#include <bits/stdc++.h>
// #include <bits/extc++.h>
// using namespace __gnu_pbds;
// gp_hash_table<int, bool> hs;
#define bit1(x) __builtin_popcount(x)
#define all(x) (x).begin(), (x).end()
#define lowbit(i) ((i) & -(i))
#define ull unsigned long long
#define int long long
// #define ll long long
#define Genshin return
#define Impact 0
#define endl '\n'
using namespace std;
const int mod = 998244353;
const int N = 2e5 + 10;
int ksm(int base, int n)
{
    int res = 1;
    while (n > 0)
    {
        if (n & 1)
            res = (res * base) % mod;
        base = (base * base) % mod;
        n >>= 1;
    }
    return res;
}
int n;
pair<int, int> a[100010];
bool cmp(pair<int, int> x, pair<int, int> y)
{
    if (x.first + x.second == y.first + y.second)
        return x.first < y.first;
    return x.first + x.second < y.first + y.second;
}
bool check(int k)
{
    vector<bool> b(n + 1);
    vector<pair<int, int>> c;
    for (int i = 1; i <= n; i++)
    {
        if (a[i].second < k)
        {
            b[i] = 1;
        }
        else
        {
            c.push_back(a[i]);
        }
    }
    sort(all(c), cmp);
    int j = n, i = c.size() - 1;
    while (i >= 0 && j > 0)
    {
        while (j > 0 && b[j] == 0)
        {
            j--;
        }
        if (j <= 0)
            break;
        while (i >= 0 && (c[i].second - max(0LL, a[j].first - c[i].first)) < k)
        {
            i--;
        }
        if (i < 0)
            break;
        j--;
        i--;
    }
    if (j <= 0)
        return 1;
    return 0;
}
void solve()
{
    cin >> n;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i].second >> a[i].first;
    }
    sort(a + 1, a + n + 1);
    int l = 1, r = 1e9;
    int ans = 1;
    while (l <= r)
    {
        int mid = (l + r) >> 1;
        if (check(mid))
        {
            ans = mid;
            l = mid + 1;
        }
        else
        {
            r = mid - 1;
        }
    }
    cout << ans << endl;
    return;
}
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
    int tt = 1;
    cin >> tt;
    while (tt--)
    {
        solve();
    }
    Genshin Impact;
}