#include<bits/stdc++.h>
using namespace std;

typedef long long int ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pair<int, int> > vii;
#define rrep(i, m, n) for(int (i)=(m); (i)<(n);  (i)++)
#define erep(i, m, n) for(int (i)=(m); (i)<=(n); (i)++)
#define  rep(i, n)    for(int (i)=0; (i)<(n);  (i)++)
#define rrev(i, m, n) for(int (i)=(n)-1; (i)>=(m); (i)--)
#define erev(i, m, n) for(int (i)=(n); (i)>=(m); (i)--)
#define  rev(i, n)    for(int (i)=(n)-1; (i)>=0; (i)--)
#define vrep(i, c)    for(__typeof((c).begin())i=(c).begin(); i!=(c).end(); i++)
#define  ALL(v)       (v).begin(), (v).end()
#define pb            push_back
template<class T, class S> inline pair<T, S> mp(T x, S y){ return make_pair(x, y); }
template<class T, class S> inline bool minup(T& m, S x){ return m>(T)x ? (m=(T)x, true) : false; }
template<class T, class S> inline bool maxup(T& m, S x){ return m<(T)x ? (m=(T)x, true) : false; }

static const int    INF = 1000000000;
static const ll     MOD = 1000000007LL;
static const double EPS = 1E-10;

template<typename T> T add(T x, T y){ if(abs(x+y) < EPS*(abs(x)+abs(y))) return 0; return x + y; }
template<typename T> inline bool semieq(T x, T y){ return abs(x - y) < EPS; }
template<typename T> inline bool semige(T x, T y){ return y - x < -EPS; }
template<typename T> inline bool semile(T x, T y){ return x - y < -EPS; }


struct Point : public complex<double>
{
public:
  Point(const double x = 0.0, const double y = 0.0) { this->real(x);  this->imag(y); }
  Point(const complex<double> w)  { this->real(w.real());  this->imag(w.imag()); }
  inline double dot(Point p){ return (conj(*this) * p).real(); }  // ??????
  inline double det(Point p){ return (conj(*this) * p).imag(); }  // ??????
};

namespace std
{
  inline bool operator < (const Point& a, const Point& b)
  {
    return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
  }
}
typedef vector<Point> Polygon;
inline Point currPoint(vector<Point> P, int i){ return P[i]; }
inline Point nextPoint(vector<Point> P, int i){ return P[(i+1)%P.size()]; }
inline Point diffPoint(vector<Point> P, int i){ return nextPoint(P, i) - currPoint(P, i); }


struct Circle : Point
{
private:
  Point p;
  double r;

public:
  Circle(Point p, double r) : p(p), r(r) {}
  Circle(double x, double y, double r) : p(Point(x, y)), r(r) {}
  inline Point center(){ return this->p; }
  inline double radius(){ return this->r; }
};


// ???????????????????¨±??????????????????????????????????????¨????????????????¨???????????????????
vector<Point> intersectionOfCC(Circle A, Circle B)
{
  vector<Point> ret;
  double d = abs(A.center() - B.center());
  double rc = (d * d + A.radius() * A.radius() - B.radius() * B.radius()) / (2.0 * d);
  double rs = sqrt(A.radius() * A.radius() - rc * rc);
  Point diff = (B.center() - A.center()) / d;
  ret.pb(A.center() + diff * Point(rc,  rs));
  ret.pb(A.center() + diff * Point(rc, -rs));
  return ret;
}

int intersectionDeterminationOfCC(Circle A, Circle B)
{
  double d = abs(A.center() - B.center());
  if(semile(d, A.radius() - B.radius())) return  1;  // B in A
  if(semile(d, B.radius() - A.radius())) return -1;  // A in B
  if(semieq(d, A.radius() - B.radius())) return  2;  // B in A????????\???
  if(semieq(d, B.radius() - A.radius())) return -2;  // A in B????????\???
  if(semieq(d, A.radius() + B.radius())) return  3;  // ?????\
  if(semige(d, A.radius() + B.radius())) return -3;  // ???????????????
  return 4;  // ????????£?????????
}

inline bool operator < (Circle& A, Circle& B)
{
  return A.radius() != B.radius() ? A.radius() < B.radius() : A.center() < B.center();
}

const int MAX_N = 12;
int n;
double x, y;
double l[MAX_N];
Point p[MAX_N];

bool C(double x)
{
  vector<Circle> c;
  rep(i, n) c.pb(Circle(p[i], sqrt(l[i] * l[i] - x * x)));
  rep(i, c.size()) rep(j, i){
    Circle A = c[i];
    Circle B = c[j];
    int det = intersectionDeterminationOfCC(A, B);
    if(det < 3) continue;
    vector<Point> vp = intersectionOfCC(A, B);
    vrep(v, vp){
      bool ok = true;
      vrep(w, c) ok &= !semige(abs(*v - w->center()), w->radius());
      if(ok) return true;
    }
  }

  sort(ALL(c));
  bool ok = true;
  rep(i, n-1){
      int det = intersectionDeterminationOfCC(c[i], c[i+1]);
      ok &= (det == -1 || det == -2);
  }
  if(ok) return true;

  vrep(v, c){
    bool ok = true;
    vrep(w, c) ok &= !semige(abs(v->center() - w->center()), w->radius());
    if(ok) return true;
  }

  return false;
}

int main()
{
  int cnt = 0;
  while(cin >> n, n){
    double mn = (double)INF;
    rep(i, n){
      cin >> x >> y >> l[i];
      p[i] = Point(x, y);
      minup(mn, l[i]);
    }

    double left = 1.0;
    double right = mn;
    rep(_, 100){
      double mid = (left + right) / 2.0;
      if(C(mid)) left = mid;
      else right = mid;
    }

    printf("%.15f\n", right);
  }


  return 0;
}

Measured memory_bytes: 1272