B

#include <bits/stdc++.h>

using namespace std;

#define ll     long long
#define _test   int _TEST; cin>>_TEST; while(_TEST--)
#define ff     first
#define ss     second
#define pb     push_back

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);

    _test
    {
        int n;
        cin>>n;

        vector<int> a;
        vector<int> b;

        int mmin = 1e9;

        for(int i=0; i<n; i++)
        {
            int k;
            cin>>k;

            b.resize(k);

            for(auto &e: b) cin>>e;

            sort(b.begin(), b.end());

            mmin = min(mmin, b[0]);

            a.pb(b[1]);
        }

        sort(a.begin(), a.end());

        a[0] = mmin;

        cout<<accumulate(a.begin(), a.end(), 0ll)<<"\n";
    }
}