#pragma GCC optimize("O3", "inline")
#include <bits/stdc++.h>
using namespace std;

typedef long long int ll;
typedef long double ld;
#define pb push_back
#define ub upper_bound
#define INF 1e18 + 100

ll dfs(int r, int p, vector<vector<pair<int, ll>>>& g, ll& ans, vector<ll>& a){
    priority_queue<ll, vector<ll>, greater<ll>> pq;
    ll me = LONG_LONG_MIN;
    for(auto& it: g[r]){
        if(it.first != p) {
            ll x = dfs(it.first, r, g, ans, a);
            ll topi = a[r] + a[it.first] - 2 * it.second;
            if(x != LONG_LONG_MIN) {
                topi = max(topi, x + a[r] + a[it.first] - 2 * it.second);
                me = max(me, x + a[r] + a[it.first] - 2 * it.second);
            }
            pq.push(topi);
        }
        if(pq.size() > 2) pq.pop();
    }
    // if(!r){
    //     priority_queue<ll, vector<ll>, greater<ll>> pq1;
    //     cout << "printing pq1: " << '\n';
    //     while(!pq.empty()){
    //         ll x = pq.top();
    //         cout << x << ' ';
    //         pq1.push(x);
    //         pq.pop();
    //     }
    //     cout << '\n';
    //     while(!pq1.empty()){
    //         ll x = pq1.top();
    //         pq.push(x);
    //         pq1.pop();
    //     }
    // }
    ll tor = LONG_LONG_MIN;
    if(pq.size() == 2){
        ll x = pq.top();
        pq.pop();
        ll y = pq.top();
        pq.pop();
        tor = y;
        me = max(me, x + y - a[r]);
    } else if(pq.size() == 1){
        ll y = pq.top();
        pq.pop();
        tor = y;
    }
    ans = max(ans, me);
    // cout << "r: " << r << ", me: " << me << ", tor: " << tor << '\n';
    if(tor == LONG_LONG_MIN) return tor;
    return tor - a[r];
}

ll solve()
{
    int n;
    cin >> n;
    vector<ll> a(n);
    for(int i = 0; i < n; i++) cin >> a[i];
    vector<vector<pair<int, ll>>> g(n, vector<pair<int, ll>>());
    for(int i = 0; i < n - 1; i++){
        int x, y;
        ll w;
        cin >> x >> y >> w;
        g[x - 1].pb({y - 1, w});
        g[y - 1].pb({x - 1, w});
    }
    ll ans = LONG_LONG_MIN;
    dfs(0, -1, g, ans, a);
    return ans;
}

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int t = 1;
    cin >> t;
    while(t--)
    {
        ll x = solve();
        cout << x << "\n";
    }
    return 0;
}