B.Groundhog and Apple Tree
心態大崩，賽時一句話寫錯，賽後一A，我好菜

typedef long long ll;
const int N=1e5+10;
#define int ll
typedef pair<int,int> pii;
int n,m;
int a[N];
vector<pii>v[N];
int dp[N][2];
void dfs(int x,int fa){
    dp[x][1]=a[x];
    priority_queue <pii,vector<pii>,greater<pii> > q;
    priority_queue <pii>q1;
    for (pii i:v[x]){
        if (i.first==fa)continue;
        dfs(i.first,x);
        dp[i.first][1]-=2*i.second;
        dp[i.first][0]+=i.second;
        dp[x][1]+=dp[i.first][1];
        if (dp[i.first][1]>=0){
            q.push({dp[i.first][0],dp[i.first][1]});
        }
        else{
            q1.push({dp[i.first][0]+dp[i.first][1],dp[i.first][0]});
        }
    }
    int r=a[x];
    int o=0;
    while (!q.empty()){
        pii t=q.top();q.pop();
        if (r<t.first)o+=t.first-r,r=t.first;
        r+=t.second;
    }
    while (!q1.empty()){
        pii t=q1.top();q1.pop();
        int e=t.first-t.second;
        if (r<t.second)o+=t.second-r,r=t.second;
        r+=e;
    }
    dp[x][0]=max(o,-dp[x][1]);
}
signed main(){
    int T,x,y,z;
    scanf("%lld",&T);
    while (T--){
        scanf("%lld",&n);
        for (int i=1;i<=n;i++){
            scanf("%lld",&a[i]);
            v[i].clear();
        }
        for (int i=1;i<n;i++){
            scanf("%lld%lld%lld",&x,&y,&z);
            v[x].push_back({y,z});v[y].push_back({x,z});
        }
        dfs(1,0);
        printf("%lld\n",dp[1][0]);
    }
    return 0;
}