#include<iostream>
#include<cstdio>
#include<cfloat>
#include<cassert>
#include<cmath>
#include<vector>
#include<algorithm>
#include<set>

using namespace std;

#define EPS (1e-12)
#define equals(a, b) (fabs((a) - (b)) < EPS )
#define dle(a, b) (equals(a, b) || a < b )

static const double PI = acos(-1);

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 a ){ return Point(x*a, y*a); }
    Point operator / ( double a ){ return Point(x/a, y/a); }
    Point operator / ( Point p ) { return Point((x*p.x+y*p.y)/(p.x*p.x+p.y*p.y), (y*p.x-x*p.y)/(p.x*p.x+p.y*p.y)); }

    double abs() { return sqrt(norm());}
    double norm() { return x*x + y*y; }

    bool operator < ( const Point &p ) const {
	return x != p.x ? x < p.x : y < p.y;
    }

    bool operator == ( const Point &p ) const {
	return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS;
    }
};

typedef Point Vector;

class Segment{
    public:
    Point p1, p2;
  Segment(Point s = Point(), Point t = Point()): p1(s), p2(t){}

};

typedef Segment Line;

static const int CIRCLE_NON = 0;
static const int CIRCLE_OUT = 1;
static const int CIRCLE_IN = 2;
static const int CIRCLE_CROSS = 3;

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

typedef vector<Point> Polygon;

double norm( Vector a ){ return a.x*a.x + a.y*a.y; }
double abs( Vector a ){ return sqrt(norm(a)); }
Point polar( double a, double r ){ return Point(cos(r)*a, sin(r)*a);}
double getDistance( Vector a, Vector b ){ return abs(a - b); }
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; }
double arg(Vector p){ return atan2(p.y, p.x); }

Point project( Segment s, Point p ){
    Vector base = s.p2 - s.p1;
    double t = dot(p - s.p1, base)/norm(base);
    return s.p1 + base*t;
}

Point reflect( Segment s, Point p ){
    return p + (project(s, p) - p)*2.0;
}

bool isOnSegment( Point a, Point b, Point c){
    if ( a == c || b == c ) return true;
    return (abs(a-c) + abs(c-b) < abs(a-b) + EPS );
}


bool isParallel( Vector a, Vector b ){
    return equals( cross(a, b), 0.0 );
}

bool isParallel( Point a1, Point a2, Point b1, Point b2){
    return isParallel( a1 - a2, b1 - b2 );
}

bool isParallel( Segment s1, Segment s2 ){
    return equals( cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0 );
}

static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

// EPS can be 0
// need to check for 920, 833, 866
int ccw( Point p0, Point p1, Point p2 ){
    Vector a = p1 - p0;
    Vector b = p2 - p0;
    if ( cross(a, b) > EPS ) return COUNTER_CLOCKWISE;
    if ( cross(a, b) < -EPS ) return CLOCKWISE;
    if ( dot(a, b) < -EPS ) return ONLINE_BACK;
    if ( norm(a) < norm(b) ) return ONLINE_FRONT;
    return ON_SEGMENT;
}

// intersect Segment p1-p2 and Segment p3-p4 ?
bool isIntersect(Point p1, Point p2, Point p3, Point p4){
    return ( ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0 &&
	     ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0 );
}

// intersect Segment s1 and Segment s2 ?
// verified by 920, 833, 866, uoa2062
bool isIntersect(Segment s1, Segment s2){
    return isIntersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

// verified by 920, 833, uoa2062
Point getCrossPoint(Segment s1, Segment s2){
    assert( isIntersect(s1, s2) );
    Vector base = s2.p2 - s2.p1;
    double d1 = abs(cross(base, s1.p1 - s2.p1));
    double d2 = abs(cross(base, s1.p2 - s2.p1));
    double t = d1/(d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1)*t;
}

Point getCrossPointLines( Line s1, Line s2){
    Vector a = s1.p2 - s1.p1;
    Vector base = s2.p2 - s2.p1;
    return s1.p1 + a * cross(base, s2.p1 - s1.p1)/cross(base, a);
}

