#include<bits/stdc++.h>
using namespace std;
#define int long long
#define endl "\n"
const int N=1e5+10;


int n;
struct sb{
	int v,w;
	friend bool operator < (sb a,sb b){
		return a.w<b.w;
	}
}a[N];

bool check(int x){
	priority_queue<int> q;
	for(int i=1;i<=n;i++){
		if(a[i].v>=x){
			q.push(a[i].w+a[i].v-x);
		}
	}
	for(int i=n;i>=1;i--){
		if(a[i].v<x){
			if(q.size()==0||q.top()<a[i].w) return false;
			q.pop();
		}
	}
	return true;
	
	
}

void solve(){
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i].v>>a[i].w;
	sort(a+1,a+n+1);
	int l=1,r=1e9+10;
	while(l<r){
		int mid=(l+r+1)>>1;
		if(check(mid)) l=mid;
		else r=mid-1;
	}
	cout<<l<<endl;
}

signed main()
{
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int t=1;
	cin>>t;
	while(t--)
		solve();
	return 0;
}