/*
Task: 1443C
Date: Dec 20, 2020
Author: aLittleLove (Minh Vu)
*/
#include<bits/stdc++.h>
#define rep(i,n) for (int i=0, _n=n; i<_n; i++)
#define FOR(i,a,b) for (int _a=(a), _b=(b), i=_a; _a<=_b?i<=_b:i>=_b; _a<=_b?i++:i--)
#define _mem(a, b) memset(a, (b), sizeof(a))
#define pb push_back
#define fi first
#define se second
#define sz(a) int((a).size())
using namespace std;
typedef long long ll;
typedef int64_t i64;
typedef pair<int, int> pii;
typedef vector<pii> vii;
typedef vector<int> vi;
const int N = 2e5 + 5;
const int inf = 1e9;
const int mod = 1e9 + 7;
const double pi = atan(1) * 4.0;
template<typename T, typename U> inline void mini(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> inline void maxi(T &x, U y) { if(x < y) x = y; }
int n;
pair<i64, i64> a[N];
bool check(i64 x)
{
i64 res = 0, cur = 0;
FOR(i,1,n)
{
if (a[i].fi <= x)
{
res = max(res, a[i].fi);
}
else
{
res = max(res, cur + a[i].se);
cur += a[i].se;
}
}
return res<=x;
}
void Solve()
{
cin >> n;
FOR(i,1,n) cin >> a[i].fi;
FOR(i,1,n) cin >> a[i].se;
i64 l = 0, r = 1e18;
i64 ans = 1e18;
while (l<=r)
{
i64 mid = (l + r)/2ll;
if (check(mid))
{
r = mid - 1;
ans = mid;
}
else l = mid + 1;
}
cout << ans << '\n';
}
int main()
{
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
//freopen("input.txt","r",stdin);
int nTest; cin >> nTest;
while (nTest--) Solve();
return 0;
}
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