#include <bits/stdc++.h>
using namespace std;
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
void solve() {
  long long n, sum = 0, cum = 0, A[201000], B[210100], p, q, l, i;
  vector<pair<long long, long long> > pp;
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> A[i];
  }
  for (i = 0; i < n; i++) {
    cin >> B[i];
  }
  for (i = 0; i < n; i++) {
    pp.push_back(make_pair(A[i], B[i]));
  }
  sort(pp.rbegin(), pp.rend());
  sum = 0;
  long long a = 0;
  for (auto p : pp) {
    if (p.first >= sum + p.second) {
      sum = sum + p.second;
    } else {
      a = 1000;
      q = max(sum, p.first);
      break;
    }
  }
  if (a != 1000) {
    cout << sum << "\n";
    ;
  } else {
    cout << q << "\n";
    ;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  long long i;
  t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}
