//include
//------------------------------------------
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>
#include <climits>
#include <queue>

using namespace std;

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef long long LL;

//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

//repetition
//------------------------------------------
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

//constant
//--------------------------------------------
const double EPS = 1e-9;
const double PI  = acos(-1.0);
const double INF = 1e9;

struct P{
  double x;
  double y;

  P(){
	x=INF,y=INF;
  }

  P(const double &s , const double &e)
  { x=s; y=e;}

  P operator - (const P &t) const
  { return P(x-t.x , y-t.y); }

  P operator + (const P &t) const
  { return P(x+t.x , y+t.y); }

  P operator * (const double &d) const
  { return P(x*d , y*d); }
  P operator / (const double &d) const
  { return P(x/d , y/d); }
};
double dis(P t){
  return sqrt(t.x*t.x+t.y*t.y);
}

P unit_vector(P t){
  double u=fabs(dis(t));
  return P(t.x/u , t.y/u);
}
P rotate(P p,double angle){
  return P(p.x*cos(angle) - p.y*sin(angle),
			   p.x*sin(angle) + p.y*cos(angle));
}
struct Circle{
  P c;
  double r;
};

pair<P, P> getCrossPoints(const Circle& c1, const Circle& c2){
  double d = dis(c2.c - c1.c);
  double a = (c1.r*c1.r + d*d - c2.r*c2.r) / (2*d);
  P e = (c2.c - c1.c) / d;
  P h = rotate(e, PI/2) * sqrt(max(c1.r*c1.r - a*a, 0.));
  if(d + min(c1.r, c2.r) <= max(c1.r, c2.r))
	return MP(c1.c + e*c1.r, c1.c + e*c1.r);

  return MP(c1.c + e*a + h, c1.c + e*a - h);
}

int main(){
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  int N;
  while(cin>>N,N){
	vector<P> p(N);
	vector<double> ls(N);
	double ub = 1000;
	REP(i,N){
	  cin >> p[i].x >> p[i].y >> ls[i];
	  ub = min(ub, ls[i]);
	}

	double lb = 0;
	REP(loop,100){
	  double h = (lb + ub) / 2.;
	  bool ok = true;

	  if(ok){
		ok = false;
		vector<double> ri(N);
		REP(i,N) ri[i] = sqrt(ls[i]*ls[i] - h*h);
		vector<P> chk;
		REP(i,N){
		  REP(j,N){
			Circle c1, c2;
			c1.c = p[i];
			c1.r = ri[i];
			c2.c = p[j];
			c2.r = ri[j];
			auto icp = getCrossPoints(c1, c2);

			P dirs[4] = {P(-EPS,0), P(EPS,0), P(0,-EPS), P(0,EPS)};
			REP(d,4){
			  chk.PB(icp.first + dirs[d]);
			  chk.PB(icp.second + dirs[d]);
			}
		  }
		  chk.PB(p[i]);
		}
		for(auto& pp: chk){
		  int cnt = 0;
		  REP(k,N){
			if(dis(p[k]-pp) <= ri[k]+EPS)
			  ++cnt;
		  }
		  if(cnt == N) ok = true;
		}
	  }

	  if(ok) lb = h;
	  else ub = h;
	}
	cout << fixed << setprecision(9) << lb << endl;
  }
  
  return 0;
}

Measured memory_bytes: 3528