#include <bits/stdc++.h>
using namespace std;

const int MAX = int(2e5);
const long long INF = (long long) 1e18;

int dTime, n;

int L[MAX + 5], R[MAX + 5], A[MAX + 5], parent[MAX + 5];
long long W[MAX + 5], E[MAX + 5], tree[MAX * 4 + 5];

vector< pair<int, int> > X[MAX + 5];

void dfs(int u, int par)
{
    L[u] = ++dTime;
    A[dTime] = u;
    parent[u] = par;
    
    W[u] += W[par];
    
    for (auto pr: X[u])
        if (pr.first != par)
        {
            int v = pr.first;
            
            E[v] = E[u] + pr.second * 2LL;
            dfs(v, u);
        }
    
    R[u] = dTime;
}

void build(int left, int right, int root)
{
    if (left == right)
    {
        int u = A[left];
        tree[root] = W[u] - E[u];
        return;
    }
    
    int mid = (left + right) / 2;
    
    build(left, mid, root * 2);
    build(mid + 1, right, root * 2 + 1);
    
    tree[root] = max(tree[root * 2], tree[root * 2 + 1]);
}

long long query(int left, int right, int a, int b, int root)
{
    if (left > b || right < a)
        return -INF;
    
    if (left >= a && right <= b)
        return tree[root];
    
    int mid = (left + right) / 2;
    
    return max(query(left, mid, a, b, root * 2), query(mid + 1, right, a, b, root * 2 + 1));
}

long long solve(int u, int par, multiset<long long>& s)
{
    long long res = -INF;
    long long maxx = -INF;
    
    if (!s.empty())
        res = W[u] - E[u] - *s.begin();
    
    if (par)
        s.insert(W[ parent[par] ] - E[par]);
    
    for (auto pr: X[u])
        if (pr.first != par)
        {
            int v = pr.first;
            long long curr = query(1, n, L[v], R[v], 1);
            
            if (maxx == -INF)
                maxx = curr;
            else
            {
                res = max(res, maxx + curr - W[par] - W[u] + 2 * E[u]);
                maxx = max(maxx, curr);
            }
            
            res = max(res, solve(v, u, s));
        }
    
    if (par)
        s.erase(s.find(W[ parent[par] ] - E[par]));
    
    return res;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(NULL);

    int t;
    cin >> t;

    while (t--)
    {
        cin >> n;
        
        for (int i = 1; i <= n; i++)
        {
            cin >> W[i];
            
            E[i] = 0;
            X[i].clear();
        }
        
        for (int i = 1; i <= n - 1; i++)
        {
            int u, v, w;
            cin >> u >> v >> w;
            
            X[u].push_back({v, w});
            X[v].push_back({u, w});
        }
        
        dTime = 0;
        dfs(1, 0);
        
        build(1, n, 1);
        multiset<long long> s;
        
        cout << solve(1, 0, s) << "\n";
    }

    return 0;
}