#include<cstdio>
#include<complex>
#include<utility>
#include<vector>
#include<cmath>

using namespace std;

double eps=1e-9;

typedef complex<double> Point;
typedef complex<double> Vector;

template<class T> bool eq(T a,T b){
	return abs(a-b)<eps;
}

template<class T> int sgn(T r){
	return eq(r,0.0)?0:(r>0?1:-1);
}

struct Circle{
	Point center;
	double r;
	Circle(Point c,double r):center(c),r(r){}
	Circle(){}
};

struct Line{
	double a,b,c;//ax+by=c
	Line(){}
	Line(double a,double b,double c):a(a),b(b),c(c){}
};

void print(Point p){
	if(isnan(p.real())||isnan(p.imag())){
		printf("NaN Point\n");
		return;
	}
	printf("(%f,%f)\n",p.real(),p.imag());
}

double pointsDistance(Point p1,Point p2){
	double dx=p1.real()-p2.real();
	double dy=p1.imag()-p2.imag();
	return sqrt(dx*dx+dy*dy);
}

double linePointDistance(Line l,Point p){
	double a=l.a,b=l.b,c=l.c;
	double x=p.real(),y=p.imag();
	double num=abs(a*x+b*y-c);
	double den=sqrt(a*a+b*b);
	return num/den;
}

Vector basisVector(Vector v){
	if(eq(v.real(),0.0)&&eq(v.imag(),0.0)) return v;
	return v/sqrt(norm(v));
}

Point linePointProjection(Line l,Point p){
	double dx=l.a,dy=l.b;
	double a=l.a,b=l.b,c=l.c;
	double x=p.real(),y=p.imag();
	Vector ba=basisVector(Vector(dx,dy));
	double num=a*x+b*y-c;
	double den=sqrt(a*a+b*b);
	Vector v=ba*(-num/den);
	return p+v;
}

vector<Point> circleLineIntersection(Circle c,Line l){
	vector<Point> res;
	Point p=linePointProjection(l,c.center);
	double d=linePointDistance(l,c.center);
	int s=sgn(d-c.r);
	if(s==1){
		return res;//empty
	}else if(s==0){
		res.push_back(p);
		return res;
	}else{
		double r=c.r;
		double t=sqrt(r*r-d*d);
		Vector e=basisVector(Vector(l.b,-l.a));
		res.push_back(p+t*e);
		res.push_back(p-t*e);
		return res;
	}
}

vector<Point> circlesIntersection(Circle c1,Circle c2){/*一致するとき処理できない*/
	double d=pointsDistance(c1.center,c2.center);
	double r1=c1.r,r2=c2.r;
	double dif=max(r1,r2)-min(r1,r2);
	double sum=r1+r2;
	if(sgn(d-sum)==1||sgn(dif-d)==1){//d>sum||dif>d
		vector<Point> v;
		return v;
	}
	double x1=c1.center.real(),y1=c1.center.imag();
	double x2=c2.center.real(),y2=c2.center.imag();
	Line l=Line(-x1*2+x2*2,-y1*2+y2*2,r1*r1-r2*r2-(x1*x1-x2*x2)-(y1*y1-y2*y2));
	return circleLineIntersection(c1,l);
}

double det(double a,double b,double c,double d){
	return a*d-b*c;
}

Point linesIntersection(Line l1,Line l2){
	double a=l1.a,b=l1.b,c=l1.c;
	double d=l2.a,e=l2.b,f=l2.c;
	double den=det(a,b,d,e);
	double numx=det(c,b,f,e);
	double numy=det(a,c,d,f);
	if(eq(den,0.0)){
		return Point(NAN,NAN);
	}
	return Point(numx/den,numy/den);
}

double x[11],y[11],l[11];

Circle circles[11];
vector<Point> cands;

bool inCircle(Circle c,Point p){//境界上でもtrue
	double d=pointsDistance(c.center,p);
	int s=sgn(d-c.r);
	if(s<=0) return true;
	return false;
}

int main(){
	while(true){
		int N;
		scanf("%d",&N);
		if(N==0) break;
		for(int i=0;i<N;i++) scanf("%lf%lf%lf",x+i,y+i,l+i);
		double lb=0;
		double ub=1000;
		for(int i=0;i<N;i++) ub=min(ub,l[i]);
		for(int stage=0;stage<100;stage++){
			double mid=(ub+lb)/2;
			for(int i=0;i<N;i++){
				circles[i]=Circle(Point(x[i],y[i]),sqrt(l[i]*l[i]-mid*mid));
			}
			cands.clear();
			for(int i=0;i<N;i++){
				for(int j=i+1;j<N;j++){
					vector<Point> tmp;
					tmp=circlesIntersection(circles[i],circles[j]);
					for(int k=0;k<tmp.size();k++){
						cands.push_back(tmp[k]);
					}
				}
			}
			//if(cands.size()==0){
				for(int i=0;i<N;i++){
					cands.push_back(circles[i].center);
				}
			//}
			bool ok=false;
			for(int i=0;i<cands.size();i++){
				bool flg=true;
				for(int j=0;j<N;j++){
					if(inCircle(circles[j],cands[i])==false) flg=false;
				}
				if(flg) ok=true;
			}
			if(ok) lb=mid;
			else ub=mid;
		}
		printf("%f\n",ub);
	}
	return 0;
}