#include <iostream>
#include <fstream>
#include <set>
#include <vector>
#include <algorithm>
#include <complex>
using namespace std;

typedef complex<double> cplx;

class union_find{
public:
  union_find(int n){
    for (int i=0;i<n;i++)
      dat.push_back(i);
  }

  void unite(int a,int b){
    dat[find(a)]=find(b);
  }
  int find(int n){
    if (dat[n]==n) return n;
    else return dat[n]=find(dat[n]);
  }
  vector<int> dat;
};

struct point{
  point(){}
  point(double x,double y,double z):x(x),y(y),z(z){}
  double x,y,z;
};

pair<double,double> cross_sphere(pair<point,double> &c1,pair<point,double> &c2)
{
  double za = c1.first.z;
  double zb = c2.first.z;
  double r = c1.second, s = c2.second;
  double dx = c1.first.x - c2.first.x;
  double dy = c2.first.y - c1.first.y;
  double l = sqrt(dx*dx + dy*dy);
  
  cplx a(0,za),b(l,zb);
  if(norm(b-a)<=0.000001)
    return make_pair(-100000,+100000);
  double zx = 0.5*(1+(r*r-s*s)/norm(b-a));
  double rooter = r*r/norm(b-a) - zx*zx;
  if(rooter<0)
    return make_pair(-100000,+100000);
  double zy = sqrt(rooter);
  cplx z (zx,zy);
  double z1 = za+imag(z*(b-a));
  double z2 = za+imag(conj(z)*(b-a));
  return make_pair(z1,z2);
}

bool cross_circle(pair<point,double> &c1,pair<point,double> &c2)
{
  double dx=c1.first.x-c2.first.x;
  double dy=c1.first.y-c2.first.y;
  double d=sqrt(dx*dx+dy*dy);

  return (d<c1.second+c2.second);
}

int main()
{
  ifstream cin("H.txt");

  int n;
  while(cin>>n,n!=0){
    vector<pair<point,double> > dat(n);
    set<double> zs;
    zs.insert(100000);
    zs.insert(-100000);
    for (int i=0;i<n;i++){
      point p;double r;
      cin>>p.x>>p.y>>p.z>>r;
      dat[i]=make_pair(p,r);
      zs.insert(p.z+r);
      zs.insert(p.z-r);
    }

    for (int i=0;i<n-1;i++){
      for (int j=i+1;j<n;j++){
	pair<double,double> cross=cross_sphere(dat[i],dat[j]);
	zs.insert(cross.first);
	zs.insert(cross.second);
      }
    }

    vector<int> nums;

    set<double>::iterator p,q;
    p=zs.begin();
    q=p;q++;
    while(q!=zs.end()){
      double z=(*p+*q)/2;

      vector<pair<point,double> > cs;
      for (int i=0;i<dat.size();i++){
	double d=abs(dat[i].first.z-z);
	if (d<dat[i].second){
	  cs.push_back(make_pair(point(dat[i].first.x,dat[i].first.y,0),
			      sqrt(dat[i].second*dat[i].second-d*d)));
	}
      }

      union_find uf(cs.size());
      for (int i=0;i<cs.size();i++){
	for (int j=0;j<cs.size();j++){
	  if (cross_circle(cs[i],cs[j]))
	    uf.unite(i,j);
	}
      }
      set<int> tmp;
      for (int i=0;i<cs.size();i++)
	tmp.insert(uf.find(i));

      nums.push_back(tmp.size());
      p++,q++;
    }

    int nsize=(unique(nums.begin(),nums.end())-nums.begin()-1);
    cout<<nsize<<endl;
    for (int i=0;i<nsize;i++)
      cout<<(nums[i]<nums[i+1]?1:0);
    cout<<endl;
  }

  return 0;
}