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

#define DEBUG 1

#define INF (1.0/0.0)
#define EPS 1e-8
#define PI 3.1415926535
#define EQ(x, y) (abs((x)-(y))<EPS)
#define X real()
#define Y imag()

typedef complex<double> Point;
typedef Point Vec;
typedef array<Point, 2> Line;
typedef vector<Point> Poly;

struct Circle {
  Point c;
  double r;
};

enum Geometory {ABC=-2, CW, ON_LINE, CCW, CAB, OUTSIDE, INSIDE, ERROR}; 

namespace std {
  bool operator<(Point a, Point b) {
    if (!EQ(a.X, b.X)) return a.X < b.X;
    if (!EQ(a.Y, b.Y)) return a.Y < b.Y;
    return false;
  }

  bool operator>(Point a, Point b) {
    return b<a;
  }

  bool operator<=(Point a, Point b) {
    return !(a>b);
  }
}

double dot(Point a, Point b) {
  return (conj(a)*b).X;
}

double cross(Point a, Point b) {
  return (conj(a)*b).Y;
}

Geometory ccw(Point a, Point b, Point c) {
  b -= a;
  c -= a;
  if (cross(b, c) > EPS) return CCW; // ccw
  if (cross(b, c) < -EPS) return CW; // cw
  if (dot(b, c) < 0) return CAB; // c - a - b
  if (norm(b) < norm(c)) return ABC; // a - b - c
  return ERROR;
}

Point proj(Line l, Point p) {
  Point v = l[1]-l[0];
  double ratio = dot(v, p-l[0]) / norm(v);
  return l[0] + ratio*v;
}

Point refl(Line l, Point p) {
  return p + (proj(l, p) - p) * 2.0;
}

Vec rotate(Vec v, double r) {
  return v*Vec(cos(r), sin(r));
}

bool IsOrthogonal(Line l, Line m) {
  Vec v1 = l[1]-l[0];
  Vec v2 = m[1]-m[0];
  return EQ(dot(v1, v2), 0.0);
}

bool IsParallel(Line l, Line m) {
  Vec v1 = l[1]-l[0];
  Vec v2 = m[1]-m[0];
  return EQ(cross(v1, v2), 0.0);
}

bool IntersectLL(Line l, Line m) {
  if (!EQ(cross(l[1]-l[0], m[1]-m[0]), 0.0)) return true;
  if (EQ(cross(l[1]-l[0], m[0]-l[0]), 0.0)) return true;
  return false;
}

bool IntersectLS(Line l, Line s) {
  Point b = l[0];
  Vec v = l[1]-l[0];
  return cross(v, s[0]-b)*cross(v, s[1]-b) < EPS;
}

bool IntersectSS(Line s, Line t) {
  if (ccw(s[0], s[1], t[0])*ccw(s[0], s[1], t[1]) > 0) return false;
  if (ccw(t[0], t[1], s[0])*ccw(t[0], t[1], s[1]) > 0) return false;
  return true;
}

bool IntersectLP(Line l, Point p) {
  return EQ(cross(l[1]-p, l[0]-p), 0.0);
}

bool IntersectSP(Line s, Point p) {
  return abs(s[0]-p)+abs(s[1]-p)-abs(s[1]-s[0]) < EPS;
}

double DistL(Line l) {
  return abs(l[0]-l[1]);
}

double DistLP(Line l, Point p) {
  return abs(p - proj(l, p));
}

double DistLL(Line l, Line m) {
  if (!IntersectLL(l, m)) return 0;
  return DistLP(l, m[0]);
}

double DistLS(Line l, Line s) {
  if (IntersectLS(l, s)) return 0;
  return min(DistLP(l, s[0]), DistLP(l, s[1]));
}

double DistSP(Line s, Point p) {
  Point r = proj(s, p);
  if (IntersectSP(s, r)) return abs(r - p);
  return min(abs(s[0]-p), abs(s[1]-p));
}

double DistSS(Line s, Line t) {
  if (IntersectSS(s, t)) return 0;

  double a = min(DistSP(s, t[0]), DistSP(s, t[1]));
  double b = min(DistSP(t, s[0]), DistSP(t, s[1]));
  return min(a, b);
}

Line PerpendBisect(Line seg) {
  Point mid = (seg[0]+seg[1])/2.0;
  return Line{mid, mid+(seg[1]-seg[0])*Vec(0, 1)};
}

