#include<bits/stdc++.h> //std==c++14
using namespace std;
 
#define EPS (1e-10)
#define equals(a,b) ( fabs(a-b) < EPS )
#define PI acos(-1)
// COUNTER CLOCKWISE
static const int CCW_COUNTER_CLOCKWISE = 1;
static const int CCW_CLOCKWISE = -1;
static const int CCW_ONLINE_BACK = 2;
static const int CCW_ONLINE_FRONT = -2;
static const int CCW_ON_SEGMENT = 0;

//Intersect Circle and Circle
static const int ICC_SEPARATE = 4;//離れている
static const int ICC_CIRCUMSCRIBE = 3;//外接
static const int ICC_INTERSECT = 2;// 交わる
static const int ICC_INSCRIBE = 1;// 内接
static const int ICC_CONTAIN = 0;//内包

struct point{
	double x,y;
	//construct
	point() {} 
	point(double x,double y):x(x),y(y){}
	//演算子
	point operator + (point p) { return point(x+p.x,y+p.y); }
	point operator - (point p) { return point(x-p.x,y-p.y); }
	point operator * (double k) { return point(x*k,y*k); }
	point operator / (double k) { return point(x/k,y/k); }
	point operator / (point p) { return point( (x*p.x + y*p.y)/p.norm()  , (-x*p.y + y*p.x)/p.norm() ) ; }
	bool operator < (point p) { return x!=p.x ? x<p.x : y<p.y; }
	bool operator == (point p) { return equals(x,p.x) && equals(y,p.y) ; }
	//function
	double arg() { return atan2(y,x) ; }
	double norm(){return x*x+y*y; }
	double abs() { return sqrt(norm() ) ;}
	double dot(point p) { return p.x*x + p.y*y; }
	double cross(point p) { return x*p.y - y*p.x; }
	point roll(double theta){ return point( cos(theta)*x - sin(theta)*y , sin(theta)*x + cos(theta)*y ) ; }	
	//input output
	void input(){cin>>x>>y;}
	void polar(double r,double theta){ x = r*cos(theta), y= r*sin(theta) ; }
	void print(){cout<<x<<' '<<y<<endl;};

};

bool sort_x(point a,point b){
	return a.x!=b.x?a.x<b.x:a.y<b.y ;
}
bool sort_y(point a,point b){
	return a.y!=b.y?a.y<b.y:a.x<b.x ;
}

typedef vector<point> polygon;

struct segment{
	point s,t;
	segment() {}
	segment(point s,point t) : s(s),t(t){}
	void input(){s.input(),t.input(); }
};
typedef segment line;

struct circle{
	point c;
	double r;
	circle() {}
	circle(point c,double r) : c(c),r(r){}
	void input(){c.input(); cin>>r; }
};

double norm(point a){	return a.norm(); }
double abs(point a){ return a.abs(); }
double arg(point a){ return a.arg(); }
double dot(point a,point b) { return a.x*b.x + a.y*b.y ; }
double cross(point a,point b) { return a.x * b.y - a.y * b.x ; }
point polar(double r,double theta){ point a; a.polar(r,theta); return a; }
point orth(point p){ return point(-p.y,p.x); }

//isOrthgonal 垂直
bool isOrthogonal(point a,point b) { return equals(dot(a,b), 0.0 ) ; }
bool isOrthogonal(point a,point b,point c,point d) { return isOrthogonal(a-b,c-d) ; }
bool isOrthogonal(line l1,line l2 ){ return isOrthogonal(l1.t-l1.s,l2.t-l2.s); }
//isParallel 平行
bool isParallel(point a,point b) { return equals(cross(a,b), 0.0) ; }
bool isParallel(point a,point b,point c,point d) { return isParallel(a-b,c-d); }
bool isParallel(line l1,line l2) { return isParallel(l1.t-l1.s,l2.t-l2.s) ; }

