#include <iostream>
#include <complex>
#include <vector>
#include <algorithm>
#include <cmath>
using namespace std;

const double EPS = 1e-10;
const double INF = 1e12;
#define EQ(n,m) (abs((n)-(m)) < EPS)
#define X real()
#define Y imag()

typedef complex<double> P;
typedef vector<P> VP;
struct L : VP{
    L(const P& a, const P& b){ resize(2); at(0)=a; at(1)=b; }
    L(){ resize(2); }
};
struct C{
    P p;
    double r;
    C(const P& p, const double& r) : p(p), r(r) {}
    C(){}
};

namespace std{
    bool operator < (const P& a, const P& b){
        return (a.X!=b.X) ? a.X<b.X : a.Y<b.Y;
    }
    bool operator == (const P& a, const P& b){
        return abs(a-b) < EPS;
    }
}

double dot(P a, P b){
    return (conj(a)*b).X;
}
double cross(P a, P b){
    return (conj(a)*b).Y;
}
int ccw(P a, P b, P c){
    b -= a;
    c -= a;
    if(cross(b,c) > EPS) return +1; //ccw
    if(cross(b,c) < -EPS) return -1; //cw
    if(dot(b,c) < -EPS) return +2; //c-a-b
    if(abs(c)-abs(b) > EPS) return -2; //a-b-c
    return 0; //a-c-b
}
P unit(const P &p){
    return p/abs(p);
}

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]);
}

double distanceLP(const L &l, const P &p) {
  return abs(p - projection(l, p));
}

VP crosspointCL(const C &c, const L &l){
    VP ret;
    P mid = projection(l, c.p);
    double d = distanceLP(l, c.p);
    if(EQ(d, c.r)){
        ret.push_back(mid);
    }else if(d < c.r){
        double len = sqrt(c.r*c.r -d*d);
        ret.push_back(mid +len*unit(l[1]-l[0]));
        ret.push_back(mid -len*unit(l[1]-l[0]));
    }
    return ret;
}

vector<L> getTangentLine(const C &c, const P &p){
    vector<L> ret;
    P dir = p -c.p;
    if(c.r < abs(dir) +EPS){
        P a = c.p + c.r*unit(dir);
        VP cp = crosspointCL(C(c.p, abs(dir)), L(a, a+dir*P(0,1)));
        for(int i=0; i<(int)cp.size(); i++){
            ret.push_back(L(p, c.p +c.r*unit(cp[i]-c.p)));
        }
    }
    return ret;
}

vector<L> getCommonTangentLine(C a, C b){
    vector<L> ret;
    if(a.p==b.p && EQ(a.r, b.r)) return ret;
    if(a.r < b.r) swap(a,b);
    P ab = b.p -a.p;
    double d = abs(ab);
    if(d+EPS > a.r+b.r){
        ret = getTangentLine(a, a.p +a.r/(a.r+b.r)*ab);
    }
    if(d+EPS > a.r-b.r){
        if(EQ(a.r, b.r)){
            P normal = unit(ab)*P(0,1)*a.r;
            ret.push_back(L(a.p +normal, b.p +normal));
            ret.push_back(L(a.p -normal, b.p -normal));
        }else{
            vector<L> tmp = getTangentLine(a, a.p +a.r/(a.r-b.r)*ab);
            copy(tmp.begin(), tmp.end(), back_inserter(ret));
        }
    }
    return ret;
}

int main(){
    while(1){
        int n;
        cin >> n;
        if(n==0) break;

        vector<C> jewel(n*2);
        for(int i=0; i<n; i++){
            int x,y,r,m;
            cin >> x >> y >> r >> m;
            jewel[2*i] = C(P(x,y), r);
            jewel[2*i+1] = C(P(x,y), r+m);
        }

        vector<L> tangent;
        tangent.reserve(5000);
        for(int i=0; i<2*n; i++){
            for(int j=i+1; j<2*n; j++){
                vector<L> tmp = getCommonTangentLine(jewel[i], jewel[j]);
                copy(tmp.begin(), tmp.end(), back_inserter(tangent));
            }
        }
        int ansmax = 1;
        for(int i=0; i<(int)tangent.size(); i++){
            int ans=0;
            for(int j=0; j<n; j++){
                if(distanceLP(tangent[i], jewel[2*j].p) +EPS > jewel[2*j].r &&
                   distanceLP(tangent[i], jewel[2*j+1].p) < jewel[2*j+1].r +EPS){
                    ans++;
                }
            }
            ansmax = max(ansmax, ans);
        }
        cout << ansmax << endl;
    }
    return 0;
}

Measured memory_bytes: 4480