#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
int v[N], w[N], n;
bool cmp1(int i, int j) 
{
   return w[i] > w[j];
}
bool cmp2(int i, int j) 
{
    return (v[i] + w[i]) > (v[j] + w[j]);
}
bool check(long long mid) 
{
    vector<int> zhong, gei;
    for (int i = 1; i <= n; i++) 
	{
        if (v[i] < mid) 
		{
			zhong.push_back(i);
		}
        else 
		{
			gei.push_back(i);
		}
    }
    if (zhong.size() > gei.size()) 
	{
		return false;
	}
    sort(zhong.begin(), zhong.end(),cmp1);
    sort(gei.begin(), gei.end(),cmp2);
    for (int i = 0; i < zhong.size(); i++) 
	{
        int x = v[gei[i]] - (w[zhong[i]] - w[gei[i]]);
        if (x < mid) 
		{
			return false;
		}
    }
    return true;
}

void solve() {
    cin>>n;
    for (int i = 1; i <= n; i++) {
    	cin>>v[i]>>w[i];
    }
    int l = 1, r = *max_element(v + 1, v + 1 + n);
    while (l < r) 
	{
        long long mid = (l + r + 1) >> 1;
        if (check(mid)) {
            l = mid;
        } else {
            r = mid - 1;
        }
    }
    printf("%d\n", l);
}

int main() {
//	freopen("int.txt","r",stdin);
//	freopen("12345.txt","w",stdout);
    int t;
    cin>>t;
    while (t--) {
        solve();
    }      
    return 0;
}