#include <bits/stdc++.h>
using namespace std;

typedef complex<double> P;
typedef pair<P,P> L;

const double EPS = 1e-8;

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

struct Circle{
  P c;
  double r;
  Circle(P c=P(0,0), double r=0):c(c),r(r){}
};

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

P proj(P p, L l){
  return l.first + dot(p - l.first, l.second - l.first) / norm(l.second - l.first) * (l.second - l.first);
}

P rotate(P p, double rad){
  double x = real(p) * cos(rad) - imag(p) * sin(rad);
  double y = real(p) * sin(rad) + imag(p) * cos(rad);
  return P(x,y);
}

vector<P> getIntersectCL(Circle c, L l){
  vector<P> res;
  P h = proj(c.c, l);
  double d = abs(c.c - h);
  if(d > c.r + EPS);
  else if(d > c.r - EPS) res.push_back(h);
  else{
    P v = l.second - l.first;
    v = (sqrt(c.r*c.r - d*d) / abs(v)) * v;
    res.push_back(h+v);
    res.push_back(h-v);
  }
  return res;
}

vector<P> getIntersectCC(Circle c1, Circle c2){
  vector<P> res;
  double r1 = c1.r, r2 = c2.r, d;
  P p1 = c1.c, p2 = c2.c;
  d = abs(p1-p2);

  if(d < EPS && abs(r1-r2) < EPS) return res; //????????¨?????????????????´???????????????????????????????????????
  if(r1 + r2< d - EPS || d + EPS < abs(r1-r2)) return res; //???????????????

  double a = (r1*r1 - r2*r2 + d*d) / (2*d);
  double h = sqrt(max(r1*r1 - a*a, 0.0));
  P tmp1 = p1 + a / d * (p2-p1);
  P tmp2 = h / d * (p2-p1);

  if(abs(tmp2) < EPS) res.push_back(tmp1);
  else {
    res.push_back(P(real(tmp1) - imag(tmp2), imag(tmp1) + real(tmp2)));
    res.push_back(P(real(tmp1) + imag(tmp2), imag(tmp1) - real(tmp2)));
  }
  return res;
}

vector<L> tangentCC(Circle c1, Circle c2){
  vector<L> res;
  double d = abs(c1.c - c2.c);
  if(d < EPS) return res;

  // ?????\???
  if(c1.r + c2.r < d - EPS){
    double t = acos((c1.r + c2.r) / d);
    res.push_back(L(c1.c + rotate(c1.r / d * (c2.c-c1.c), t), c2.c + rotate(c2.r / d * (c1.c-c2.c), t)));
    res.push_back(L(c1.c + rotate(c1.r / d * (c2.c-c1.c), -t), c2.c + rotate(c2.r / d * (c1.c-c2.c), -t)));
  }
  else if(c1.r + c2.r < d + EPS){
    P p = c1.c + c1.r / d * (c2.c-c1.c);
    res.push_back(L(p, p + rotate(c2.c-c1.c, M_PI/2.0)));
  }

  // ?????\???
  if(abs(c1.r-c2.r) < d - EPS){
    double t1 = acos((c1.r - c2.r) / d), t2 = M_PI - t1;
    res.push_back(L(c1.c + rotate(c1.r / d * (c2.c-c1.c), t1), c2.c + rotate(c2.r / d * (c1.c-c2.c), -t2)));
    res.push_back(L(c1.c + rotate(c1.r / d * (c2.c-c1.c), -t1), c2.c + rotate(c2.r / d * (c1.c-c2.c), t2)));
  }
  else if(abs(c1.r - c2.r) < d + EPS){
    P p = c1.c + c1.r / d * (c2.c-c1.c);
    res.push_back(L(p, p + rotate(c2.c-c1.c, M_PI/2)));
  }

  return res;
}


int n;
vector<Circle> v,w;

int calc(L l){
  int sum = 0;
  for(int k=0;k<n;k++){
    if(getIntersectCL(v[k], l).size() <= 1 && getIntersectCL(w[k], l).size() >= 1){
      sum++;
    }
  }
  return sum;
}

int solve(){
  int ans = 1;
  vector<P> pv;

  for(int i=0;i<n;i++){
    for(int j=i+1;j<n;j++){
      vector<P> res = getIntersectCC(w[i],w[j]);
      for(int k=0;k<res.size();k++){
        pv.push_back(res[k]);
      }
      
      vector<L> resl = tangentCC(w[i],w[j]);
      for(int k=0;k<resl.size();k++){
        ans = max(ans, calc(resl[k]));
        //pv.push_back(resl[k].first);
        //pv.push_back(resl[k].second);
      }
      
      resl = tangentCC(v[i],v[j]);
      for(int k=0;k<resl.size();k++){
        ans = max(ans, calc(resl[k]));
        //pv.push_back(resl[k].first);
        //pv.push_back(resl[k].second);
      }
    }
  }
  
  //pv.erase(unique(pv.begin(), pv.end()), pv.end());

  
  for(int i=0;i<pv.size();i++){
    for(int j=i+1;j<pv.size();j++){
      ans = max(ans, calc(L(pv[i], pv[j])));
    }
  }  

  return ans;
}

int main(){
  while(cin >> n && n){
    v.clear();
    w.clear();
    for(int i=0;i<n;i++){
      double x,y,r,m;
      cin >> x >> y >> r >> m;
      v.push_back(Circle(P(x,y), r));
      w.push_back(Circle(P(x,y), r+m));
    }
    cout << solve() << endl;
  }
}

Measured memory_bytes: 1340