#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef long double LD;
typedef tuple<double,double,double> ddd;
#define mem(arr,val) memset((arr),(val),(sizeof(arr)))
const double eps = 1e-8;
const int INF = 0x3f3f3f;
const int Size = 2e6+5;
const double pi = acos(-1.0);
inline int sgn(double x) {return fabs(x)<eps?0:(x<0?-1:1);}
struct Point
{
    int x,y;
    Point(int x = 0,int y = 0):x(x),y(y){}
    bool operator<(const Point p) {return x < p.x || (x == p.x && y < p.y);}
    bool operator==(const Point p) {return x == p.x && y == p.y;}
    Point operator+(const Point p) {return Point(x+p.x,y+p.y);}
    Point operator-(const Point p) {return Point(x-p.x,y-p.y);}
};
typedef Point Vector;
inline int Cross(Vector A,Vector B) {return A.x*B.y-A.y*B.x;}
inline int Dot(Vector A,Vector B) {return A.x*B.x+A.y*B.y;}
inline double Distance(Point A,Point B) {return hypot(A.x-B.x,A.y-B.y);}
inline int Dist(Point A,Point B) {return hypot(A.x-B.x,A.y-B.y)*hypot(A.x-B.x,A.y-B.y);}
inline vector <Point> ConvexHull(vector <Point> p)
{
    sort(p.begin(),p.end());
    p.erase(unique(p.begin(),p.end()),p.end());
    int n = p.size(),m = 0;
    vector <Point> ch(n+1);
    for(int i = 0;i < n;++i)
    {
        while(m > 1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }
    int k = m;
    for(int i = n-2;~i;--i)
    {
        while(m > k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }
    if(n > 1) --m;
    ch.resize(m);
    return ch;
}
inline int Diameter(vector <Point>& points)
{
    vector <Point> p = ConvexHull(points);
    int n = p.size();
    if(n == 1) return 0;
    if(n == 2) return Dist(p[0],p[1]);
    p.push_back(p[0]);
    int ans = 0;
    for(int u = 0,v = 1;u < n;++u)
    {
        for(;;)
        {
            int diff = Cross(p[u+1]-p[u],p[v+1]-p[v]);
            if(diff <= 0)
            {
                ans = max(ans,Dist(p[u],p[v]));
                if(!diff) ans = max(ans,Dist(p[u],p[v+1]));
                break;
            }
            v = (v+1)%n;
        }
    }
    return ans;
}
int main(int argc,char *argv[])
{
    ios::sync_with_stdio(false);cin.tie(0);
    int t,n;cin>>t;
    while(t--)
    {
        cin>>n;
        vector <Point> p;
        for(int i = 0,x,y,w;i < n;++i)
        {
            cin>>x>>y>>w;
            p.push_back(Point(x,y));
            p.push_back(Point(x+w,y));
            p.push_back(Point(x,y+w));
            p.push_back(Point(x+w,y+w));
        }
        cout<<Diameter(p)<<'\n';
    }
    return 0;
}