point project(line l,point p){
	point base = l.t-l.s;
	double r = dot(p-l.s,base) / norm(base) ;
	return l.s + base*r;
}
point reflect(line l,point p){
	return p + (project(l,p) - p) *2.0;
}

int ccw(point p0,point p1,point p2){
	point a = p1-p0;
	point b = p2-p0;
	if(cross(a,b) > EPS ) return CCW_COUNTER_CLOCKWISE ;
	if(cross(a,b) < -EPS ) return CCW_CLOCKWISE;
	if(dot(a,b) < -EPS ) return CCW_ONLINE_BACK;
	if(a.norm() < b.norm() ) return CCW_ONLINE_FRONT;
	return CCW_ON_SEGMENT;
}


//intersect
bool intersect(point p1,point p2,point p3,point p4){return (ccw(p1,p2,p3)*ccw(p1,p2,p4) <= 0 && ccw(p3,p4,p1)*ccw(p3,p4,p2) <= 0 ) ; }
bool intersect(line l1,line l2) { return intersect(l1.s,l1.t,l2.s,l2.t) ; }
bool intersect(polygon p,line l){
	int n = p.size();
	for(int i=0;i<n;i++)  if(intersect(line(p[i],p[(i+1)%n] ) , l ) ) return true;
	return false;
}
int intersect(circle c1,circle c2){
	if(c1.r < c2.r) swap(c1,c2);
	double d = abs(c1.c-c2.c);
	double r = c1.r + c2.r;
	if(equals(d,r) ) return ICC_CIRCUMSCRIBE;
	if(d > r ) return ICC_SEPARATE;
	if(equals(d+c2.r,c1.r) ) return ICC_INSCRIBE;
	if( d + c2.r < c1.r ) return ICC_CONTAIN;
	return ICC_INTERSECT;
}

//bool intersectsc(line l,circle c){ return distancesp(l,c.c) <= c.r ; } distanceののち
int intersectcs(circle c,line l ){// 0		1		2
	if(norm(project(l,c.c) - c.c )  - c.r*c.r  > EPS ) return 0;
	double d1 = abs(c.c-l.s),d2  = abs(c.c-l.t);
	if(d1 < c.r + EPS && d2 < c.r + EPS ) return 0;
	if( (d1<c.r - EPS && d2 > c.r +EPS) || (d1 > c.r +EPS &&d2 < c.r -EPS ) ) return 1;
	point h = project(l,c.c) ;
	if(dot(l.s-h,l.t-h) < 0 ) return 2;
	return 0;
}

//distance
//line point
double distancelp(line l,point p){ return abs(cross(l.t-l.s,p-l.s)/ abs(l.t-l.s)  ); }
//segment point
double distancesp(line l,point p){ 
	if(dot(l.t-l.s,p-l.s) < 0.0 ) return abs(p-l.s);
	if(dot(l.s-l.t,p-l.t) < 0.0 ) return abs(p-l.t);
	return distancelp(l,p);
}
//segment segment 
double distancess(line l1,line l2){
	if(intersect(l1,l2) ) return 0.0;
	return min( min(distancesp(l1,l2.s) ,distancesp(l1,l2.t) ) , min(distancesp(l2,l1.s),distancesp(l2,l1.t)  ) );
}

