#include <bits/stdc++.h>


using namespace std;
const long long mod = 1e9+7;

#define int long long

int ans;
int n, m, k;
int a[100020];

string cott = "aeiou";
string s[123456];

bool vow(char a) {return (cott.find((a)) != -1);}

void solve() {
    cin >> n;
    int sum = 0;
    vector <vector <int> > v;
    for(int i = 1; i <= n; i++) {
        cin >> m;
        vector <int> vv;
        for(int j = 1; j <= m; j++) {
            cin >> a[j];
            if(j <= m / 2 && m % 2 == 0) sum += a[j];
            if(m % 2 && j <= m / 2 + 1) vv.push_back(a[j]);
        }
        if(vv.size())
        v.push_back(vv);
    }
    vector <pair <int, int> > trr;
    for(int i = 0; i < v.size(); i++) {
        int cur = 0;
        for(int j = 0; j < v[i].size(); j++) {
            cur += v[i][j];
        }
        trr.push_back({cur, v[i].back()});
    }
    sort(trr.begin(), trr.end());
    reverse(trr.begin(), trr.end());
    int cur =1;
    for(int j = 0; j < trr.size(); j++, cur ^= 1)
        if(cur)
            sum += trr[j].first;
        else sum += trr[j].first - trr[j].second;
    cout << sum<<endl;
}
 main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int T;
    cin >> T;
    while(T--) {
        solve();
    }

}