#include <bits/stdc++.h>
using namespace std;

using i64 = long long;

int __OneWan_2024 = [](){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	return 0;
}();

void sol() {
    int n;
    cin >> n;
    vector<int>v(n), w(n);
    for (int i = 0; i < n; i++)
        cin >> v[i] >> w[i];
    int l = 1, r = 1e9;

    auto check = [&](int mid) {
        vector<int>c1;
        set<int>st;
        for (int i = 0; i < n; i++) {
            if(v[i] < mid) c1.push_back(w[i]);
            else {
                st.insert(v[i] - mid + w[i]);
            }
        }
        sort(rbegin(c1), rend(c1));
        for (int i = 0; i < c1.size(); i++) {
            auto pos = st.lower_bound(c1[i]);
            if(pos == st.end()) return false;
            st.erase(pos);
        }
        return true;
    };

    while(l < r) {
        int mid = l + r + 1 >> 1;
        if(check(mid)) l = mid;
        else r = mid - 1;
    }

    cout << l << endl;
}

int main() {
    int t;
    cin >> t;
    while(t--)
        sol();
	return 0;
}