#include<bits/stdc++.h>

using namespace std;

#define endl '\n'
#define hh cout<<endl;
#define No cout<<"No"<<endl;
#define Yes cout<<"Yes"<<endl;
#define NO cout<<"NO"<<endl;
#define YES cout<<"YES"<<endl;
typedef long long ll;
int n;
int v[100001],w[100001];
vector<int> a,b;
bool cmpa(int a,int b)
{
    return w[a]>w[b];
}
bool cmpb(int a,int b)
{
    return (v[a]+w[a])>(v[b]+w[b]);
}
bool check(ll x)
{
    a.clear();
    b.clear();
    int i;
    for(i=1;i<=n;i++)
    {
        if(v[i]<x)
            a.push_back(i);
        else
            b.push_back(i);
    }
    if(a.size()>b.size())
        return 0;
    sort(a.begin(),a.end(),cmpa);
    sort(b.begin(),b.end(),cmpb);
    int l = a.size();
    for(i=0;i<l;i++)
    {
        int t = v[b[i]]-w[a[i]]+w[b[i]];
        if(t<x)
            return 0;
    }
    return 1;
}
void solve()
{
    cin>>n;
    int i;
    for(i=1;i<=n;i++)
        cin>>v[i]>>w[i];
    int l = 1,r = 1e9;
    while(l<r)
    {
        ll mid = (l+r+1)/2;
        if(check(mid))
            l = mid;
        else
            r = mid-1;
    }
    cout<<l<<endl;
    return;
}
signed main()
{
    int T = 1;
    cin>>T;
    while(T--)
        solve();
    return 0;
}