#include <bits/stdc++.h>

using namespace std;
using ll = long long;
// #define int ll
using PII = pair<ll, ll>;

#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()

template<typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }
template<typename T> bool IN(T a, T b, T x) { return a<=x&&x<b; }
template<typename T> T ceil(T a, T b) { return a/b + !!(a%b); }

template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}
template<typename T,typename V> typename enable_if<is_class<T>::value==0>::type
fill_v(T &t, const V &v) { t=v; }
template<typename T,typename V> typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t, const V &v ) { for(auto &e:t) fill_v(e,v); }

template<class S,class T>
ostream &operator <<(ostream& out,const pair<S,T>& a) {
    out<<'('<<a.first<<','<<a.second<<')'; return out;
}
template<class T>
ostream &operator <<(ostream& out,const vector<T>& a){
    out<<'[';
    for(const T &i: a) out<<i<<',';
    out<<']';
    return out;
}
template<class T>
ostream &operator <<(ostream& out, const set<T>& a) {
    out<<'{';
    for(const T &i: a) out<<i<<',';
    out<<'}';
    return out;
}
template<class T, class S>
ostream &operator <<(ostream& out, const map<T,S>& a) {
    out<<'{';
    for(auto &i: a) out<<i<<',';
    out<<'}';
    return out;
}

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0}; // DRUL
const int INF = 1<<30;
const ll LLINF = 1LL<<60;
const ll MOD = 1000000007;

using R = long double; // Rにmint渡せるようにする
using P = complex<R>;
using L = pair<P,P>;
using G = vector<P>;
struct C {
    P c; R r;
    C() {}
    C(const P &a, const R &b) : c(a), r(b) {}
};
struct S : public L {
    S() {}
    S(const P &a, const P &b) : L(a,b) {}
};

const R EPS = 1e-8;
const R PI = atan(1)*4;

inline int sgn(const R& r) { return (r>EPS) - (r<-EPS); }
inline R dot(const P& a, const P& b) {
    return real(a)*real(b) + imag(a)*imag(b);
}
inline R det(const P& a, const P& b) {
    return real(a)*imag(b) - imag(a)*real(b);
}
inline P vec(const L& l) {return l.second - l.first;}
namespace std {
	bool operator < (const P& a, const P& b) {
		return sgn(real(a-b)) ? real(a-b) < 0 : sgn(imag(a-b)) < 0;
	}
	bool operator == (const P& a, const P& b) {
		return sgn(real(a-b)) == 0 && sgn(imag(a-b)) == 0;
	}
    bool cmp_y (const P& a, const P& b) {
        return sgn(imag(a-b)) ? imag(a-b) < 0 : sgn(real(a-b)) < 0;
    }
}

// P,L,Sについて入力
inline istream& operator>>(istream& is, P& p) {
    R x, y;
    is >> x >> y;
    p = P(x, y);
    return is;
}
inline istream& operator>>(istream& is, L& l) {
    P a, b;
    is >> a >> b;
    l = L(a, b);
    return is;
}
inline istream& operator>>(istream& is, S& s) {
    P a, b;
    is >> a >> b;
    s = S(a, b);
    return is;
}

// 線分abから見たcの位置
enum CCW{LEFT=1, RIGHT=2, BACK=4, FRONT=8, ON_SEG=16};
int ccw(P a, P b, P c) {
	P p = (c-a)/(b-a);
	if(sgn(imag(p)) > 0) return LEFT;
	if(sgn(imag(p)) < 0) return RIGHT;
	if(sgn(real(p)) < 0) return BACK;
	if(sgn(real(p)-1) > 0) return FRONT;
	return ON_SEG;
}

int intersect(const C& a, const C& b) {
	R dist = sqrt(norm(a.c-b.c)), r1 = a.r + b.r, r2 = abs(a.r - b.r);
	if(sgn(r1-dist) < 0)  return 4;	// 円が離れている
	if(sgn(r1-dist) == 0) return 3;	// 外接
	if(sgn(r2-dist) < 0 && sgn(dist-r1) < 0) return 2; // 交差
	if(sgn(dist-r2) == 0) return 1; // 内接
	return 0;	// 内部に含む
}

vector<P> crosspoint(C a, C b) {
	R d = abs(a.c-b.c);
	R t = (a.r*a.r-b.r*b.r+d*d)/2/d, h = sqrt(a.r*a.r-t*t);
	P m = t/abs(b.c-a.c)*(b.c-a.c)+a.c;
    auto n_vector = [&](P p) -> P { return P(-p.imag(), p.real())/abs(p); };
	P n = n_vector(a.c-b.c);
	vector<P> ret(2, m);
	ret[0] -= h*n; ret[1] += h*n;
	if(ret[1] < ret[0]) swap(ret[0], ret[1]);
	return ret;
}

signed main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    while(1) {
        ll n;
        cin >> n;
        if(!n) break;
        vector<C> cir(n);
        REP(i, n) cin >> cir[i].c >> cir[i].r;

        R ans = 0;
        REP(i, n) {
            bool flag = true;
            vector<pair<R,P>> v;
            REP(j, n) {
                if(i == j) continue;
                if(intersect(cir[i], cir[j]) <= 1 && cir[i].r < cir[j].r) {
                    flag = false;
                    break;
                } else if(intersect(cir[i], cir[j]) == 2) {
                    auto vp = crosspoint(cir[i], cir[j]);
                    for(auto p: vp) {
                        R ang = atan2(cir[i].c.imag()-p.imag(), cir[i].c.real()-p.real());
                        v.push_back({ang, p});
                    }
                }
            }
            if(!flag) continue;
            sort(ALL(v));
            // cout << "i=" << i << " " << v << endl;
            if(v.size() == 0) ans += 2*PI*cir[i].r;
            REP(j, v.size()) {
                // 弧v[j],v[j+1]が他の円に含まれているか
                R diff;
                if(j+1 == (ll)v.size()) diff = v[0].first-v[j].first+2*PI;
                else diff = v[j+1].first-v[j].first;
                R arg = v[j].first + diff/2;
                P m = {cir[i].c.real() + cos(arg+PI) * cir[i].r,
                    cir[i].c.imag() + sin(arg+PI) * cir[i].r};
                // cout << arg << " " << cos(arg+PI) << " " << sin(arg+PI) << endl;
                bool flag = true;
                REP(k, n) {
                    if(i == k) continue;
                    if(sgn(abs(cir[k].c - m) - cir[k].r) < 0) {
                        flag = false;
                        break;
                    }
                }
                // cout << a << " " << b << " " << diff << " " << arg << " " << m << " " << flag << endl;
                if(flag) ans += cir[i].r * diff;
            }
        }

        cout << fixed << setprecision(9) << ans << endl;
    }

    return 0;
}



Measured memory_bytes: 3596