#include <vector>
#include <iostream>
#include <complex>
#include <cassert>
#include <cstdio>

using namespace std;



const double EPS = 1e-5;
const double INF = 1e12;
typedef complex<double> P;
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(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};

typedef vector<P> G;

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

vector<C> houseki;
vector<C> power;
int N;

void init() {
  houseki.clear();
  power.clear();
}

vector<L> lines(C c1, C c2) {
  P o1 = c1.p;
  P o2 = c2.p;
  double r1 = c1.r;
  double r2 = c2.r;
  double d = abs(o1 - o2);

  if (d > r1 + r2) {
    
  }
}

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 * (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]);
}


bool intersectA(C c, L l) {
  double d = distanceLP(l, c.p);
  double r = c.r;
  return r - d > EPS;
}
bool intersectB(C c, L l) {
  double d = distanceLP(l, c.p);
  double r = c.r;
  return r - d > -EPS;
}

vector<L> commonTangents(const C& c1, const C& c2)
{
  P o1 = c1.p;
  P o2 = c2.p;
  double r1 = c1.r;
  double r2 = c2.r;
    double a = abs(o2 - o1);
    if (a < EPS) { return vector<L>(); }

    vector<L> rslt;
    P rot = (o2 - o1) / a;
    
    double xs[] = {r1 * (r1 + r2) / a, r1 * (r1 - r2) / a};
    for (int i = 0; i < 2; ++i) {
        double x1 = xs[i];
        if (x1 < -r1 || r1 < x1) { continue; }

        double ys[] = {sqrt(r1 * r1 - x1 * x1), -sqrt(r1 * r1 - x1 * x1)};
        for (int j = 0; j < 2; ++j) {
            double y1 = ys[j];
            // これは接点が１つしかない場合。y1 が 0 になる。
            if (abs(y1) < EPS) {
                rslt.push_back(L(P(x1, 0), P(x1, 1)));
                break;
            }
            
            double x2 = (a * y1 * y1 + x1 * r1 * r1) / (r1 * r1);
            if (x2 < a - r2 || a + r2 < x2) { continue; }
            double y2 = (r1 * r1 - x1 * x2) / y1;
            P p1 = P(x1, y1) * rot + o1;
            P p2 = P(x2, y2) * rot + o1;
            rslt.push_back(L(p1, p2));
        }
    }

    return rslt;
}

void solve() {
  if (N == 1) {
    printf("1\n");
    return;
  }
  vector<C> circles(houseki.begin(), houseki.end());
  circles.insert(circles.end(), power.begin(), power.end());
  int mn = 0;
  for (int i = 0; i < circles.size(); i++) {
    for (int j = i + 1; j < circles.size(); j++) {
      vector<L> ls = commonTangents(circles[i], circles[j]);
      for (int k = 0; k < ls.size(); k++) {
        int cnt = 0;
        for (int m = 0; m < N; m++) {
          if (!intersectA(houseki[m], ls[k]) &&
              intersectB(power[m], ls[k])) {
            cnt++;
          }
        }
        mn = max(cnt, mn);
      }
    }
  }
  printf("%d\n", mn);
}

int main() {
  while (true) {
    cin >> N;
    init();

    if (N == 0) {
      return 0;
    }
    for (int i = 0;  i < N; i++) {
      int x, y, r, m;
      cin >> x >> y >> r >> m;
      houseki.push_back(C(P(x, y), r));
      power.push_back(C(P(x, y), r + m));
    }
    solve();
  }
}

Measured memory_bytes: 960