Point CrossPointLL(Line l, Line m) {
  double A = cross(l[1]-l[0], m[1]-m[0]);
  double B = cross(l[1]-l[0], l[1]-m[0]);
  if (abs(A) < EPS && abs(B) < EPS) return m[0];
  if (abs(A) < EPS) assert(0);
  return m[0] + B / A * (m[1]-m[0]);
}

vector<Point> CrossPointCL(Circle c, Line l) {
  vector<Point> ret;
  double d = DistLP(l, c.c);
  if (d < c.r + EPS) {
    double ratio = (d > c.r) ? 0.0 : sqrt(c.r*c.r - d*d);
    Vec sgn = (l[0]-l[1]) / abs(l[0]-l[1]);
    ret.emplace_back(proj(l, c.c) + ratio*sgn);
    ret.emplace_back(proj(l, c.c) - ratio*sgn);
  }
  return ret;
}

vector<Point> CrossPointCS(Circle c, Line s) {
  vector<Point> ret;
  vector<Point> res = CrossPointCL(c, s);
  if (s[0] > s[1]) swap(s[0], s[1]);
  for (Point p : res) {
    if (s[0] <= p && p <= s[1]) ret.emplace_back(p);
  }
  return ret;
}

vector<Point> CrossPointCC(Circle c1, Circle c2) {
  vector<Point> ret;
  double d = abs(c1.c - c2.c);
  double rc = (d*d + c1.r*c1.r - c2.r*c2.r) / (2*d);
  double dfr = c1.r*c1.r - rc*rc;

  if (EQ(dfr, 0.0)) dfr = 0.0;
  else if(dfr < 0.0) return ret;

  double rs = sqrt(dfr);
  Vec sgn = (c2.c - c1.c) / d;
  ret.emplace_back(c1.c + sgn*Point(rc, rs));
  if (dfr > 0.0) ret.emplace_back(c1.c + sgn*Point(rc, -rs));
  return ret;
}

// Get the intersection of a circle and a segment, which is obviously a segment
Line CapCS(Circle c, Line s) {
  Point inf(INF, INF);
  vector<Point> cros = CrossPointCS(c, s);
  if (cros.empty()) return Line{inf, inf};

  if (cros.size() == 1) {
    double ad = abs(s[0]-c.c);
    double bd = abs(s[1]-c.c);
    if (ad < min(bd, c.r)) cros.push_back(s[0]);
    else if (bd < min(ad, c.r)) cros.push_back(s[1]);
    else {
      Point p = cros[0];
      cros.push_back(p); // avoid an undefined behavior
    }
  }

  if (cros[1] < cros[0]) {
    swap(cros[0], cros[1]);
  }

  return Line{cros[0], cros[1]};
}

// Note that ccw(a, b, c) != CCW when a, b, c are colinear
Poly GrahamScan(vector<Point> ps) {
  int k = 0;
  int n = ps.size();
  Poly ret(n*2);

  sort(ps.begin(), ps.end());
  for (int i=0; i<n; i++) {
    while (k > 1 && ccw(ret[k-2], ret[k-1], ps[i]) != CCW) k--;
    ret[k++] = ps[i];
  }

  int k_ = k;
  for (int i=n-1; i>=0; i--) {
    while (k > k_ && ccw(ret[k-2], ret[k-1], ps[i]) != CCW) k--;
    ret[k++] = ps[i];
  }

  ret.resize(k-1);
  return ret;
}

double CalcArea(Poly ps) {
  double ret = 0.0;
  for (int i=0; i<ps.size(); i++) {
    ret += cross(ps[i], ps[(i+1)%ps.size()]);
  }
  return ret/2.0;
}

bool IsConvex(Poly ps) {
  return GrahamScan(ps).size() == ps.size();
}

Geometory ContainsPoint(Poly poly, Point p) {
  bool in = false;
  int n = poly.size();
  for (int i=0; i<n; i++) {
    Point a = poly[i];
    Point b = poly[(i+1)%n];
    Vec u = a - p;
    Vec v = b - p;

    if (u.Y > v.Y) swap(u, v);

    double cr = cross(u, v);
    if (u.Y <= 0 && 0 < v.Y && cr > EPS) in ^= 1;
    if (IntersectSP({a, b}, p)) return ON_LINE;
  }

  if (in) return INSIDE;
  return OUTSIDE;
}

// Convex* requires the elements of ps to be arranged counter clockwise.
pair<int, int> ConvexDiameterApexes(Poly ps) {
#if DEBUG
  assert (IsConvex(ps));
#endif

  int n = ps.size();
  int is = 0;
  int js = 0;
  for (int i=1; i<n; i++) {
    if (ps[i].Y > ps[is].Y) is = i;
    if (ps[i].Y < ps[js].Y) js = i;
  }

