#include <bits/stdc++.h>

using namespace std;
using ll = long long;
// #define int ll
using PII = pair<ll, ll>;

#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()

template<typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }
template<typename T> bool IN(T a, T b, T x) { return a<=x&&x<b; }
template<typename T> T ceil(T a, T b) { return a/b + !!(a%b); }

template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) { 
    return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}
template<typename T,typename V> typename enable_if<is_class<T>::value==0>::type
fill_v(T &t, const V &v) { t=v; }
template<typename T,typename V> typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t, const V &v ) { for(auto &e:t) fill_v(e,v); }

template<class S,class T>
ostream &operator <<(ostream& out,const pair<S,T>& a){
    out<<'('<<a.first<<','<<a.second<<')'; return out;
}
template<class T>
ostream &operator <<(ostream& out,const vector<T>& a){
    out<<'['; for(T i: a) {out<<i<<',';} out<<']'; return out;
}

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0}; // DRUL
const int INF = 1<<30;
const ll LLINF = 1LL<<60;
const ll MOD = 1000000007;

const double EPS = 1e-8;

using R = long double; // Rにmint渡せるようにする
using P = complex<R>;
using L = pair<P,P>;
using G = vector<P>;
struct C {
    P c; R r;
    C() {}
    C(const P &a, const R &b) : c(a), r(b) {}
};
struct S : public L {
    S() {}
    S(const P &a, const P &b) : L(a,b) {}
};

inline int sgn(const R& r) { return (r>EPS) - (r<-EPS); }
inline R dot(const P& a, const P& b) {
    return real(a)*real(b) + imag(a)*imag(b);
}
inline R det(const P& a, const P& b) {
    return real(a)*imag(b) - imag(a)*real(b);
}
inline P vec(const L& l) {return l.second - l.first;}
namespace std {
	bool operator < (const P& a, const P& b) {
		return sgn(real(a-b)) ? real(a-b) < 0 : sgn(imag(a-b)) < 0;
	}
	bool operator == (const P& a, const P& b) {
		return sgn(real(a-b)) == 0 && sgn(imag(a-b)) == 0;
	}
    bool cmp_y (const P& a, const P& b) {
        return sgn(imag(a-b)) ? imag(a-b) < 0 : sgn(real(a-b)) < 0;
    }
}

// P,L,Sについて入力
inline istream& operator>>(istream& is, P& p) {
    R x, y;
    is >> x >> y;
    p = P(x, y);
    return is;
}
inline istream& operator>>(istream& is, L& l) {
    P a, b;
    is >> a >> b;
    l = L(a, b);
    return is;
}
inline istream& operator>>(istream& is, S& s) {
    P a, b;
    is >> a >> b;
    s = S(a, b);
    return is;
}

// 線分abから見たcの位置
enum CCW{LEFT=1, RIGHT=2, BACK=4, FRONT=8, ON_SEG=16};
int ccw(P a, P b, P c) {
	P p = (c-a)/(b-a);
	if(sgn(imag(p)) > 0) return LEFT;
	if(sgn(imag(p)) < 0) return RIGHT;
	if(sgn(real(p)) < 0) return BACK;
	if(sgn(real(p)-1) > 0) return FRONT;
	return ON_SEG;
}

int intersect(const C& a, const C& b) {
	R dist = sqrt(norm(a.c-b.c)), r1 = a.r + b.r, r2 = abs(a.r - b.r);
	if(sgn(r1-dist) < 0)  return 4;	// 円が離れている
	if(sgn(r1-dist) == 0) return 3;	// 外接
	if(sgn(r2-dist) < 0 && sgn(dist-r1) < 0) return 2; // 交差
	if(sgn(dist-r2) == 0) return 1; // 内接
	return 0;	// 内部に含む
}

