#include <iostream>
#include <cstdio>
#include <iomanip>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <bitset>
#include <stack>
#include <utility>
#include <numeric>
#include <algorithm>
#include <functional>
#include <cctype>
#include <complex>
#include <string>
#include <sstream>
#include <fstream>
#include <cassert>
using namespace std;

//common

typedef int  i32;
typedef long long i64,ll;
typedef long double ld;

#define BR "\n"
#define ALL(c) (c).begin(),(c).end()
#define REP(i,n) for(int i=0;i<(int)(n);++i)
#define FOR(i,l,r) for(int i=(int)l;i<(int)(r);++i)
#define EACH(it,o) for(auto it = (o).begin(); it != (o).end(); ++it)
#define IN(l,v,r) ((l)<=(v) && (v)<(r))

//config
//#define NDEBUG
//#define INF 1<<30
//#define EPS 1e-8
//const ll MOD =100000007;

//debug
#ifdef NDEBUG
#define DUMP(x)
#define DUMPLN(x)
#define DEBUG(x)
#define DEBUGLN(x)
#define LINE()
#define LINELN()
#define CHECK(exp,act)
#define STOP(e)
#else
#define DUMP(x)  cerr << #x << " = " << (x)
#define DUMPLN(x)  DUMP(x) <<endl
#define DEBUG(x) DUMP(x) << LINE() << " " << __FILE__
#define DEBUGLN(x) DEBUG(x)<<endl
#define LINE()    cerr<< " (L" << __LINE__ << ")"
#define LINELN()    LINE()<<endl
#define CHECK(exp,act)  if(exp!=act){DUMPLN(exp);DEBUGLN(act);}
#define STOP(e)  CHECK(e,true);if(!(e)) exit(1);
#endif

template<class T> inline string toString(const vector<T>& x) {
	stringstream ss;
	REP(i,x.size()){
		if(i!=0)ss<<" ";
		ss<< x[i];
	}
	return ss.str();
}

template<class T> inline string toString(const vector<vector<T> >& map) {
	stringstream ss;
	REP(i,map.size()){
		if(i!=0)ss<<BR;
		ss<< toString(map[i]);
	}
	return ss.str();
}
template<class K,class V>  string toString(map<K,V>& x) {
	string res;stringstream ss;
	for(auto& p:x)ss<< p.first<<":" << p.second<<" ";
	return ss.str();
}

string BITtoString(int bit){
    stringstream ss;
    while(bit!=0){ss<<(bit%2);bit/=2;}
    string res=ss.str();reverse(ALL(res));
    return res;
}

template<typename T,typename V> inline T pmod(T v,V MOD){
	return (v%MOD+MOD)%MOD;
}
#define nextInt(n) scanf("%d",&n)
#define defInt(n) int n;nextInt(n)
#define nextLong(n) scanf("%lld",&n)
#define defLong(n) ll n;nextLong(n)
#define nextDouble(n) scanf("%lf",&n)

class Task{
	public:
	ll r,w;
	Task(ll r,ll w):r(r),w(w){}
	 bool operator < (Task const &_r ) const{
	 	return  r<_r.r;
	 }
};

class Main{
	public:
	void run(){
	//	ifstream cin("in");
	//	ofstream cout( "out" );
		while(true){
			int N;cin >>N;
			if(N==0)return;
			vector<Task> ts;
			REP(i,N){
				ll r,w;cin >> r >> w;
				ts.push_back(Task(r,w));
			} 
			sort(ALL(ts));
			ll MR=0;REP(i,N)MR=max(MR,ts[i].r);
			ll sum=0;REP(i,N)sum+=ts[i].r;
			
			ll res;
			if(sum>=2*MR){
				res=sum;
			}else{
				res=2*MR;
				ll space=2*MR-sum;
				vector<bool> dp(space+1);
				dp[0]=true;
				for(int i=0;i<N-1;i++){
					for(int d=space;d>=0;d--){
						if(dp[d] && ts[i].w+d<=space)dp[ts[i].w+d]=true;
					}
				}
				ll useM=0;for(int d=0;d<=space;d++)if(dp[d])useM=d;
				res-=useM;
			}
			REP(i,N) res+=ts[i].w;

			cout << res<<endl;
		}
	}
};
int main(){
	cout <<fixed<<setprecision(3);	
	ios::sync_with_stdio(false);
	Main().run();
	return 0;
}

Measured memory_bytes: 1248