#include<bits/stdc++.h>

#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-14)
#define equals(a,b) (fabs((a)-(b)) < EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

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

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

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

};

struct Segment{
  Point p1,p2;
  Segment(Point p1 = Point(),Point p2 = Point()):p1(p1),p2(p2){}
  bool operator <  (const Segment& s) const { return ( p2 == s.p2 ) ? p1 < s.p1 : p2 < s.p2; }
  bool operator == (const Segment& s) const { return ( s.p1 == p1 && s.p2 == p2 ) || ( s.p1 == p2 && s.p2 == p1 ); }

};

typedef Point Vector;
typedef Segment Line;

double dot(Point a,Point b){ return a.x*b.x + a.y*b.y; }

double cross(Point a,Point b){ return a.x*b.y - a.y*b.x; }

double norm(Point a){ return a.x*a.x+a.y*a.y; }

double abs(Point a){ return sqrt(norm(a)); }

int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point 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;
}

pair<Point, Point> crosspointCC( Point C1, double r1, Point C2, double r2) {
  complex<double> c1(C1.x,C1.y);
  complex<double> c2(C2.x,C2.y);
  complex<double> A = conj(c2-c1), B = (r2*r2-r1*r1-(c2-c1)*conj(c2-c1)), C = r1*r1*(c2-c1);
  complex<double> D = B*B-4.0*A*C;
  complex<double> z1 = (-B+sqrt(D))/(2.0*A)+c1, z2 = (-B-sqrt(D))/(2.0*A)+c1;
  return pair<Point, Point>(Point(z1.real(),z1.imag()),Point(z2.real(),z2.imag()));
}

// ??? a ?????? b ????????????????????????
bool insideCC(Point a,double ra,Point b,double rb){
  double d = sqrt(norm(a-b));
  double r1 = max(ra,rb);
  double r2 = min(ra,rb);
  
  if(!equals(d,r1-r2) && d < r1-r2) return ra < rb; 
  return false;
}


//cross product of pq and pr
double cross3p(Point p,Point q,Point r) { return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
  
//returns true if point r is on the same line as the line pq
bool collinear(Point p,Point q,Point r) { return fabs(cross3p(p,q,r)) < EPS; }
  
//returns true if point t is on the left side of line pq
bool ccwtest(Point p,Point q,Point r){
  return cross3p(p,q,r) > 0; //can be modified to accept collinear points
}
 
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}



bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2-l.p1, m.p2-m.p1)) > EPS || // non-parallel
         abs(cross(l.p2-l.p1, m.p1-l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2-l.p1, s.p1-l.p1)*       // s[0] is left of l
         cross(l.p2-l.p1, s.p2-l.p1) < EPS; // s[1] is right of l
}
bool intersectLP(Line l,Point p) {
  return abs(cross(l.p2-p, l.p1-p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1-p)+abs(s.p2-p)-abs(s.p2-s.p1) < EPS; // triangle inequality
}

Point projection(Line l,Point p) {
  double t = dot(p-l.p1, l.p1-l.p2) / norm(l.p1-l.p2);
  return l.p1 + (l.p1-l.p2)*t;
}
Point reflection(Line l,Point p) {
  return p + (projection(l, p) - p) * 2;
}
double distanceLP(Line l, Point p) {
  return abs(p - projection(l, p));
}
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l,Line m){
  double A = cross(l.p2-l.p1,m.p2-m.p1);
  double B = cross(l.p2-l.p1,l.p2-m.p1);
  if(abs(A) < EPS && abs(B) < EPS){
    vector<Point> vec;
    vec.push_back(l.p1),vec.push_back(l.p2),vec.push_back(m.p1),vec.push_back(m.p2);
    sort(vec.begin(),vec.end());
    assert(vec[1] == vec[2]); //???????????°??????????????????
    return vec[1];
    //return m.p1;
  }
  if(abs(A) < EPS)assert(false);
  return m.p1 + (m.p2-m.p1)*(B/A);
}





// <---------

inline bool LT(double a,double b) { return !equals(a,b) && a < b; }
inline bool LTE(double a,double b) { return equals(a,b) || a < b; }

int n;
Point ps[110];
double rs[110];

bool insideAny(int i) {
  REP(j,i+1,n) if( insideCC(ps[i],rs[i],ps[j],rs[j]) ) return true;
  return false;
}

bool trivialFail(int i) {
  if( insideAny(i) ) return true;
  REP(j,i+1,n) if( ps[i] == ps[j] && equals(rs[i],rs[j]) ) return true;
  return false;
}

