#include<bits/stdc++.h>
#define endl '\n'
using namespace std;
using ll = long long;
void solve() {
int n;
cin >> n;
vector<ll> weight(n + 1);
for(int i = 1; i <= n; i++) cin >> weight[i];
vector<vector<pair<int, ll>>> g(n + 1);
for(int i = 1; i < n; i++) {
int u, v, w; cin >> u >> v >> w;
g[u].push_back({v, w});
g[v].push_back({u, w});
}
int root = 1;
for(int i = 1; i <= n; i++) {
if(g[i].size() == 1) {
root = 1;
break;
}
}
ll ans = LLONG_MIN;
auto dfs = [&](auto&& self, int u, int p) -> ll {
if(g[u].size() == 1 && g[u][0].first == p) { // leaf
return weight[u];
}
priority_queue<ll> pq;
ll mx = weight[u];
for(auto &[v, w]: g[u]) {
if(v == p) continue;
ll x = self(self, v, u);
mx = max(mx, (weight[u] - 2 * w) + x);
pq.push((weight[u] - 2 * w) + x);
}
if(pq.size() >= 2) {
ll x = pq.top(); pq.pop();
x += pq.top() - weight[u];
ans = max(ans, x);
}
ans = max(ans, mx);
return mx;
};
dfs(dfs, root, 0);
cout << ans << endl;
return;
}
int main() {
ios::sync_with_stdio(false); cin.tie(0);
int tc = 1;
cin >> tc;
for (int t = 1; t <= tc; t++) {
// cout << "Case " << t << ": ";
solve();
}
return 0;
}