T = int(input())
anss = []
for _ in range(T):
n = int(input())
dic = {}
a = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]
c = [[] for i in range(n)]
for i in range(n):
c[i].append(a[i])
c[i].append(b[i])
ssum = 0
ans = int(1e9)
c.sort()
for i in range(n-1,-1,-1):
ans = min(ans , max(ssum,c[i][0]))
ssum += c[i][1]
anss.append(str(min(ans,ssum)))
print('\n'.join(anss))#include<bits/stdc++.h>
#define ll long long int
#define ld long double
#define ull unsigned long long int
#define PI 3.14159
#define llinf LLONG_MAX
#define inf INT_MAX
#define _inf INT_MIN
#define _llinf LLONG_MIN
using namespace std;
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
ll t;
cin>>t;
while(t--) {
ll n;
cin>>n;
vector<pair<ll, ll>> v(n);
for(int i=0; i<n; i++) {
cin>>v[i].first;
}
for(int i=0; i<n; i++) {
cin>>v[i].second;
}
sort(v.begin(), v.end());
ll suff[n];
suff[n-1] = v[n-1].second;
for(int i=n-2; i>=0; i--) {
suff[i] = suff[i+1] + v[i].second;
}
ll ans = min(suff[0], v[n-1].first);
for(int i=n-2; i>=0; i--) {
ll x = max(v[i].first, suff[i+1]);
ans = min(ans, x);
}
cout<<ans<<"\n";
// cout<<suff[0]<<"\n";
}
}1301A - Three Strings | 460A - Vasya and Socks |
1624C - Division by Two and Permutation | 1288A - Deadline |
1617A - Forbidden Subsequence | 914A - Perfect Squares |
873D - Merge Sort | 1251A - Broken Keyboard |
463B - Caisa and Pylons | 584A - Olesya and Rodion |
799A - Carrot Cakes | 1569B - Chess Tournament |
1047B - Cover Points | 1381B - Unmerge |
1256A - Payment Without Change | 908B - New Year and Buggy Bot |
979A - Pizza Pizza Pizza | 731A - Night at the Museum |
742A - Arpa’s hard exam and Mehrdad’s naive cheat | 1492A - Three swimmers |
1360E - Polygon | 1517D - Explorer Space |
1230B - Ania and Minimizing | 1201A - Important Exam |
676A - Nicholas and Permutation | 431A - Black Square |
474B - Worms | 987B - High School Become Human |
1223A - CME | 1658B - Marin and Anti-coprime Permutation |