#include <cstdio>
#include <iostream>
#include <vector>
#include <list>
#include <cmath>
#include <fstream>
#include <algorithm>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <complex>
#include <iterator>
#include <cstdlib>
#include <cstring>
#include <sstream>

using namespace std;

#define EPS (1e-10)
#define EQ(a,b) (abs((a) - (b)) < EPS)
#define EQV(a,b) (EQ((a).real(),(b).real()) && EQ((a).imag(),(b).imag()))

typedef complex<double> P;
typedef pair<P,P> Edge;
typedef long long ll;

const double PI=4*atan(1.0);
const int MAX_SIZE = 10000;

// àÏ
double dot(P a, P b) {
  return (a.real() * b.real() + a.imag() * b.imag());
}
// OÏ
double cross(P a, P b) {
  return (a.real() * b.imag() - a.imag() * b.real());
}
// _cª¼üabãÉ é©È¢©
int is_point_on_line(P a, P b, P c) {
  return EQ( cross(b-a, c-a), 0.0 );
}
// 2¼üÌ¼s»è
int is_orthogonal(P a1, P a2, P b1, P b2) {
  return EQ( dot(a1-a2, b1-b2), 0.0 );
}
// 2¼üÌ½s»è
int is_parallel(P a1, P a2, P b1, P b2) {
  return EQ( cross(a1-a2, b1-b2), 0.0 );
}
// _a,bðÊé¼üÆ_cÌÔÌ£
double distance_l_p(P a, P b, P c) {
  return abs(cross(b-a, c-a)) / abs(b-a);
}
// _a,bð[_Æ·éüªÆ_cÆÌ£
double distance_ls_p(P a, P b, P c) {
  if ( dot(b-a, c-a) < EPS ) return abs(c-a);
  if ( dot(a-b, c-b) < EPS ) return abs(c-b);
  return abs(cross(b-a, c-a)) / abs(b-a);
}
// _ª½p`ÌÉ¶Ý·é©Ç¤©
bool isInPolygon(vector<P> &points,P s){
	if(points.size()==1)return false;
	vector<P> v;
	for(int i=0;i<(int)points.size();i++)v.push_back(points[i]-s);
	int sign=0;
	for(int i=1;i<=(int)v.size();i++){
		int prv=(i-1+v.size())%v.size();
		int cur=i%v.size();
		double c=cross(v[prv],v[cur]);
		if(EQ(c,0))continue;
		else if(sign==0){
			if(c>0)sign=1;
			else sign=-1;
		}
		else{
			if(sign==-1&&c>0)return false;
			else if(sign==1&&c<0)return false;
		}
	}
	return true;
}
struct Rec{
	vector<P> p;
};
// a1,a2ð[_Æ·éüªÆb1,b2ð[_Æ·éüªÌð·»è
int is_intersected_ls(P a1, P a2, P b1, P b2) {
    // üªª½sÈêÍdÈÁÄ¢È¢±ÆÉ·é
    if(abs(cross(a2-a1,b2-b1)) < EPS){
        return 0;
    }
    return ( cross(a2-a1, b1-a1) * cross(a2-a1, b2-a1) < EPS ) &&
        ( cross(b2-b1, a1-b1) * cross(b2-b1, a2-b1) < EPS );
}// aÆbÌé`ªÚµÄ¢é©Ç¤©(Ç¿ç©ªÇ¿©çðÜñÅ¢éàÌàÓ­Þ
bool isTouchRectangle(Rec &a,Rec &b){
	// aÌe¸_ªbÌÉ¶ÝµÄ¢é©`FbN
	for(int i=0;i<4;i++)if(isInPolygon(b.p,a.p[i]))return true;
	// t
	for(int i=0;i<4;i++)if(isInPolygon(a.p,b.p[i]))return true;
	// eÓª¼ûÌÇê©ÌÓÆÚµÄ¢é©
	for(int i=0;i<4;i++){
		int curi=i;
		int prvi=(i-1+4)%4;
		for(int j=0;j<4;j++){
			int curj=j;
			int prvj=(j-1+4)%4;
			if(is_intersected_ls(a.p[curi],a.p[prvi],b.p[curj],b.p[prvj]))return true;
		}
	}
	return false;
}
// a1,a2ð[_Æ·éüªÆb1,b2ð[_Æ·éüªÌð_vZ
P intersection_ls(P a1, P a2, P b1, P b2) {
  P b = b2-b1;
  double d1 = abs(cross(b, a1-b1));
  double d2 = abs(cross(b, a2-b1));
  double t = d1 / (d1 + d2);

