// ACM-ICPC国内予選2013 E. つながれた風船

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

using namespace std;

const double EPS = 1e-10;

typedef complex<double> P;
typedef pair<P,double> circle;

double cross(P a, P b) { return imag(conj(a)*b); }

bool containPoint(const circle& c, const P& p){
	double dist = abs(c.first-p);
	return dist < c.second+EPS;
}

bool crossCircle(const circle& c1, const circle& c2){
	double r1 = c1.second;
	double r2 = c2.second;
	double d = abs(c1.first-c2.first);
	if(d<r1||d<r2)
		return d-abs(r1-r2)>EPS;
	return r1+r2-d>-EPS;
}

void crossPoint(vector<P> &res, const circle& c1, const circle& c2){
	double r1 = c1.second;
	double r2 = c2.second;
	double r3 = abs(c1.first-c2.first);
	double rc = (r3*r3+r1*r1-r2*r2)/(2*r3);
	double rs = sqrt(r1*r1-rc*rc);
	P dif = (c2.first-c1.first)/r3;
	res.push_back(c1.first+dif*P(rc, rs));
	res.push_back(c1.first+dif*P(rc,-rs));
}

bool valid(const vector<circle>& vc){
	vector<P> vp;
	for(int i=0;i<vc.size();i++){
		vp.push_back(vc[i].first);
		for(int j=i+1;j<vc.size();j++){
			if(crossCircle(vc[i], vc[j]))
				crossPoint(vp, vc[i], vc[j]);
		}
	}
	for(int i=0;i<vp.size();i++){
		bool ok = true;
		for(int j=0;j<vc.size();j++)
			if(!containPoint(vc[j], vp[i])) ok = false;
		if(ok) return true;
	}
	return false;
}

int main(){
	int n;
	int x[10], y[10], l[10]; 
	while(cin >> n &&  n){
		int minL = 100000;
		for(int i=0;i<n;i++){
			cin >> x[i] >> y[i] >> l[i];
			minL = min(minL, l[i]);
		}
		double low = 1.0, high = minL;
		for(int i=0;i<200;i++){
			double mid = 0.5*(low+high);
			vector<circle> vc;
			for(int j=0;j<n;j++){
				double r = sqrt(l[j]*l[j]-mid*mid);
				vc.push_back(make_pair(P(x[j], y[j]), r));
			}
			if(valid(vc)) low  = mid;
			else          high = mid;
		}
		printf("%.8lf\n", 0.5*(low+high));
	}
}