  int maxi, maxj;
  double maxd = norm(ps[is]-ps[js]);
  int i = is;
  int j = js;
  do {
    Vec a = ps[i+1] - ps[i];
    Vec b = ps[j+1] - ps[j];
    if (cross(a, b) > -EPS) j = (j+1)%n;
    else i = (i+1)%n;

    double d = norm(ps[i]-ps[j]);
    if (d > maxd) {
      maxd = d;
      maxi = i;
      maxj = j;
    }
  } while (i != is || j != js);

  return make_pair(maxi, maxj);
}

Line ClosestPair(vector<Point> ps) {
  auto CompareY = [](const Point &a, const Point &b) {
    if (a.Y != b.Y) return a.Y < b.Y;
    return a.X < b.X;
  };

  function<Line(Point*,int)> Rec = [&Rec, &CompareY](Point *ps, int n) {
    if (n <= 1) return Line{Point(0, 0), Point(INF, INF)};
    
    int m = n/2;
    double x = ps[m].X;
    Line a = Rec(ps, m);
    Line b = Rec(ps+m, n-m);
    double mind = DistL(a);
    Line ret = a;
    if (DistL(b) < mind) {
      mind = DistL(b);
      ret = b;
    }

    sort(ps, ps+n, CompareY);
    vector<Point> qs;
    qs.reserve(n);
    for (int i=0; i<n; i++) {
      if (abs(ps[i].X - x) >= mind) continue;

      for (int j=0; j<qs.size(); j++) {
        Point p1 = ps[i];
        Point p2 = qs[qs.size()-1-j];
        if (p1.Y - p2.Y >= mind) break;

        double d = abs(p1-p2);
        if (mind > d) {
          mind = d;
          ret = Line{p1, p2};
        }
      }

      qs.emplace_back(ps[i]);
    }

    return ret;
  };

  int n = ps.size();
  assert (n >= 2);
  sort(ps.begin(), ps.end());
  return Rec(&ps[0], n);
}

// Convex* requires the elements of ps to be arranged counter clockwise.
// <left, right> or <upper, lower>
pair<Poly, Poly> CutConvex(Poly ps, Line l) {
#if DEBUG
  assert (IsConvex(ps));
#endif

  //if (l[0].Y > l[1].Y) swap(l[0], l[1]);
  //else if (EQ(l[0].Y, l[1].Y) && l[0].X > l[1].X) swap(l[0], l[1]);

  Poly left;
  Poly right;
  for (int i=0; i<ps.size(); i++) {
    Point a = ps[i];
    Point b = ps[(i+1)%ps.size()];

    if (ccw(l[0], l[1], a) != CW) left.emplace_back(a);
    else right.emplace_back(a);

    Line m{a, b};
    if (IntersectLS(l, m)) {
      Point p = CrossPointLL(l, m);
      left.emplace_back(p);
      right.emplace_back(p);
    }
  }

  return make_pair(left, right);
}

Circle Circum(Point a, Point b, Point c) {
  Circle ret{{INF, INF}, 0.0};
  Line l{a, b};
  Line m{b, c};
  Line lp = PerpendBisect(l);
  Line mp = PerpendBisect(m);
  if (IsParallel(lp, mp)) return ret;

  ret.c = CrossPointLL(lp, mp);
  ret.r = abs(a-ret.c);
  return ret;
}

int n;
double ls[114514];
Point ps[114514];
Circle cs[114514];

bool check(double K) {
  vector<Point> qs;

  for (int i=0; i<n; i++) {
    if (ls[i] < K) return false;
    double r = sqrt(ls[i]*ls[i]-K*K);
    cs[i] = {ps[i], r};
    qs.push_back(ps[i]);
  }

  for (int i=0; i<n; i++) {
    for (int j=i+1; j<n; j++) {
      vector<Point> cros = CrossPointCC(cs[i], cs[j]);
      qs.insert(qs.end(), cros.begin(), cros.end());
    }
  }

  for (Point &c : qs) {
    bool fail = false;
    for (int i=0; i<n; i++) {
      if (abs(cs[i].c-c) >= cs[i].r+EPS) {
        fail = true;
        break;
      }
    }

    if (!fail) return true;
  }

  return false;
}

int main() {
  while (1) {
    scanf("%d", &n);
    if (n == 0) return 0;

    for (int i=0; i<n; i++) {
      int x, y;
      scanf("%d%d%lf", &x, &y, &ls[i]);
      ps[i] = Point(x, y);
    }
  
    double low = 0.0;
    double high = 400;
    for (int i=0; i<40; i++) {
      double mid = (low+high)/2;
      if (check(mid)) low = mid;
      else high = mid;
    }
    printf("%.10f\n", low);
  }
}

Measured memory_bytes: 5948