#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <climits>
#include <cassert>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <complex>
#include <stack>
#include <queue>
#include <list>
#include <set>
#include <map>
#include <bitset>
#include <functional>
#include <iterator>

using namespace std;

#define dump(n) cout<<"# "<<#n<<'='<<(n)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define iter(c) __typeof__((c).begin())
#define foreach(i,c) for(iter(c) i=(c).begin();i!=(c).end();++i)
#define all(c) (c).begin(),(c).end()
#define mp make_pair

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;
typedef pair<int,int> pii;

const int INFTY=1<<29;
const double EPS=1e-9;
const double PI=acos(-1);

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}
template<typename T>
ostream& operator<<(ostream& os,const vector<T>& a){
	os<<'[';
	rep(i,a.size()) os<<(i?" ":"")<<a[i];
	return os<<']';
}

struct Point{
	double x,y;
	Point(){}
	Point(double x,double y):x(x),y(y){}
};
Point operator+(Point a,Point b){
	return Point(a.x+b.x,a.y+b.y);
}
Point operator-(Point a,Point b){
	return Point(a.x-b.x,a.y-b.y);
}
Point operator*(double c,Point p){
	return Point(c*p.x,c*p.y);
}
double Abs(Point p){
	return sqrt(p.x*p.x+p.y*p.y);
}
double Abs2(Point p){
	return p.x*p.x+p.y*p.y;
}
double Dot(Point a,Point b){
	return a.x*b.x+a.y*b.y;
}
double Cross(Point a,Point b){
	return a.x*b.y-a.y*b.x;
}
Point Rot(Point p,double t){
	return Point(cos(t)*p.x-sin(t)*p.y,sin(t)*p.x+cos(t)*p.y);
}

struct Line{
	Point pos,dir;
	Line(){}
	Line(Point p,Point d):pos(p),dir(d){}
	Line(double px,double py,double dx,double dy):pos(px,py),dir(dx,dy){}
};
Point Proj(Line l,Point p){
	Point a=p-l.pos,b=l.dir;
	return l.pos+Dot(a,b)/Abs2(b)*b;
}
double DistLP(Line l,Point p){
	return Abs(Proj(l,p)-p);
}

struct Circle{
	Point center;
	double radius;
	Circle(){}
	Circle(Point c,double r):center(c),radius(r){}
	Circle(double x,double y,double r):center(x,y),radius(r){}
};
vector<Line> Intangent(Circle c1,Circle c2)
{
	double r1=c1.radius,r2=c2.radius;
	double d=Abs(c1.center-c2.center);
	vector<Line> res;
	if(d>r1+r2+EPS){
		double t=acos((r1+r2)/d);
		rep(i,2){
			Point p1=c1.center+Rot(r1/d*(c2.center-c1.center),(i?1:-1)*t);
			Point p2=c2.center+Rot(r2/d*(c1.center-c2.center),(i?1:-1)*t);
			res.push_back(Line(p1,p2-p1));
		}
	}
	else if(d>r1+r2-EPS){
		Point p=c1.center+r1/d*(c2.center-c1.center);
		res.push_back(Line(p,Rot(p-c1.center,PI/2)));
	}
	return res;
}
vector<Line> Extangent(Circle c1,Circle c2)
{
	double r1=c1.radius,r2=c2.radius;
	double d=Abs(c1.center-c2.center);
	vector<Line> res;
	if(d>abs(r2-r1)+EPS){
		double t=acos((r1-r2)/d);
		rep(i,2){
			Point p1=c1.center+Rot(r1/d*(c2.center-c1.center),(i?1:-1)*t);
			Point p2=c2.center+Rot(r2/d*(c2.center-c1.center),(i?1:-1)*t);
			res.push_back(Line(p1,p2-p1));
		}
	}
	else if(d>abs(r2-r1)-EPS){
		Point p=c1.center+r1/d*(c2.center-c1.center);
		res.push_back(Line(p,Rot(p-c1.center,PI/2)));
	}
	return res;
}

vector<Line> Tangent(Circle c1,Circle c2)
{
	vector<Line> in=Intangent(c1,c2),ex=Extangent(c1,c2);
	in.insert(in.end(),all(ex));
	return in;
}

int main()
{
	for(int n;cin>>n,n;){
		vector<Circle> js,ms;
		rep(i,n){
			int x,y,r,m; cin>>x>>y>>r>>m;
			js.emplace_back(x,y,r);
			ms.emplace_back(x,y,r+m);
		}
		
		vector<Line> ts;
		rep(i,n) repi(j,i+1,n){
			vector<Line> temp;
			temp=Tangent(js[i],js[j]); ts.insert(ts.end(),all(temp));
			temp=Tangent(ms[i],ms[j]); ts.insert(ts.end(),all(temp));
			temp=Tangent(js[i],ms[j]); ts.insert(ts.end(),all(temp));
			temp=Tangent(ms[i],js[j]); ts.insert(ts.end(),all(temp));
		}
		
		int res=1;
		for(Line t:ts){
			int temp=0;
			rep(i,n){
				double d=DistLP(t,js[i].center);
				if(js[i].radius-EPS<d && d<ms[i].radius+EPS)
					temp++;
			}
			res=max(res,temp);
		}
		cout<<res<<endl;
	}
	
	return 0;
}

Measured memory_bytes: 2804