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

// 10514
double getDistance(Segment s, Point p){
    if ( dot(s.p2 - s.p1, p - s.p1) < 0.0 ) return abs(p - s.p1);
    if ( dot(s.p1 - s.p2, p - s.p2) < 0.0 ) return abs(p - s.p2);
    return abs(cross(s.p2 - s.p1, p - s.p1)/abs(s.p2 - s.p1));
}
double getDistance(Segment s1, Segment s2){
    if ( isIntersect(s1, s2) ) return 0.0;
    return min( min(getDistance(s1, s2.p1), getDistance(s1, s2.p2)),
		min(getDistance(s2, s1.p1), getDistance(s2, s1.p2)));
}

bool isIntersect( Circle c1, Line l ){
    double d = getDistanceLP(l, c1.c);
    return ( equals(d, c1.r) || d < c1.r );
}

pair<Point, Point> getTangentPoints(Point p, Circle c){
  double d = abs(c.c - p);
  double t = arg(c.c - p);
  double b = sqrt(d*d - c.r * c.r);
  double a = asin(c.r / d);
  Point p1 = p + polar(b, t + a);
  Point p2 = p + polar(b, t - a);
  return make_pair(p1, p2);
}

/*
 return tangent points on c1
 */
vector<Point> getCommonTangent(Circle c1, Circle c2){
  vector<Point> tp;
  Point base = c2.c - c1.c;
  double l = abs(base);
  double a = arg(base); // base alpha
  if ( abs(c1.r - c2.r) < l  ){
    double th1 = acos((c1.r - c2.r)/l);
    tp.push_back(c1.c + polar(c1.r, a + th1));
    tp.push_back(c1.c + polar(c1.r, a - th1));
    if ( c1.r + c2.r < l ){
      double th2 = acos((c1.r + c2.r)/l);
      tp.push_back(c1.c + polar(c1.r, a + th2));
      tp.push_back(c1.c + polar(c1.r, a - th2));
    }
  }

/*
  if ( (equals(l, abs(c1.r - c2.r)) || equals(c1.r + c2.r, l) ) && !equals(l, 0) ) {
    tp.push_back(c1.c + polar(c1.r, a));
  }
  */
  if ( equals(c1.r + c2.r, l) && !equals(l, 0) ) { // out
    tp.push_back(c1.c + polar(c1.r, a));
  }

  if ( equals(l, abs(c1.r - c2.r)) && !equals(l, 0) ) { //in
    tp.push_back(c1.c + polar(c1.r, a + acos(-1)));
  }

  
  return tp;
}

int N;
Circle C[50];
Circle T[100]; // target circle
int M[50];

int solve(){
  if ( N == 1 ) return 1;
  vector<Line> L;

  for ( int i = 0; i < N; i++ ) {
    T[i] = C[i];
    T[i+N] = Circle(C[i].c, C[i].r + M[i]);
  }

  for ( int i = 0; i < 2*N-1; i++ ){
    for ( int j = i+1; j < 2*N; j++ ){
      vector<Point> ap = getCommonTangent(T[i], T[j]);
      for ( int k = 0; k < ap.size(); k++ ){
	Vector v = ap[k] - T[i].c;
	v = polar(abs(v), arg(v) + acos(-1)/2.0);
	L.push_back(Line(ap[k], ap[k] + v));
      }
    }
  }

  int ans = 0;
  for ( int l = 0; l < L.size(); l++ ){
    int cnt = 0;
    for ( int i = 0; i < N; i++ ){
      double d = getDistanceLP(L[l], C[i].c);
      if ( dle(C[i].r, d) && dle(d, C[i].r + M[i]) ) cnt++;
    }
    ans = max(ans, cnt);
  }

  return ans;
}

int main(){

  while(1){
    cin >> N;
    if ( N == 0 ) break;
    for ( int i = 0; i < N; i++ ){
      cin >> C[i].c.x >> C[i].c.y >> C[i].r >> M[i];
    }
    cout << solve() << endl;
  }
			  
  return 0;
}

Measured memory_bytes: 2812