bool intersectsc(line l,circle c){ return distancesp(l,c.c) <= c.r ; }

//crosspoint 
//segment segment
point crosspointss(line l1,line l2){
	for(int k=0;k<2;k++){
		if(distancesp(l1,l2.s) < EPS ) return l2.s;
		if(distancesp(l1,l2.t) < EPS ) return l2.t;
		swap(l1,l2);
	}
	point base = l2.t-l2.s;
	double d1 = abs(cross(base,l1.s-l2.s) );
	double d2 = abs(cross(base,l1.t-l2.s) );
	double t = d1/(d1+d2);
	return l1.s + (l1.t-l1.s) * t;
}
//line line
point crosspointll(line l1,line l2){
	double a = cross(l1.t-l1.s,l2.t-l2.s);
	double b = cross(l1.t-l1.s,l1.t-l2.s);
	if(abs(a) < EPS && abs(b) < EPS ) return l2.s;
	return l2.s + (l2.t-l2.s) * (b/a) ;
}
//circle line
polygon crosspointCL(circle c,line l){
	polygon ps;
	point pr = project(l,c.c);
	point e = (l.t - l.s) / abs(l.t-l.s) ;
	if(equals(distancelp(l,c.c),c.r) ){
		ps.emplace_back(pr);
		return ps;
	}
	double base = sqrt(c.r*c.r - norm(pr-c.c) );
	ps.emplace_back(pr + e*base ) ;
	ps.emplace_back(pr - e*base ) ;
	return ps;
}
//circle segment
polygon crosspointCS(circle c,line l ){
	polygon res = crosspointCL(c,l);
	if(intersectcs(c,l) == 2 ) return res;
	if(res.size() > 1u ){//一つのみ削る
		if(dot(l.s-res[0] ,l.t-res[0] ) > 0) swap(res[0],res[1] );
		res.pop_back();
	}
	return res;
}
polygon crosspointcc(circle c1,circle c2){
	polygon p(2);
	double d = abs(c1.c-c2.c);
	double a = acos( (c1.r *c1.r + d*d -c2.r*c2.r) /(2*c1.r*d ) );
	double t = arg(c2.c-c1.c);
	p[0] = c1.c + polar(c1.r,t+a);
	p[1] = c1.c + polar(c1.r,t-a);
	//if(cross(c2.c-c1.c,p[0]-c1.c) > EPS) swap(p[0],p[1]); //c1に関する偏角の順
	return p;
}

int contains(polygon g,point p) { //IN:2 ON:1 OUT:0
    int n = g.size();
    bool f = false;
    for(int i=0;i<n;i++){
	point a = g[i] - p,b = g[(i+1)%n] - p;
	if( fabs(cross(a,b) ) < EPS && dot(a,b) < EPS) return 1;
	if( a.y > b.y ) swap(a,b);
	if( a.y < EPS && EPS < b.y && cross(a,b) > EPS ) f = !f;
    }
    return (f?2:0) ;
}

polygon andrewscan(polygon &s){ //convex hull
	polygon u,l;
	if(s.size() < 3) return s;
	//sort(s.begin(),s.end() );
	//最も左で最も右の点にする
	sort(s.begin(),s.end(),sort_y);
	u.push_back(s[0]);
	u.push_back(s[1]);
	l.push_back(s[s.size()-1]);
	l.push_back(s[s.size()-2]);
	for(int i=2;i<s.size();i++){
		for(int n = u.size();n>=2&&ccw(u[n-2],u[n-1],s[i]) != CCW_CLOCKWISE;n--)//凸包の辺上を含めない
		//for(int n = u.size();n>=2&&ccw(u[n-2],u[n-1],s[i]) == CCW_COUNTER_CLOCKWISE;n--)//凸包の辺上を含める場合
		u.pop_back();
		u.push_back(s[i]);
	}
	for(int i=s.size()-3;i>=0;i--){
		for(int n=l.size();n>=2&&ccw(l[n-2],l[n-1],s[i]) != CCW_CLOCKWISE;n--)//凸包の辺上を含めない	
		//for(int n=l.size();n>=2&&ccw(l[n-2],l[n-1],s[i]) == CCW_COUNTER_CLOCKWISE;n--)//凸包の辺上を含める場合
		l.pop_back();
		l.push_back(s[i]);
	}
	reverse(l.begin(),l.end());
	for(int i=u.size()-2;i>=1;i--)l.push_back(u[i]);
	return l;
}