Point vir;
bool comp_angle(const Point &a,const Point &b) {
  return LT(atan2(vir.y-a.y,vir.x-a.x),atan2(vir.y-b.y,vir.x-b.x));
}

bool comp_dist(Point a,Point b) {
  return LTE(abs(a-vir),abs(b-vir));
}

pair<Point,Point> crosspointCL(Point cp,double r,Line l) {
  double dist = distanceLP(l,cp);
  Vector v = (l.p1-l.p2) / abs(l.p1-l.p2);
  if( equals(dist,0) ) {
    return pair<Point,Point>(Point(cp+v*r),Point(cp-v*r));
  } else {
    double x = sqrt(r*r-dist*dist);
    return pair<Point,Point>(Point(cp+v*x),Point(cp-v*x));
  }
}

bool visibleCheckPoint(Point p,int i) {
  REP(j,i+1,n) {
    double dist = abs(p-ps[j]);
    if( LT(dist,rs[j]) ) return false;
  }
  return true;
}

bool visibleCheckSeg(Segment seg,int i) {
  deque<Point> deq;
  deq.push_back(seg.p1);
  deq.push_back(seg.p2);
  rep(j,2) {
    double dist = abs(deq[j]-ps[i]);
    if( equals(dist,rs[i]) || dist < rs[i] ) if( visibleCheckPoint(deq[j],i) ) return true;
  }
  return false;
  REP(j,i+1,n) {
    double dist = distanceLP(seg,ps[j]);
    if( LTE(rs[j],dist) ) continue;
    pair<Point,Point> pp = crosspointCL(ps[j],rs[j],seg);
    if( onSegment(seg.p1,seg.p2,pp.first)  ) deq.push_back(pp.first);
    if( onSegment(seg.p1,seg.p2,pp.second) ) deq.push_back(pp.second);
  }
  
  // sort
  vir = seg.p1;
  sort(deq.begin(),deq.end(),comp_dist);
  
  // check
  rep(j,(int)deq.size()-1) {
    Point p1 = deq[j];
    Point p2 = deq[j+1];
    Point mp = (p1+p2)/2.0;
    double dist = abs(mp-ps[i]);
    if( equals(dist,rs[i]) || dist < rs[i] ) if( visibleCheckPoint(mp,i) ) return true;
  }
  return false;
}

bool visibleCheckArcJ(int i,int j) {
  deque<Point> deq;
  REP(k,i,n) {
    if( ps[j] == ps[k] && equals(rs[j],rs[k]) ) continue;
    {
      double  dist = abs(ps[k]-ps[j]); 
      double rdist = rs[k]+rs[j];
      if( equals(dist,rdist) || dist > rdist ) continue;
    }
    pair<Point,Point> pp = crosspointCC(ps[j],rs[j],ps[k],rs[k]);
    deq.push_back(pp.first);
    deq.push_back(pp.second);
  }
  vir = ps[j];
  sort(deq.begin(),deq.end(),comp_angle);
  rep(k,(int)deq.size()) {
    Point p1 = deq[k] - ps[j];
    Point p2 = deq[(k+1)%(int)deq.size()] - ps[j];
    Point mp = ( p1 + p2 ) / 2.0;
    mp = mp + ps[j];
    Vector v = ( mp - ps[j] ) / abs( mp - ps[j] );
    Segment seg = Segment(ps[j]+v*rs[j],ps[j]-v*rs[j]);
    if( visibleCheckSeg(seg,i) ) return true;
  }
  return false;
}

void compute() {
  int cnt = 0;
  rep(i,n) { // check the i-th circle whether the circle is visible or not
    if( trivialFail(i) ) continue;
    bool success = false;
    bool success2 = true;
    REP(j,i+1,n) { 
      {
	double  dist = abs(ps[i]-ps[j]); 
	double rdist = rs[i]+rs[j];
	if( equals(dist,rdist) || dist > rdist ) continue;
      }
      if( insideCC(ps[j],rs[j],ps[i],rs[i]) ) continue; 
      success2 = false;
      if( visibleCheckArcJ(i,j) ) { success = true; break; }
    }
    if( success || success2 ) ++cnt;
  }
  cout << cnt << endl;
}

int main() {
  while( cin >> n, n ) {
    rep(i,n) cin >> ps[i].x >> ps[i].y >> rs[i];
    compute();
  }
  return 0;
}

Measured memory_bytes: 1360