  return a1 + (a2-a1) * t;
}
// a1,a2ðÊé¼üÆb1,b2ðÊé¼üÌð·»è
int is_intersected_l(P a1, P a2, P b1, P b2) {
  return !EQ( cross(a1-a2, b1-b2), 0.0 );
}
// a1,a2ðÊé¼üÆb1,b2ðÊé¼üÌð_vZ
P intersection_l(P a1, P a2, P b1, P b2) {
  P a = a2 - a1; P b = b2 - b1;
  return a1 + a * cross(b, b1-a1) / cross(b, a);
}
// PÊxNgðßé
P normalVector(P p){
	return p/abs(p);
}
// @üxNgðßé
P unitVector(P a){
	return P(-a.imag(),a.real());
}
// PÊ@üxNgðßé
P unitNormalVector(P tmp){
	P e=P(-tmp.imag(),tmp.real());
	e/=abs(e);
	return e;
}
// ÀWÌñ](ÀWpÉ é_ð,¼vñèÉa(WA)ñ])
P roundPoint(P p,double a){
	return P(cos(a)*p.real()-sin(a)*p.imag(),sin(a)*p.real()+cos(a)*p.imag());
}
/*
~üÆüªÌð·»è
*/
bool isCircleCrossLine(P a,P b,P c,double r){
	double d1 = abs(a-c);
	double d2 = abs(b-c);
    // üªªÉÜÜêéÆ«A±±ÌRgAEgðÍ¸¹Îtrue(ð·)ÆÈé
	//if(d1<r&&d2<r)
	//	return true;
	double d = distance_ls_p(a,b,c);
	return (EQ(d,r)||d<r);
}
// Op`ÌàÉ_ª é©Ç¤©
// OÏÌ³ª·×Ä¯¶ÈçàÉ_ è
bool isInTriangle(P p1,P p2,P p3,P s){
	P a=p1-s;
	P b=p2-s;
	P c=p3-s;
	return ((cross(a,b)>0&&cross(b,c)>0&&cross(c,a)>0)||(cross(a,b)<0&&cross(b,c)<0&&cross(c,a)<0));
}
// é`ÌÉ_ª¶Ý·é©Ç¤©
bool isInRectangle(P p1,P p2,P p3,P p4,P s){
	P a=p1-s;
	P b=p2-s;
	P c=p3-s;
    P d=p4-s;
	return ((cross(a,b)>0&&cross(b,c)>0&&cross(c,d)>0&&cross(d,a)>0)
        ||(cross(a,b)<0&&cross(b,c)<0&&cross(c,d)<0&&cross(d,a)<0));
}
// Op`ÌÊÏðÀW©çvZ
double calcAreaOfTriangle(P a,P b,P c){
	return abs((b.real()-a.real())*(c.imag()-a.imag()) - (c.real()-a.real())*(b.imag()-a.imag()))/2;
}
// ^¦çê½~ÌÍÍàÉ_ª¶Ý·é©Ç¤©
bool isContainingDot(P c,double r,P a){
	return (((c.real()-a.real())*(c.real()-a.real())
		+(c.imag()-a.imag())*(c.imag()-a.imag())<r*r)
		||EQ((c.real()-a.real())*(c.real()-a.real())
		+(c.imag()-a.imag())*(c.imag()-a.imag()),r*r));
}
// ½p`ÌÊÏö®
double calcPolygonArea(vector<P> p){
	double sum=0;
	for(int i = 0; i < p.size(); i++)
		sum+=cross(p[i],p[(i+1)%(p.size())]);
	return sum/2;
}
// 2xNgÔÌpx
// a©çbÖ¶üèÅ½x©(0->2*PI)
double diffAngle(P a,P b){
    double angle=atan2(cross(a,b),dot(a,b));
    if(angle<0)
        return 2*PI+angle;
    return angle;
}
// 2ÂÌxNgÌdÈÁÄ¢éªÌ·³ðÔ·
// àµdÈÁÄ¢È¯êÎ0ðÔ·
double multipleLength(P a,P b,P c,P d){
    Edge e1=make_pair(a,b);
    Edge e2=make_pair(c,d);
    // ½sÅ é©Ç¤©
    if(!(is_parallel(e1.first,e2.first,e1.second,e2.second)
        &&is_parallel(e1.first,e1.second,e2.first,e2.second)))
        return 0;
    double dist=0;
    // ¼ûæÁÄ¢é
    if(EQ(distance_ls_p(e1.first,e1.second,e2.first),0)&&EQ(distance_ls_p(e1.first,e1.second,e2.second),0))
        dist=abs(e2.first-e2.second);
    else if(EQ(distance_ls_p(e2.first,e2.second,e1.first),0)&&EQ(distance_ls_p(e2.first,e2.second,e1.second),0))
        dist=abs(e1.first-e1.second);
    else if(EQ(distance_ls_p(e1.first,e1.second,e2.first),0)){
        // Ç¿çªüãÉ é©
        if(EQ(distance_ls_p(e2.first,e2.second,e1.first),0))
            dist=abs(e1.first-e2.first);
        else
            dist=abs(e1.second-e2.first);
    }
    else if(EQ(distance_ls_p(e1.first,e1.second,e2.second),0)){
        if(EQ(distance_ls_p(e2.first,e2.second,e1.first),0))
            dist=abs(e1.first-e2.second);
        else
            dist=abs(e1.second-e2.second);
    }
    return dist;
}
// 2_ðÊé¼arÌ~Ì_ðßé
pair<P,P> calcCircleCenterPoint(P dot1,P dot2,double r){
    double v=abs(dot1-dot2);
    double x = sqrt(r*r - (v/2)*(v/2));
    // ñgÌPÊ@üxNg
    P hose[2];
