#include <bits/stdc++.h>
 
#define ISLOOSE(a,b)    (disdis(a, b) + get<2>(a) * get<2>(a) <= get<2>(b) * get<2>(b))
 
using namespace std;

double disdis(const tuple<double, double, double>& a, const tuple<int, int, int>& b)
{
	return (get<0>(a) - get<0>(b)) * (get<0>(a) - get<0>(b)) + (get<1>(a) - get<1>(b)) * (get<1>(a) - get<1>(b));
}

int disdis(const tuple<int, int, int>& a, const tuple<int, int, int>& b)
{
    return (get<0>(a) - get<0>(b)) * (get<0>(a) - get<0>(b)) + (get<1>(a) - get<1>(b)) * (get<1>(a) - get<1>(b));
}
 
double heron(double a, double b, double c)
{
    double s = (a + b + c) / 2;
    return sqrt(s*(s - a)*(s - b)*(s - c));
}
 
double heron2(double a, double b, double c, double d, double e, double f)
{
    return sqrt((a*d*(b + c + e + f - a - d) + b*e*(c + a + f + d - b - e) + c*f*(a + b + d + e - c - f) - a*b*f - a*e*c - d*b*c - d*e*f) / 144.0);
}
 
tuple<double, double, double> com(const tuple<int, int, int>& a, const tuple<int, int, int>& b)
{
    if (ISLOOSE(a, b)) {
        return a;
    }
    else if (ISLOOSE(b, a)) {
        return b;
    }
    else {
        double l = heron(get<2>(a), get<2>(b), sqrt(disdis(a, b))) * 2 / sqrt(disdis(a, b));
        double d1 = sqrt(get<2>(a) * get<2>(a) - l * l);
        double d2 = sqrt(get<2>(b) * get<2>(b) - l * l);
        return tuple<double, double, double>(get<0>(a) + (get<0>(b) - get<0>(a)) * d1 / (d1 + d2), get<1>(a) + (get<1>(b) - get<1>(a)) * d1 / (d1 + d2), l);
    }
}
 
double two(const tuple<int, int, int>& a, const tuple<int, int, int>& b)
{
    if (ISLOOSE(a, b)) {
        return (double)get<2>(a);
    }
    else if (ISLOOSE(b, a)) {
        return (double)get<2>(b);
    }
    else {
        double d = sqrt(disdis(a, b));
        return heron(get<2>(a), get<2>(b), d) * 2 / d;
    }
}
 
double three(const tuple<int, int, int>& a, const tuple<int, int, int>& b, const tuple<int, int, int>& c)
{
    tuple<double, double, double> temp;
 
    if (ISLOOSE(a, b) && ISLOOSE(a, c))
        return get<2>(a);
    if (ISLOOSE(b, a) && ISLOOSE(b, c))
        return get<2>(b);
    if (ISLOOSE(c, a) && ISLOOSE(c, b))
        return get<2>(c);
 
    if (ISLOOSE(temp = com(a, b), c))
        return get<2>(temp);
    if (ISLOOSE(temp = com(b, c), a))
        return get<2>(temp);
    if (ISLOOSE(temp = com(c, a), b))
        return get<2>(temp);
 
    return heron2(get<2>(a) * get<2>(a), get<2>(b) * get<2>(b), get<2>(c) * get<2>(c), disdis(b, c), disdis(c, a), disdis(a, b))
        * 3.0 / heron(sqrt(disdis(a, b)), sqrt(disdis(b, c)), sqrt(disdis(c, a)));
}
 
int main()
{
    int n;
    double res;
	cout << fixed << setprecision(7);
    while (cin >> n, n) {
        vector< tuple<int, int, int> > str(n);
        for (int i = 0; i < n; i++) {
            cin >> get<0>(str[i]) >> get<1>(str[i]) >> get<2>(str[i]);
        }
        if (n == 1) {
            cout << (double)get<2>(str[0]) << endl;
        }
        else if (n == 2) {
            cout << two(str[0], str[1]) << endl;
        }
        else {
            res = 100000000.0;
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    for (int k = j + 1; k < n; k++) {
                        res = min(res, three(str[i], str[j], str[k]));
                    }
                }
            }
            cout << res << endl;
        }
    }
    return 0;
}

Measured memory_bytes: 3276