#include <bits/stdc++.h>

using namespace std;

#define EPS (1e-10)
#define equals(a, b) (fabs((a) - (b)) < EPS)
 
struct Point{
    double x, y;
     
    Point(double x = 0, double y = 0): x(x), y(y) {}
 
    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 a) { return Point(a * x, a * y); }
    Point operator / (double a) { return Point(x / a, y / a); }
 
    double norm() {return x * x + y * y; }
    double abs() {return sqrt(norm()); }
 
    bool operator < (const Point &p) const{
        return (x != p.x ? x < p.x : y < p.y);
    }
 
    bool operator == (const Point &p) const{
        return (fabs(x - p.x) < EPS && fabs(y - p.y) < EPS);
    }
};
 
typedef Point Vector;

struct Segment{
    Point p1, p2;
    Segment(Point p1, Point p2): p1(p1), p2(p2) {}
};

typedef Segment Line;
 
double cross(Vector a, Vector b){
    return a.x * b.y - a.y * b.x;
}
 
struct Circle{
    Point c;
    double r;
 
    Circle(Point c = Point(), double r = 0.0): c(c), r(r) {}
};
 
double norm(Vector a){
    return a.x * a.x + a.y * a.y;
}
 
double abs(Vector a){
    return sqrt(norm(a));
}
 
double arg(Vector p){
    return atan2(p.y, p.x);
}
 
Vector polar(double a, double r){
    return Point(cos(r) * a, sin(r) * a);
}
 
pair<Point, Point> getCrossPoints(Circle c1, Circle c2){
    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);
    return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

Point getCrossPoint(Segment s1, Segment s2){
    Vector base = s2.p2 - s2.p1;
    double d1 = abs(cross(base, s1.p1 - s2.p1));
    double d2 = abs(cross(base, s1.p2 - s2.p1));
    double t = d1 / (d1 + d2);
    return s1.p1 + (s1.p2 - s1.p1) * t;
}
double dist(double x1,double y1,double x2,double y2){
    return sqrt( (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2)  );
}

int n;
double tmpp[15][3];
double max_h;
vector<double> p[15];

double findans(double x,double y){
    double st = 0.99,en = max_h+0.1;
    while(en-st > 0.00000001){
        double half = (st + en) / 2.0;
        bool flag = true;
        for(int i = 0;i < n;i++){
            if( (half*half + (p[i][0]-x)*(p[i][0]-x) + (p[i][1]-y)*(p[i][1]-y)) > p[i][2]*p[i][2] ){
                flag = false;
                break;
            }
        }
        if(flag) st = half;
        else en = half;
    }
    return  st;
}


int main(){
    while(true){
        cin >> n;
        if(n == 0)break;
        max_h = 301;
        bool ch[15];
        for(int i = 0;i < n;i++){
            p[i].clear();
            ch[i] = true;
            for(int j = 0;j < 3;j++){
                cin >> tmpp[i][j];
                if(j == 2)max_h=min(max_h,tmpp[i][j]);
            }
        }
        int sum = 0;
        for(int i = 0;i < n;i++){
            for(int j = 0;j < n;j++){
                if(ch[i] == false || ch[j] == false)continue;
                if(i == j)continue;
                if(tmpp[i][2] >= dist(tmpp[i][0],tmpp[i][1],tmpp[j][0],tmpp[j][1]) + tmpp[j][2]){
                    sum++;
                    ch[i] = false;
                }
            }
        }
        int count = 0;
        for(int i = 0;i < n;i++){
            if(ch[i] == false)continue;
            for(int j = 0;j < 3;j++){
                p[count].push_back(tmpp[i][j]);
            }
            count++;
        }
        n -= sum;
    //    cout << "n:" << n << endl;
        if(n == 1){
            printf("%.7lf\n",p[0][2]);
            continue;
        }
        if(n == 2){
            Circle c1 = {Point(p[0][0], p[0][1]), p[0][2]};
            Circle c2 = {Point(p[1][0], p[1][1]), p[1][2]};
            pair<Point, Point> ansp = getCrossPoints(c1, c2);

            Segment s1 = {Point(p[0][0], p[0][1]), Point(p[1][0], p[1][1])};
            Segment s2 = {Point(ansp.first.x, ansp.first.y), Point(ansp.second.x, ansp.second.y)};
            Point ansp2 = getCrossPoint(s1, s2);
            double ans = findans(ansp2.x,ansp2.y);
            for(int i = 0;i < 2;i++) ans = max(ans,findans(p[i][0],p[i][1]));
            printf("%.7lf\n",ans);
            continue;
        }
        vector<int> v;
        for(int i = 0;i < n-3;i++)v.push_back(0);
        for(int i = 0;i < 3;i++)v.push_back(1);
        double tmp[4][4];
        double ans = 0;
        do{
            int cnt = 0;
            for(int i = 0;i < n;i++){
                if(v[i] == 0)continue;
                for(int j = 0;j < 3;j++)tmp[cnt][j] = p[i][j];
                cnt++;
            }
            Circle c[3];
            for(int i = 0;i < 3;i++) c[i] = {Point(tmp[i][0], tmp[i][1]), tmp[i][2]};
            pair<Point, Point> ansp1 = getCrossPoints(c[0], c[1]);
            pair<Point, Point> ansp2 = getCrossPoints(c[0], c[2]);
            Segment s1 = {Point(ansp1.first.x, ansp1.first.y), Point(ansp1.second.x, ansp1.second.y)};
            Segment s2 = {Point(ansp2.first.x, ansp2.first.y), Point(ansp2.second.x, ansp2.second.y)};
            Point ansp3 = getCrossPoint(s1, s2);
            ans = max(ans,findans(ansp3.x,ansp3.y));

        }while(next_permutation(v.begin(),v.end()));
        for(int i = 0;i < n;i++)ans = max(ans,findans(p[i][0],p[i][1]));
        for(int i = 0;i < n;i++){
            for(int j = i+1;j < n;j++){
                Circle c1 = {Point(p[i][0], p[i][1]), p[i][2]};
                Circle c2 = {Point(p[j][0], p[j][1]), p[j][2]};
                pair<Point, Point> ansp = getCrossPoints(c1, c2);

                Segment s1 = {Point(p[i][0], p[i][1]), Point(p[j][0], p[j][1])};
                Segment s2 = {Point(ansp.first.x, ansp.first.y), Point(ansp.second.x, ansp.second.y)};
                Point ansp2 = getCrossPoint(s1, s2);
                ans = max(ans,findans(ansp2.x,ansp2.y));                
            }
        }
        printf("%.7lf\n",ans);
    }
}


Measured memory_bytes: 3700