double diameter(polygon &s){
	polygon p = s;
	int n = p.size();
	if(n==2) return abs(p[0]-p[1]);
	int i=0,j=0;
	for(int k=0;k<n;k++){
		if(p[i] < p[k]) i = k;
		if(!(p[j]<p[k]) ) j = k;
	}
	double res = 0;
	int si = i,sj = j;
	while( i != sj || j != si ){
		res = max(res,abs(p[i]-p[j]) );
		if(cross(p[(i+1)%n]-p[i],p[(j+1)%n]-p[j] ) < 0.0) i = (i+1)%n;
		else j = (j+1)%n;
	}
	return res;
}
bool isconvex(polygon p){
	bool f = 1;
	int n = p.size();
	for(int i=0;i<n;i++){
		int t = ccw(p[(i+n-1)%n],p[i],p[(i+1)%n] );
		f&= t!=CCW_CLOCKWISE;
	}
	return f;
}
double area(polygon p){
	double res =  0.0;
	for(int i=0;i<p.size();i++) res += cross(p[i],p[ (i+1)%p.size() ]);
	return res/2.0;
}
double area(circle c1,circle c2){
	double d = abs(c1.c-c2.c);
	if(c1.r + c2.r <= d + EPS ) return 0.0;
	if(d<=abs(c1.r-c2.r) ){
		double r = min(c1.r,c2.r);
		return PI*r*r;
	}
	double rc = (d*d + c1.r*c1.r -c2.r*c2.r)/(2*d);
	double th = acos(rc/c1.r);
	double ph = acos( (d-rc)/c2.r);
	return c1.r*c1.r*th + c2.r*c2.r*ph - d * c1.r * sin(th) ;
}

polygon convex_cut(polygon p,line l){
	polygon q;
	int n = p.size();
	for(int i=0;i<n;i++){
		point a = p[i] , b = p[(i+1)%n];
		if(ccw(l.s,l.t,a) != -1 ) q.push_back(a);
		if(ccw(l.s,l.t,a) * ccw(l.s,l.t,b) < 0) q.push_back(crosspointss(line(a,b),l) );
	}
	return q;
}
//[s,t) 再帰 devide and conquer
double inf  = 1e10;
double closest_pair_dac(polygon &p,int s,int t,double &res){
	if(t-s<=1)return inf;
	if(t-s==2){
		sort(p.begin()+s,p.begin()+t,sort_y);
		return (p[s]-p[s+1]).abs();
	}
	int mid = (s+t)/2;
	double x = p[mid].x;
	res = min(closest_pair_dac(p,s,mid,res),closest_pair_dac(p,mid,t,res) );
	auto it = p.begin();
	auto its = it+s,itm = it+mid,itt = it + t;
	inplace_merge(its,itm,itt,sort_y);
	vector<point> tmp;
	for(int i=s;i<t;i++){
		if(abs(p[i].x-x) >= res) continue;
		for(int j=tmp.size()-1;j>=0;j--){
			point d = p[i]-tmp[j];
			if(d.y >= res) break;
			res = min( res , d.abs() );
		}
		tmp.push_back(p[i]);
	}
	return res;
}
double closest_pair(polygon &p){
	double res = inf;
	sort(p.begin(),p.end());
	return  closest_pair_dac(p,0,p.size(),res);
}