    double x1=-(dot1.imag()-dot2.imag());
    double y1=(dot1.real() - dot2.real());
    hose[0]=P(x1,y1);
    double y2=-y1;
    double x2=-x1;
    hose[1]=P(x2,y2);
    double dd1=abs(hose[0]);
    double dd2=abs(hose[1]);
    hose[0]/=dd1;hose[0]*=x;
    hose[1]/=dd2;hose[1]*=x;
    P tmp=(dot1+dot2);
    tmp/=2;
    hose[0]+=tmp;
    hose[1]+=tmp;
    return make_pair(hose[0],hose[1]);
}
// 4üªª[_ÈOÅNXµÄ¢é©Ç¤©ð»è
bool checkCross(const vector<Edge> &vec){
    for(int i=0;i<vec.size();i++){
        for(int j=i+1;j<vec.size();j++){
            // üªªNXµÄ¢é©Ç¤©
            if(is_intersected_ls(vec[i].first,vec[i].second,vec[j].first,vec[j].second)){
                // µÄ¢éêA[_ÈOÅNXµÄ¢éÈçAfalse
                P p=intersection_ls(vec[i].first,vec[i].second,vec[j].first,vec[j].second);
                if(!(EQ(p,vec[i].first)||EQ(p,vec[i].second)))
                    return false;
            }
        }
    }
    return true;
}
// ø«Å^¦çê½4ÂÌ_ªé`ðìéÇ¤©ð»è
bool checkRec(const vector<P> &squ){
    vector<int> v;
    for(int i=0;i<squ.size();i++)v.push_back(i);
    do{
        vector<Edge> ve;
        for(int i=0;i<4;i++)
            ve.push_back(make_pair(squ[v[i]],squ[v[(i+1)%4]]));
        // ±±Å·×ÄÌüªªNX·é©Ç¤©ðvZ
        if(checkCross(ve)){
            // üªÌ·³ðmF
            if(EQ(abs(ve[0].first-ve[0].second),abs(ve[2].first-ve[2].second)))
                if(EQ(abs(ve[1].first-ve[1].second),abs(ve[3].first-ve[3].second)))
                    // ¼s
                    if(is_orthogonal(ve[0].first,ve[0].second,ve[1].first,ve[1].second))
                        if(is_orthogonal(ve[2].first,ve[2].second,ve[3].first,ve[3].second))
                        return true;
        }
    }while(next_permutation(v.begin(),v.end()));
    return false;
}
// ø«Å^¦çê½4ÂÌ_ª³û`ðìé©Ç¤©ð»è
bool checkSqu(const vector<P> &squ){
    vector<int> v;
    for(int i=0;i<squ.size();i++)v.push_back(i);
    do{
        vector<Edge> ve;
        for(int i=0;i<4;i++)
            ve.push_back(make_pair(squ[v[i]],squ[v[(i+1)%4]]));
        // ±±Å·×ÄÌüªªNX·é©Ç¤©ðvZ
        if(checkCross(ve)){
            // üªÌ·³ðmF
            double d=abs(ve[0].first-ve[0].second);
            for(int i=1;i<4;i++){
                double d2=abs(ve[i].first-ve[i].second);
                if(!EQ(d,d2))return false;
            }
            // ¼smF
            if(is_orthogonal(ve[0].first,ve[0].second,ve[1].first,ve[1].second))
                if(is_orthogonal(ve[2].first,ve[2].second,ve[3].first,ve[3].second))
                    return true;
        }
    }while(next_permutation(v.begin(),v.end()));
    return false;
}
// ñ~Ì¤ÊÚüð\¬·é4¼üðßé(ñ~Í¨Ý¢Úµ½èÇ¿ç©ðÓ­ñ¾èµÈ¢)
vector<pair<P,P> > calcCommonTangentialLine(P p1,double r1,P p2,double r2){
	vector<pair<P,P> > res;
	if(r1>r2){
		swap(r1,r2);
		swap(p1,p2);
	}
	// ¤ÊOÚü
	{
		double d=abs(p1-p2);
		double a=abs(r1-r2);
		double b=sqrt(d*d-a*a);
		double sita=acos(b/d);
		P e=normalVector(roundPoint((roundPoint((p2-p1),sita)),PI/2));
		res.push_back(make_pair(e*r1+p1,e*r2+p2));
		P e2=normalVector(roundPoint((roundPoint((p2-p1),-sita)),-PI/2));
		res.push_back(make_pair(e2*r1+p1,e2*r2+p2));
	}
	// ¤ÊàÚü
	{
		P cp=(r1*p1+r2*p2)/(r1+r2);
		double u=abs(cp-p1);
		double sita=acos(r1/u);
		P e=normalVector(roundPoint(cp-p1,sita));
		res.push_back(make_pair(e*r1+p1,-e*r2+p2));
		P e2=normalVector(roundPoint(cp-p1,-sita));
		res.push_back(make_pair(e2*r1+p1,-e2*r2+p2));
	}
	return res;
}