// 点aを通る接線を返す
// pl = ((a, 接線と円の交点), (a, 接線と円の交点))
pair<L,L> tangent(C c, P a) {
    pair<L,L> pl;
    if(sgn(abs(a-c.c)-c.r) == 0) { // 点aが円周上にあるとき 要verify
        auto normal = [](P a) {
            L vp({a*P(0,1), a*P(0,-1)});
            return vp;
        };
        L l = normal(a-c.c); // 法線ベクトル
        l.first = a; l.second += a;
        pl.first = pl.second = l;
    } else if(sgn(abs(a-c.c)-c.r) > 0) { // 点aが円の外側にあるとき
        R xp = a.real() - c.c.real();
        R yp = a.imag() - c.c.imag();
        R A = sqrt(xp*xp + yp*yp - c.r*c.r);
        R B = xp*xp + yp*yp;
        P p1(c.r*(xp*c.r + yp*A)/B , c.r*(yp*c.r - xp*A)/B);
        P p2(c.r*(xp*c.r - yp*A)/B , c.r*(yp*c.r + xp*A)/B);
        pl = make_pair(L(a, p1+c.c), L(a, p2+c.c));
    } else { // 点 a が円の内側にあるとき
        pl.first = pl.second = L(P(INF,INF), P(INF,INF));
    }
    return pl;
}

// 2つの円の共通接線の計算に使用
// flag=true のとき内接線, falseのとき外接線
L common_tangent(const C& c1, const C& c2, bool flag) {
    R xp = c2.c.real() - c1.c.real();
    R yp = c2.c.imag() - c1.c.imag();
    R r = flag ? c1.r + c2.r : c1.r - c2.r;
    R A = sqrt(xp*xp + yp*yp - r*r);
    R B = xp*xp + yp*yp;
    P p1(c1.r*(xp*r + yp*A)/B, c1.r*(yp*r - xp*A)/B);
    P p2(c1.r*(xp*r - yp*A)/B, c1.r*(yp*r + xp*A)/B);
    p1 += c1.c; p2 += c1.c;
    return L(p1, p2);
}
// 2円の共通接線を返す
// vl = {(c1の接点, c2の接点), …, (c1の接点, c2の接点)}
vector<L> common_tangent(C c1, C c2) {
    vector<L> vl;
    int pos = intersect(c1, c2);
    // 2つの共通内接線を求める
    L pp1 = common_tangent(c1, c2, true);
    L pp2 = common_tangent(c2, c1, true);
    if(pos == 4) { // 2つの円が離れているとき
        vl.push_back(L(pp1.first, pp2.first));
        vl.push_back(L(pp1.second, pp2.second));
    } else if(pos == 3) { // 外接するとき
        vl.push_back(tangent(c1, pp1.first).first);
    }
    // 2つの共通外接線を求める
    pp1 = common_tangent(c1, c2, false);
    pp2 = common_tangent(c2, c1, false);
    if(pos >= 2) { // 2つの円が交わるとき
        vl.push_back(L(pp1.first, pp2.second));
        vl.push_back(L(pp1.second, pp2.first));
    } else if(pos == 1) { // 2つの円が内接するとき
        vl.push_back(tangent(c1, pp1.first).first);
    }
    return vl;
}

// 射影
P inline projection(const L &l, const P &p) {
    R t = dot(p-l.first, l.first-l.second) / norm(l.first-l.second);
    return l.first + t*(l.first-l.second);
}
R dist(const L& l, const P& p) {
    P q = projection(l, p);
    return abs(p-q);
}

signed main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    while(1) {
        ll n;
        cin >> n;
        if(n == 0) break;
        vector<R> m(n*2);
        vector<C> c(n*2);
        REP(i, n) cin >> c[i].c >> c[i].r >> m[i];
        REP(i, n) c[i+n].c = c[i].c, c[i+n].r = c[i].r + m[i], m[i+n]=m[i];
        if(n == 1) {
            cout << 1 << endl;
            continue;
        }

        ll ans = 0;
        REP(i, 2*n) FOR(j, i+1, 2*n) {
            if(abs(i-j) == n) continue;
            auto vl = common_tangent(c[i], c[j]);   
            for(auto l: vl) {
                ll ret = 0;
                REP(k, n) {
                    R d = dist(l, c[k].c) - c[k].r;
                    if(sgn(d)>=0 && sgn(m[k]-d)>=0) {
                        ret++;
                    }
                }
                chmax(ans, ret);
            }
        }
        cout << ans << endl;
    }

    return 0;
}


Measured memory_bytes: 3528