#include <bits/stdc++.h>
#define int long long
#define endl '\n'
#define FOR(i, a, n) for (int i = (a); i < (n); ++i)
#define REP(i, n) FOR(i, 0, n)
using namespace std;

using T = long double;
const T INF = 1e10;
const T EPS = 1e-10;
const T PI = acos(-1.0);
T torad(int deg) {return (T)(deg) * PI / 180;}
T todeg(T ang) {return ang * 180 / PI;}
template <typename T> inline bool eq(T p, T q) { return abs(p - q) < EPS; }
inline int sgn(T x) { return (T(0) < x) - (x < T(0)); }

/* Point */
using P = complex<T>;
#define x real()
#define y imag()
inline T dot(P v, P w) { return (conj(v) * w).x; }
inline T cross(P v, P w) { return (conj(v) * w).y; }
inline T orient(P a, P b, P c) { return cross(b - a, c - a); }
inline bool isOrth(P v, P w) { return dot(v, w) == 0; }
inline bool isPara(P v, P w) { return cross(v, w) == 0; }
inline P unit(P v) { return v / abs(v); }
inline P translate(P p, P v) { return p + v; }
inline P scale(P p, P c, T k) { return c + (p - c) * k; }
inline P rot(P p, T a) { return p * polar(T(1), a); }
inline P rot90(P p) { return {-p.y, p.x}; }
inline P linearTransform(P p, P q, P fp, P fq, P r) { return fp + (r - p) * (fq - fp) / (q - p); }
bool cmpX(const P& a, const P& b) { return a.x != b.x ? a.x < b.x : a.y < b.y; }
bool cmpY(const P& a, const P& b) { return a.y != b.y ? a.y < b.y : a.x < b.x; }
namespace std {
    istream& operator>>(istream& is, P& p) { T xx, yy; is >> xx >> yy; p = P(xx, yy); return is; }
    bool operator < (const P& a, const P& b) { return cmpX(a, b); }
}

/* Line */
struct L : array<P, 2> {
    P v; T c;
    L() = default;
    explicit L(P a, P b) : array<P, 2>({a, b}), v(b - a), c(cross(v, a)) {}
    T side(P p) { return cross(v, p) - c; }
    P proj(P p) { return p - rot90(v) * side(p) / norm(v); }
    P refl(P p) { return p - rot90(v) * T(2) * side(p) / norm(v); }
    bool onLine(P p) { return abs(side(p)) < EPS; }
    bool onSegment(P p) { return onLine(p) && dot(this->operator[](0) - p, this->operator[](1) - p) <= EPS; }
    friend istream& operator>>(istream& is, L& l) { P p, q; is >> p >> q; l = L(p, q); return is; }
    friend ostream& operator<<(ostream& os, const L& l) { return os << '{' << l[0] << ", " << l[1] << '}'; }
};

/* Circle */
struct C : P {
    T r;
    C() = default;
    C(P p, T r) : P(p), r(r) {}
    friend istream& operator>>(istream& is, C& c) { P p; T r; is >> p >> r; c = C(p, r); return is; }
    friend ostream& operator<<(ostream& os, const C& c) { return os << '(' << c.x << ", " << c.y << ", " << c.r << ')'; }
};

int ccw(P a, P b, P c) {
    b -= a; c -= a;
    if (cross(b, c) > EPS) return 1;         // counter clockwise
    if (cross(b, c) < -EPS) return -1;       // clockwise
    if (dot(b, c) < -EPS) return 2;          // c--a--b on line
    if (norm(b) < norm(c) - EPS) return -2;  // a--b--c on line or a==b
    return 0;                                // a--c--b on line or a==c or b==c
}

// intersect
bool isInterPL(P p, L l) { return (ccw(l[0], l[1], p) != 1); }
bool isInterPS(P p, L s) { return (ccw(s[0], s[1], p) == 0); }
bool isInterLL(L l, L m) { return (!isPara(l.v, m.v)); }
bool isInterLS(L l, L s) {
    if (eq(s[0], s[1])) return isInterPL(s[0], l);
    return (ccw(l[0], l[1], s[0]) * ccw(l[0], l[1], s[1]) <= 0);
}
bool isInterSS(L s, L t) {
    if (eq(s[0], s[1])) return isInterPL(s[0], t);
    if (eq(t[0], t[1])) return isInterPL(t[0], s);
    return (ccw(s[0], s[1], t[0]) * ccw(s[0], s[1], t[1]) <= 0 &&
            ccw(t[0], t[1], s[0]) * ccw(t[0], t[1], s[1]) <= 0);
}
int isInterCC(C a, C b) {
    T d = abs(b - a);
    if (a == b && a.r == b.r) return 0;         // ∞ cp (A = B)
    if (a.r + d - b.r < -EPS) return +1;        // 0 cp (A in B)
    if (b.r + d - a.r < -EPS) return -1;        // 0 cp (B in A)
    if (abs(a.r + d - b.r) < EPS) return +2;    // 1 cp (A in B)
    if (abs(b.r + d - a.r) < EPS) return -2;    // 1 cp (B in A)
    if (abs(a.r + b.r - d) < EPS) return 3;     // 1 cp (outside)
    if (a.r + b.r - d < -EPS) return 4;         // 0 cp (outside)
    return 5;                                   // 2 cp
}