class Circle{
public:
	double r;
	double m;
	P p;
};
Circle cs[100];

int main(){
	int N;
	while(cin>>N&&N){
		for(int i=0;i<N;i++){
			double x,y;
			cin>>x>>y>>cs[i].r>>cs[i].m;
			cs[i].p=P(x,y);
		}
		if(N==1){
			cout<<1<<endl;
			continue;
		}
		int maxC=0;
		for(int i=0;i<N;i++){
			for(int j=i+1;j<N;j++){
				for(int p=0;p<2;p++){
					for(int q=0;q<2;q++){
						double a=p?cs[i].m:0;
						double b=q?cs[j].m:0;
						vector<pair<P,P> > res
						=calcCommonTangentialLine(cs[i].p,cs[i].r+a,cs[j].p,cs[j].r+b);
						// »ê¼êÌÚüÉÂ¢Ä²×é
						for(int k=0;k<(int)res.size();k++){
							// ±ÌÚüÅ¢­ÂÆêé©
							int cnt=0;
							P p1=res[k].first;
							P p2=res[k].second;
							for(int l=0;l<N;l++){
								double d=distance_l_p(res[k].first,res[k].second,cs[l].p)-cs[l].r;
								if(EQ(d,0)||EQ(d,cs[l].m)||(d>0&&d<cs[l].m))cnt++;
							}
							maxC=max(maxC,cnt);
						}
					}
				}
			}
		}
		cout<<maxC<<endl;
	}

	return 0;
}

Measured memory_bytes: 0