#include<bits/stdc++.h>
#define f first
#define s second
#define mp make_pair
#define pi M_PI
#define inf 1<<30
#define eps (1e-5)
#define equals(a,b) (fabs((a)-(b))<eps)
using namespace std;

class Point{
public:
  double x,y;
  Point(double x=0,double y=0):x(x),y(y){}

  Point operator+(Point p){ return Point(x+p.x,y+p.y);}
  Point operator-(Point p){ return Point(x-p.x,y-p.y);}
  Point operator*(double k){ return Point(x*k,y*k);}
  Point operator/(double k){ return Point(x/k,y/k);}
  bool operator<(Point p)const{ return (x!=p.x ? x<p.x : y<p.y);}
  bool operator==(Point p)const{ return fabs(x-p.x)<eps && fabs(y-p.y)<eps;}

  double abs(){ return sqrt(norm());}
  double norm(){ return (x*x+y*y);}
};
typedef Point Vector;
typedef vector<Point> Polygon;

class Segment{
public:
  Point p1,p2;
  Segment(Point p1,Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;

class Circle{
public:
  Point c;
  double r;
  Circle(Point c=Point(),double r=0.0):c(c),r(r){}
};

double norm(Vector a){ return (a.x*a.x+a.y*a.y);}
double abs(Vector a){ return sqrt(norm(a));}
double dot(Vector a,Vector b){ return (a.x*b.x+a.y*b.y);}
double cross(Vector a,Vector b){ return (a.x*b.y-a.y*b.x);}

Point rotate(Point base,Point a,double r){
  Point b=a-base;
  a.x=b.x*cos((r/180)*M_PI)-b.y*sin((r/180)*M_PI);
  a.y=b.x*sin((r/180)*M_PI)+b.y*cos((r/180)*M_PI);
  a=a+base;
  return a;
}

double getDistanceLP(Line l,Point p){
  return abs(cross(l.p2-l.p1,p-l.p1)/abs(l.p2-l.p1));
}

bool iscrossCL1(Circle c,Line l){
  if((getDistanceLP(l,c.c)-c.r)<-eps)return true;
  return false;
}
bool iscrossCL2(Circle c,Line l){
  if((getDistanceLP(l,c.c)-c.r)<eps)return true;
  return false;
}

// ??¢???????????? return 4
// ?????\?????? return 3
// ????????? return 2
// ?????\?????? return 1
// ?????? return 0
int intersect(Circle a,Circle b){
  double dis=abs(a.c-b.c),sumr=a.r+b.r,minr=min(a.r,b.r),maxr=max(a.r,b.r);
  if((sumr-dis)<-eps)return 4;
  if(equals(sumr,dis))return 3;
  if((maxr-(dis+minr))<-eps)return 2;
  if(equals(dis+minr,maxr))return 1;
  return 0;
}

vector<Line> getCommonTangent(Circle a,Circle b){
  vector<Line> vp;
  int intersection=intersect(a,b);
  if(intersection==0)return vp;
  if(intersection==1){
    Vector v=b.c-a.c;
    if(b.r<a.r)v=(v*a.r)/abs(v);
    else v=(v*a.r*(-1))/abs(v);
    vp.push_back(Line(a.c+v,a.c+v));
    return vp;
  }
  if(intersection==3){
    Vector v=b.c-a.c;
    v=v*a.r/abs(v);
    vp.push_back(Line(a.c+v,a.c+v));
  }
  double d=abs(b.c-a.c),c,s;
  Vector v=(b.c-a.c)/d,v1=v*a.r,v2=v*b.r;
  Point p1,p2;

  c=sqrt(d*d-(a.r-b.r)*(a.r-b.r));
  s=(180*asin(c/d))/pi;

  if(a.r<b.r){
    vp.push_back(Line(rotate(a.c,a.c+v1,180-s),rotate(b.c,b.c-v2,360-s)));
    vp.push_back(Line(rotate(a.c,a.c+v1,180+s),rotate(b.c,b.c-v2,s)));
  }
  else {
    vp.push_back(Line(rotate(a.c,a.c+v1,s),rotate(b.c,b.c-v2,180+s)));
    vp.push_back(Line(rotate(a.c,a.c+v1,360-s),rotate(b.c,b.c-v2,180-s)));
  }
  if(intersection==2 || intersection==3)return vp;
  
  c=sqrt(d*d-(a.r+b.r)*(a.r+b.r));
  s=(180*asin(c/d))/pi;
  
  vp.push_back(Line(rotate(a.c,a.c+v1,s),rotate(b.c,b.c-v2,s)));
  vp.push_back(Line(rotate(a.c,a.c+v1,360-s),rotate(b.c,b.c-v2,360-s)));
  
  return vp;
}

int main()
{
  int n,a,b,c,d;

  while(1){
    cin>>n;
    if(n==0)break;
    vector<pair<Circle,Circle> > v;
    for(int i=0;i<n;i++){
      cin>>a>>b>>c>>d;
      v.push_back(mp(Circle(Point(a,b),c),Circle(Point(a,b),c+d)));
    }
    int ans=1;
    for(int i=0;i<n;i++){
      for(int j=i+1;j<n;j++){
	vector<Line> V;
	vector<Line> v1=getCommonTangent(v[i].f,v[j].f);
	vector<Line> v2=getCommonTangent(v[i].f,v[j].s);
	vector<Line> v3=getCommonTangent(v[i].s,v[j].f);
	vector<Line> v4=getCommonTangent(v[i].s,v[j].s);
	V.insert(V.begin(),v1.begin(),v1.end());
	V.insert(V.begin(),v2.begin(),v2.end());
	V.insert(V.begin(),v3.begin(),v3.end());
	V.insert(V.begin(),v4.begin(),v4.end());
	for(int k=0;k<V.size();k++){
	  int sum=0;
	  for(int z=0;z<n;z++){
	    if(!iscrossCL1(v[z].f,V[k]) && iscrossCL2(v[z].s,V[k]))sum++;
	  }
	  ans=max(ans,sum);
	}
      }
    }
    cout<<ans<<endl;
  }
  return 0;
}

Measured memory_bytes: 1284