// Slower C++ solution:
#include <iostream>

#include <vector>

#include <string>

#include <algorithm>

#include <complex>

#include <iomanip>

#include <assert.h>

using namespace std;

typedef complex<double> P;

const double EPS = 1e-10;

int n;

double l[10];



struct C {

	P p;

	double r;



	C() {

		p = P(0, 0);

		r = 0;

	}



	C(const P& p, double r) : p(p), r(r) {

	}



	bool in(P t) {

		return norm(p - t) < r * r + EPS;

	}



	bool in(C t) {

		return abs(p - t.p) + t.r < r + EPS;

	}

} c[10];



bool check(double h) {

	for (int i = 0; i < n; i++) {

		if (l[i] * l[i] - h * h < EPS) return false;

		c[i].r = sqrt(l[i] * l[i] - h * h);

	}



	vector<P> cs;

	for (int i = 0; i < n; i++) {

		cs.push_back(c[i].p);

	}



	for (int i = 0; i < n; i++) {

		for (int j = i + 1; j < n; j++) {

			C c1 = c[i], c2 = c[j];

			if (abs(c1.p - c2.p) > c1.r + c2.r) return false; // ????????????

			if (c1.in(c2) || c2.in(c1)) continue;



			P v = c2.p - c1.p;

			double t = (c1.r * c1.r + norm(v) - c2.r * c2.r) / (2 * abs(v));

			double theta = acos(t / c1.r);

			//assert(-1.0 <= t / c1.r && t / c1.r <= 1.0);

			P b[2];

			b[0] = c1.p + v / abs(v) * c1.r * polar(1.0, theta);

			b[1] = c1.p + v / abs(v) * c1.r * polar(1.0, -theta);

			cs.push_back(b[0]);

			cs.push_back(b[1]);

		}

	}



	for (int i = 0; i < cs.size(); i++) {

		bool flag = true;

		for (int m = 0; m < n; m++) {

			if (!c[m].in(cs[i])) {

				flag = false;

				break;

			}

		}

		if (flag) return true;

	}

	return false;

}



int main() {

	cin.tie(0);

	ios::sync_with_stdio(false);



	while (cin >> n , n) {

		for (int i = 0; i < n; i++) {

			double x, y;

			cin >> x >> y >> l[i];

			c[i].p = P(x, y);

		}

		check(0);

		double ok = 0, ng = 100000;

		for (int loop = 0; loop < 1000; loop++) {

			double h = (ok + ng) / 2;

			if (check(h)) ok = h;

			else ng = h;

		}

		cout << setprecision(15) << ok << endl;

	}

}

// Faster C++ solution for the same problem (measured speedup: 4.9616258692936075x):
#include <iostream>

#include <vector>

#include <string>

#include <algorithm>

#include <complex>

#include <iomanip>

#include <assert.h>

using namespace std;

typedef complex<double> P;

const double EPS = 1e-10;

int n;

double l[10];



struct C {

	P p;

	double r;



	C() {

		p = P(0, 0);

		r = 0;

	}



	C(const P& p, double r) : p(p), r(r) {

	}



	bool in(P t) {

		return norm(p - t) < r * r + EPS;

	}



	bool in(C t) {

		return abs(p - t.p) + t.r < r + EPS;

	}

} c[10];



bool check(double h) {

	for (int i = 0; i < n; i++) {

		if (l[i] * l[i] - h * h < EPS) return false;

		c[i].r = sqrt(l[i] * l[i] - h * h);

	}



	vector<P> cs;

	for (int i = 0; i < n; i++) {

		cs.push_back(c[i].p);

	}



	for (int i = 0; i < n; i++) {

		for (int j = i + 1; j < n; j++) {

			C c1 = c[i], c2 = c[j];

			if (abs(c1.p - c2.p) > c1.r + c2.r) return false; // ????????????

			if (c1.in(c2) || c2.in(c1)) continue;



			P v = c2.p - c1.p;

			double t = (c1.r * c1.r + norm(v) - c2.r * c2.r) / (2 * abs(v));

			double theta = acos(t / c1.r);

			//assert(-1.0 <= t / c1.r && t / c1.r <= 1.0);

			P b[2];

			b[0] = c1.p + v / abs(v) * c1.r * polar(1.0, theta);

			b[1] = c1.p + v / abs(v) * c1.r * polar(1.0, -theta);

			cs.push_back(b[0]);

			cs.push_back(b[1]);

		}

	}



	for (int i = 0; i < cs.size(); i++) {

		bool flag = true;

		for (int m = 0; m < n; m++) {

			if (!c[m].in(cs[i])) {

				flag = false;

				break;

			}

		}

		if (flag) return true;

	}

	return false;

}



int main() {

	cin.tie(0);

	ios::sync_with_stdio(false);



	while (cin >> n , n) {

		for (int i = 0; i < n; i++) {

			double x, y;

			cin >> x >> y >> l[i];

			c[i].p = P(x, y);

		}

		check(0);

		double ok = 1, ng = 300;

		for (int loop = 0; loop < 100; loop++) {

			double h = (ok + ng) / 2;

			if (check(h)) ok = h;

			else ng = h;

		}

		cout << setprecision(15) << ok << endl;

	}

}