#include <bits/stdc++.h>
using namespace std;
#define ll long long
int n;

struct dui {
	ll v;
	ll w;
} a[100005], b[100005]; //a按重量，b按能力
bool cmp1(dui a, dui b) {
	return a.w > b.w;
}

bool cmp2(dui a, dui b) {
	return (a.v + a.w) > (b.v + b.w);
}

bool check(ll v) {
	vector<ll>power;
	vector<ll>leizhui;

	for (int i = 0; i < n; i++)

		if (a[i].v < v)
			leizhui.push_back(a[i].w);

	for (int i = 0; i < n; i++)

		if (b[i].v > v)
			power.push_back(b[i].v + b[i].w - v);

	if (power.size() < leizhui.size())
		return false;

	for (int i = 0; i < leizhui.size(); i++)

		if (leizhui[i] > power[i])
			return false;
	return true;
}

void solve() {
	cin >> n;
	ll maxv = 0;
	ll minv = 10000000099;

	for (int i = 0; i < n; i++) {

		ll x, y;
		maxv = max(maxv, x);
		minv = min(minv, x);
		cin >> x >> y;
		a[i] = {x, y};
		b[i] = {x, y};
	}

	sort(a, a + n, cmp1);
	sort(b, b + n, cmp2);
	ll midv = (maxv + minv) >> 1;

	while (minv < maxv) {
		midv = (1 + maxv + minv) >> 1;

		if (check(midv))
			minv = midv;
		else
			maxv = midv - 1;
	}

	cout << maxv << endl;
}

int main() {
	int t;
	cin >> t;

	while (t--)
		solve();
}