#include <iostream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <cassert>
#include <cctype>
#include <cmath>
#include <complex>
#include <cstdio>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using namespace std;

#define EPS 1e-9
#define INF 1e9
#define PI 4.0*atan(1.0)
#define rep(i,n) for(int i=0;i<n;i++)

typedef complex<double> P;
typedef vector<P> G;

namespace std{
  bool operator < (const P& a, const P& b) {
    return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
  }
}

double cross(const P& a, const P& b) {
  return imag(conj(a)*b);
}
double dot(const P& a, const P& b) {
  return real(conj(a)*b);
}

struct L : public vector<P> {
  L(){}
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};

struct C {
  P p; double r;
  C(const P &p, double r) : p(p), r(r) { }
};

int ccw(P a, P b, P c) {
  b -= a; c -= a;
  if (cross(b, c) > 0)   return +1;       // counter clockwise
  if (cross(b, c) < 0)   return -1;       // clockwise
  if (dot(b, c) < 0)     return +2;       // c--a--b on line
  if (norm(b) < norm(c)) return -2;       // a--b--c on line
  return 0;
}

bool intersectLL(const L &l, const L &m) {
  return abs(cross(l[1]-l[0], m[1]-m[0])) > EPS || // non-parallel
         abs(cross(l[1]-l[0], m[0]-l[0])) < EPS;   // same line
}
bool intersectLS(const L &l, const L &s) {
  return cross(l[1]-l[0], s[0]-l[0])*       // s[0] is left of l
         cross(l[1]-l[0], s[1]-l[0]) < EPS; // s[1] is right of l
}
bool intersectLP(const L &l, const P &p) {
  return abs(cross(l[1]-p, l[0]-p)) < EPS;
}
bool intersectSS(const L &s, const L &t) {
  return ccw(s[0],s[1],t[0])*ccw(s[0],s[1],t[1]) <= 0 &&
         ccw(t[0],t[1],s[0])*ccw(t[0],t[1],s[1]) <= 0;
}
bool intersectSP(const L &s, const P &p) {
  return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS; // triangle inequality
}

P projection(const L &l, const P &p) {
  double t = dot(p-l[0], l[0]-l[1]) / norm(l[0]-l[1]);
  return l[0] + t*(l[0]-l[1]);
}
P reflection(const L &l, const P &p) {
  return p + 2.0 * (projection(l, p) - p);
}
double distanceLP(const L &l, const P &p) {
  return abs(p - projection(l, p));
}
double distanceLL(const L &l, const L &m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m[0]);
}
double distanceLS(const L &l, const L &s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s[0]), distanceLP(l, s[1]));
}
double distanceSP(const L &s, const P &p) {
  const P r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s[0] - p), abs(s[1] - p));
}
double distanceSS(const L &s, const L &t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),
             min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}
P crosspoint(const L &l, const L &m) {
  double A = cross(l[1] - l[0], m[1] - m[0]);
  double B = cross(l[1] - l[0], l[1] - m[0]);
  if (abs(A) < EPS && abs(B) < EPS) return m[0]; // same line
  if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
  return m[0] + B / A * (m[1] - m[0]);
}

int N,bug=0;
double r[100],m[50];
P p[100];

int main(){
	while(cin>>N&&N){
		double x,y;
		rep(i,N){
			cin>>x>>y>>r[i]>>m[i];
			p[i]=p[N+i]=P(x,y);
			r[N+i]=r[i]+m[i];
		}
		int ans=0;
		rep(i,N*2)for(int j=i+1;j<N*2;j++){
			if(j==i+N)continue;
			P p1=p[i],p2=p[j],p3=p2-p1;
			double r1=r[i],r2=r[j],d=abs(p3);
			int flag=r1+r2<d+1e-5;
			double t1=asin((r2-r1)/d)+PI/2.0,t2=(r1+r2<d?PI/2.0-asin((r1+r2)/d):0.0);//cout<<t1<<" "<<t2<<" "<<(r1+r2)/d<<endl;
			P P1=p1+p3/abs(p3)*r1*P(cos(t1),sin(t1)),P2=p2+p3/abs(p3)*r2*P(cos(t1),sin(t1));
			P P3=p1+p3/abs(p3)*r1/P(cos(t1),sin(t1)),P4=p2+p3/abs(p3)*r2/P(cos(t1),sin(t1));
			P P5=p1+p3/abs(p3)*r1*P(cos(t2),sin(t2)),P6=p2-p3/abs(p3)*r2*P(cos(t2),sin(t2));
			P P7=p1+p3/abs(p3)*r1/P(cos(t2),sin(t2)),P8=p2-p3/abs(p3)*r2/P(cos(t2),sin(t2));
			L l[]={L(P1,P2),L(P3,P4),L(P5,P6),L(P7,P8)};
			rep(h,4){
				if(!flag&&(h==2||h==3))continue;
				int res=0;if(bug)cout<<i<<" "<<j<<" "<<h<<" ";
						rep(k,N){if(r[k]-EPS<distanceLP(l[h],p[k])&&distanceLP(l[h],p[k])<r[k]+m[k]+EPS){res++;if(bug)cout<<"o";}if(bug)cout<<m[k]<<":"<<distanceLP(l[h],p[k])-r[k]<<" ";if(abs(r[k]-distanceLP(l[h],p[k]))>EPS&&abs(r[k]-distanceLP(l[h],p[k]))<EPS/*||i==19&&j==52&&h==2*/){cout<<fixed<<setprecision(10)<<i<<" "<<j<<" "<<h<<" "<<k<<":"<<distanceLP(l[h],p[k])<<" "<<r[k]<<" "<<r[k]+m[k]<<endl;}}if(bug)cout<<endl;
				ans=max(ans,res);
				//if(res==10)cout<<i<<" "<<j<<" "<<h<<" ";
			}
		}
		cout<<(ans>0?ans:1)<<endl;
	}
}

Measured memory_bytes: 1004