// distance
T distancePL(P p, L l) { return (abs(p - l.proj(p))); }
T distancePS(P p, L s) {
    P h = s.proj(p);
    if (isInterPS(h, s)) return abs(p - h);
    return min(abs(p - s[0]), abs(p - s[1]));
}
T distanceLL(L l, L m) {
    if (isInterLL(l, m)) return 0.0;
    return distancePL(m[0], l);
}
T distanceLS(L l, L s) {
    if (isInterLS(l, s)) return 0;
    return min(distancePL(s[0], l), distancePL(s[1], l));
}
T distanceSS(L s, L t) {
    if (isInterSS(s, t)) return 0;
    return min({distancePS(s[0], t), distancePS(s[1], t), distancePS(t[0], s), distancePS(t[1], s)});
}

// crosspoint
vector<P> crosspointLL(L l, L m) {
    if (!isInterLL(l, m)) return vector<P>();
    vector<P> res;
    T d = cross(m[1] - m[0], l[1] - l[0]);
    res.push_back(l[0] + (l[1] - l[0]) * cross(m[1] - m[0], m[1] - l[0]) / d);
    return res;
}
vector<P> crosspointLS(L l, L s) {
    if (!isInterLS(l, s)) return vector<P>();
    vector<P> res;
    T d = cross(s[1] - s[0], l[1] - l[0]);
    res.push_back(l[0] + (l[1] - l[0]) * cross(s[1] - s[0], s[1] - l[0]) / d);
    return res;
}
vector<P> crosspointLC(L l, C c, bool dupl = false) {
    if (abs(c - l.proj(c)) > c.r) return vector<P>();
    vector<P> res;
    T d = distancePL(c, l), h2 = c.r * c.r - d * d;
    assert(h2 >= -EPS);
    P p = l.proj(c), h = l.v * sqrt(h2) / abs(l.v);
    res.push_back(p - h);
    if (dupl || abs(h) > EPS) res.push_back(p + h);
    return res;
}
vector<P> crosspointSS(L s, L t) {
    if (!isInterSS(s, t)) return vector<P>();
    vector<P> res;
    T d = cross(t[1] - t[0], s[1] - s[0]);
    if (d) {
        res.push_back(s[0] + (s[1] - s[0]) * cross(t[1] - t[0], t[1] - s[0]) / d);
    } else {
        if (ccw(s[0], s[1], t[0]) == 0) res.push_back(t[0]);
        if (ccw(s[0], s[1], t[1]) == 0) res.push_back(t[1]);
        if (ccw(t[0], t[1], s[0]) == 0) res.push_back(s[0]);
        if (ccw(t[0], t[1], s[1]) == 0) res.push_back(s[1]);
    }
    return res;
}
vector<P> crosspointSC(L s, C c, bool dupl = false) {
    if (abs(c - s.proj(c)) > c.r) return vector<P>();
    vector<P> res;
    T d = distancePL(c, s), h2 = c.r * c.r - d * d;
    assert(h2 >= -EPS);
    P p = s.proj(c), h = s.v * sqrt(h2) / abs(s.v);
    if (isInterPS(p - h, s)) res.push_back(p - h);
    if (dupl || (abs(h) > EPS && isInterPS(p + h, s))) res.push_back(p + h);
    return res;
}
vector<P> crosspointCC(C c1, C c2, bool dupl = false) {
    P d = c2 - c1; T d2 = norm(d);
    if (d2 == 0) { assert(c1.r != c2.r); return vector<P>(); }
    vector<P> res;
    T pd = (d2 + c1.r * c1.r - c2.r * c2.r) / 2;
    T h2 = c1.r * c1.r - pd * pd / d2;
    if (h2 >= 0) {
        P p = c1 + d * pd / d2, h = rot90(d) * sqrt(h2 / d2);
        res.push_back(p - h);
        if (dupl || abs(h) > EPS) res.push_back(p + h);
    }
    return res;
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);

    int n;
    while (cin >> n, n) {
        vector<P> ps(n);
        vector<int> l(n);
        REP (i, n) cin >> ps[i] >> l[i];

        int j = -1;
        REP (i, n) if (j == -1 || l[i] < l[j] - EPS) j = i;

        bool f = true;
        REP (i, n) if (i != j) {
            T r = sqrt(l[i] * l[i] - l[j] * l[j]);
            f &= (abs(ps[i] - ps[j]) <= r + EPS);
        }

        if (f) {
            cout << (T)l[j] << endl;
            continue;
        }

        auto check = [&](T m) -> bool {
            vector<C> cs(n);
            REP (i, n) cs[i] = C(ps[i], sqrt(l[i] * l[i] - m * m));
            vector<P> cps;
            REP (i, n) FOR (j, i + 1, n) {
                for (P& p : crosspointCC(cs[i], cs[j])) {
                    cps.emplace_back(p);
                }
            }
            for (P& p : cps) {
                bool ok = true;
                REP (i, n) {
                    ok &= (abs(cs[i] - p) <= cs[i].r + EPS);
                }
                if (ok) return true;
            }
            return false;
        };

        T ok = 0, ng = l[j];
        REP (i, 100) {
            T m = (ok + ng) / 2;
            if (check(m)) ok = m;
            else ng = m;
        }
        cout << ok << endl;
    }
}


Measured memory_bytes: 3352