#include "bits/stdc++.h"
#pragma warning(disable:4996)
using namespace std;


/* 幾何の基本 */

#include <complex>

typedef long double ld;
typedef complex<ld> Point;
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()

const ld eps = 1e-9, pi = acos(-1.0);
const ld dtop = pi / 180.;
const ld ptod = 1. / dtop;

namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}

// 点の入力
Point input_point() {
	ld x, y;
	cin >> x >> y;
	return Point(x, y);
}

// 誤差つき等号判定
bool eq(ld a, ld b) {
	return (abs(a - b) < eps);
}

// 内積
ld dot(Point a, Point b) {
	return real(conj(a) * b);
}

// 外積
ld cross(Point a, Point b) {
	return imag(conj(a) * b);
}

// 直線の定義
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
	Point operator[](const int _num) {
		if (_num == 0)return a;
		else if (_num == 1)return b;
		else assert(false);
	}
};

// 円の定義
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW
int ccw(Point a, Point b, Point c) {
	b -= a; c -= a;
	if (cross(b, c) > eps) return 1;   // a,b,cが反時計周りの順に並ぶ
	if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ
	if (dot(b, c) < 0) return 2;       // c,a,bの順に直線に並ぶ
	if (norm(b) < norm(c)) return -2;  // a,b,cの順に直線に並ぶ
	return 0;                          // a,c,bの順に直線に並ぶ
}


/* 交差判定 */

// 直線と直線の交差判定
bool isis_ll(Line l, Line m) {
	return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// 直線と線分の交差判定
bool isis_ls(Line l, Line s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// 線分と線分の交差判定
bool isis_ss(Line s, Line t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

// 点の直線上判定
bool isis_lp(Line l, Point p) {
	return (abs(cross(l.b - p, l.a - p)) < eps);
}

// 点の線分上判定
bool isis_sp(Line s, Point p) {
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// 垂線の足
Point proj(Line l, Point p) {
	ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
	return l.a + t * (l.a - l.b);
}

// 直線と直線の交点
Point is_ll(Line s, Line t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) {
	return abs(p - proj(l, p));
}

// 直線と直線の距離
ld dist_ll(Line l, Line m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, Line t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


/* 円 */

// 円と円の交点
vector<Point> is_cc(Circle c1, Circle c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

// 円と直線の交点
vector<Point> is_lc(Circle c, Line l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		Point nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

// 円と線分の距離
vector<Point> is_sc(Circle c, Line l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

// 円と点の接線
vector<Line> tangent_cp(Circle c, Point p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}

// 円と円の接線
vector<Line> tangent_cc(Circle c1, Circle c2) {
	vector<Line> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), ALL(nret));
	}
	else {
		Point v = c2.p - c1.p;
		v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}


/* 多角形 */

typedef vector<Point> Polygon;

// 面積
ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	REP(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
		angle += arg((c - b) / (b - a));
	}
	return angle > eps;
}

// 円の内外判定
//  0 => out
//  1 => on
//  2 => in
int is_in_polygon(const Polygon &poly, Point p) {
	ld angle = 0;
	int n = poly.size();
	REP(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n];
		if (isis_sp(Line(a, b), p)) return 1;
		angle += arg((b - p) / (a - p));
	}
	return eq(angle, 0) ? 0 : 2;
}

// 凸包
Polygon convex_hull(vector<Point> ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	Polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}

// 凸カット
vector<Polygon> convex_cut(const Polygon &ps, const Line l) {
	int n = ps.size();
	Polygon Q;
	Polygon R;
	REP(i, n) {
		Point A = ps[i], B = ps[(i + 1) % n];
		Line m = Line(A, B);
		if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
		if (ccw(l.a, l.b, A) != 1) R.push_back(A);
		if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m)) {
			Q.push_back(is_ll(l, m));
			R.push_back(is_ll(l, m));
		}
	}
	vector<Polygon>polys;
	if (!Q.empty()) {
		polys.push_back(Q);
	}
	if (!R.empty()) {
		polys.push_back(R);
	}
	return polys;
}


/* アレンジメント */
void add_point(vector<Point> &ps, Point p) {
	for (Point q : ps) if (abs(q - p) < eps) return;
	ps.push_back(p);
}

typedef int Weight;

struct Edge { int from, to; Weight weight; };

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to, Weight weight) {
	g[from].push_back(Edge{ from, to, weight });
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
	int n = p.size(), m = s.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (isis_sp(s[i], p[j]))
			vec.emplace_back(abs(s[i].a - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			add_edge(g, from, to, abs(p[from] - p[to]));
		}
	}
	return g;
}

Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
	int n = p.size(), m = c.size();
	Graph g(n);
	REP(i, m) {
		vector<pair<ld, int>> vec;
		REP(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
			vec.emplace_back(arg(c[i].p - p[j]), j);
		sort(ALL(vec));
		REP(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			ld angle = vec[j + 1].first - vec[j].first;
			add_edge(g, from, to, angle * c[i].r);
		}
		if (vec.size() >= 2) {
			int from = vec.back().second, to = vec.front().first;
			ld angle = vec.front().first - vec.back().first;
			add_edge(g, from, to, angle * c[i].r);
		}
	}
	return g;
}


/* 双対グラフ */

// 線分集合は既にアレンジメントされていなければならない．
// 内側の円は時計回りで，外側の円は反時計回りで得られる．
// 変数 polygon は，vector<int> で表される多角形の集合であり，
// vector<int> で表される 多角形のi番目は，その頂点の頂点集合pにおける番号である．
vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
	int N = p.size();
	polygon.clear();
	REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
	vector<vector<tuple<ld, int, bool>>> tup(N);
	REP(i, s.size()) {
		int a = -1, b = -1;
		REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
		REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
		assert(a >= 0 && b >= 0);
		tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
		tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
	}
	REP(i, N) sort(ALL(tup[i]));
	REP(i, N) {
		REP(j, tup[i].size()) {
			ld angle; int pos = j, from = i, to; bool flag;
			tie(angle, to, flag) = tup[i][j];
			if (flag) continue;
			vector<int> ps;
			while (!flag) {
				ps.push_back(from);
				get<2>(tup[from][pos]) = true;
				seg2p[from][to].push_back(polygon.size());
				seg2p[to][from].push_back(polygon.size());
				angle += pi + eps;
				if (angle > pi) angle -= 2 * pi;
				auto it = lower_bound(ALL(tup[to]), make_tuple(angle, 0, false));
				if (it == tup[to].end()) it = tup[to].begin();
				from = to; tie(angle, to, flag) = *it;
				pos = it - tup[from].begin();
			}
			polygon.push_back(ps);
		}
	}
	Graph g(polygon.size());
	REP(i, N) REP(j, i) {
		if (seg2p[i][j].size() == 2) {
			int from = seg2p[i][j][0], to = seg2p[i][j][1];
			g[from].push_back(Edge{ from, to });
			g[to].push_back(Edge{ to, from });
		}
	}
	return g;
}


/* ビジュアライザ */
const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(int r, int g, int b) {
	fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p),cordy(p)

void draw_point(Point p) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(p), 2);
}

void draw_segment(Line l) {
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(l.a), cord(l.b));
}

void draw_line(Line l) {
	Point v = l.b - l.a;
	Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
	fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
	int n = p.size();
	REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(Circle c) {
	fprintf(stderr, "circle(%d, %d, %d)\n", cord(c.p), (int)(zoom * c.r));
}

long double getdis(vector<Line>&l, vector<Line>&r) {
	long double amin = 9999999999;
	for (int i = 0; i < 5; ++i) {
		for (int j = 0; j < 5; ++j) {
			amin = min(dist_ss(l[i], r[j]),amin);
		}
	}
	return amin;
}

int main() {
	while (1) {
		int N, M, L; cin >> N >> M >> L;
		if (!N)break;
		vector<vector<Line>>stars(N);
		for (int i = 0; i < N; ++i) {
			long double x, y, a, r;
			cin >> x >> y >> a >> r;
			Point center(x, y);
			vector<Point>pos;
			for (int j = 0; j < 5; ++j) {
				Point np = center + r*Point(cos((90+a+ 72.0*j)*dtop), sin((90 + a + 72.0*j)*dtop));
				pos.push_back(np);
			}
			for (int j = 0; j < 5; ++j) {
				Line nl(pos[(j * 2) % 5], pos[(j * 2 + 2) % 5] );
				stars[i].push_back(nl);
			}
		}
		vector<vector<long double>>dists(N, vector<long double>(N));
		for (int i = 0; i < N; ++i) {
			for (int j = 0; j < N; ++j) {
				dists[i][j] = getdis(stars[i], stars[j]);
			}
		}
		for (int k = 0; k < N; ++k) {
			for (int i = 0; i < N; ++i) {
				for (int j = 0; j < N; ++j) {
					dists[i][j] = min(dists[i][j],dists[i][k] + dists[k][j]);
				}
			}
		}
		cout <<fixed<<setprecision(22)<< dists[M - 1][L - 1] << endl;
	}
	return 0;
}

Measured memory_bytes: 28332