%d%d", &u, &v, &w);
			g[u].push_back({v, w});
			g[v].push_back({u, w});
			val[u].push_back(w);
			val[v].push_back(w);
		}

		_for(i, 1, n) 
		{
			sort(val[i].begin(), val[i].end());
			rep(j, 0, val[i].size()) mp[i][val[i][j]] = j;
		}

		dfs(1, 0);

		ll ans = 1e18;
		rep(i, 0, dp[1].size() - 1)
			ans = min(ans, dp[1][i]);
		printf("%lld\n", ans);
	}
	
	return 0;
}