polygon tangent(circle c,point p){//点から円への接戦
	circle c2 = circle(p,sqrt(norm(c.c-p)-c.r*c.r ) );
	polygon res = crosspointcc(c,c2);
	sort(res.begin(),res.end() );
	return res;
}
vector<line> tangent(circle c1,circle c2){//円の共通接戦
    vector<line> res;
    if(c1.r < c2.r ) swap(c1,c2);
    point g  = c2.c-c1.c;
    if( equals( g.norm() ,0.0 ) ) return res;
    point u = g/g.abs();
    point v = orth(u);
    for(int s=1;s>=-1;s-=2){
	double h = (c1.r + s*c2.r)/g.abs();
	if( equals(1-h*h,0.0) ){
		res.emplace_back( line(c1.c+u*c1.r,c1.c+(u+v)*c1.r) );
	}else if(1-h*h>0) {
		point uu = u*h,vv = v*sqrt(1-h*h) ;
		res.emplace_back( line(c1.c+(uu+vv)*c1.r,c2.c-(uu+vv)*c2.r*s) );
		res.emplace_back( line(c1.c+(uu-vv)*c1.r,c2.c-(uu-vv)*c2.r*s) );
	}
    }
	return res;
}
polygon tangent_point(circle c1,circle c2){//円の共通接戦における接点集合
    vector<line> ls = tangent(c1,c2);
    polygon res ;
    for(auto l:ls){
	polygon tmp = crosspointCL(c1,l);
	if(tmp.size()!=0)res.emplace_back(tmp[0]);
    }
    sort(res.begin(),res.end());
    return res;
}

double calcu(circle c,point a,point b){
	point va = c.c-a,vb = c.c - b;
	double f = cross(va,vb);
	double res = 0.0;
	if(equals(f,0.0) )return res;
	if(max(abs(va),abs(vb) ) < c.r + EPS) return f;
	point d( dot(va,vb),cross(va,vb) );
	if( distancesp(line(a,b),c.c) > c.r -EPS ) return c.r*c.r*atan2(d.y,d.x);
	auto u = crosspointCS(c,line(a,b) );
	if(u.empty() ) return res;
	if(u.size() > 1u && dot(u[1]-u[0],a-u[0] ) > 0 ) swap(u[0],u[1]);
	u.emplace(u.begin(),a);
	u.emplace_back(b);
	for(int i=1;i<u.size();i++)res+=calcu(c,u[i-1],u[i]);
	return res;
}
double area(polygon ps,circle c){
	if(ps.size() < 3u) return 0.0;
	double res = 0.0;
	for(int i=0;i<ps.size();i++) res += calcu(c,ps[i],ps[(i+1)%ps.size()] );
	return res/2;
}


//double inf = 1000;
typedef pair<point,double> mp;
int main(){
    	while(1){
		int n;
		cin>>n;
		if(n==0)break;
		double lm = inf,mm = 0;
		vector<mp> a(n);
		for(int i=0;i<n;i++){
		    a[i].first.input();
		    cin>>a[i].second;
		    lm = min(a[i].second,lm);
		}
		if(n != 1)
		while( lm - mm > EPS){
		    vector<circle> c(n);
		    double l = (lm+mm)/2;
		    for(int i=0;i<n;i++){
			c[i] = circle(a[i].first, sqrt(a[i].second*a[i].second - l*l )  );
		    }
		    bool f = false;
		    for(int i=0;i<n;i++)if(!f)
			for(int j=i+1;j<n;j++)
			    if( intersect(c[i],c[j]) == ICC_SEPARATE ){
				f = true;
				break;
			    }
		    if( f ){
			lm = l;
			continue;
		    }
		    polygon ps;
		    for(int i=0;i<n;i++){
			ps.push_back( c[i].c  );
			for(int j=i+1;j<n;j++){
			    if( intersect(c[i],c[j] ) == ICC_CONTAIN )continue;
				polygon tmp = crosspointcc(c[i],c[j]);
				for(int k=0;k<tmp.size();k++) ps.push_back(tmp[k]);
			}
		    }
		    /*if(ps.size() == 0){
			mm = l;
			continue;
		    }*/
		    bool ff = false;
		    for(int i=0;i<ps.size();i++){
			bool flag = true;
			for(int j=0;j<n;j++){
			    if( (c[j].c - ps[i] ).abs()   <=   c[j].r  + EPS){
			    }else flag = false;
			}
			if(flag){
			    ff = true;
			    break;
			}
		    }
		    if(ff){
			mm = l;
		    }else{
			lm = l;
		    }
		}
		printf("%0.10lf\n", lm);
	}
	return 0;
}



Measured memory_bytes: 3732