#include "bits/stdc++.h"
#include <sys/timeb.h>
#include <fstream>

using namespace std;

#define repl(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define rep(i,n) repl(i,0,n)
#define replrev(i,a,b) for(int i=(int)(b)-1;i>=(int)(a);i--)
#define reprev(i,n) replrev(i,0,n)
#define repi(itr,ds) for(auto itr=ds.begin();itr!=ds.end();itr++)
#define all(a) a.begin(),a.end()
#define mp make_pair
#define mt make_tuple
#define INF 2000000000
#define INFL 1000000000000000000LL
#define EPS (1e-10)
#define MOD 1000000007
#define PI 3.1415926536
#define RMAX 4294967295

typedef long long ll;
typedef pair<int, double> P;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<P> vP;
typedef vector<vector<int> > vvi;
typedef vector<vector<bool> > vvb;
typedef vector<vector<ll> > vvll;
typedef vector<vector<char> > vvc;
typedef vector<vector<string> > vvs;
typedef vector<vector<double> > vvd;
typedef vector<vector<P> > vvP;
typedef priority_queue<int, vector<int>, greater<int> > pqli;
typedef priority_queue<ll, vector<ll>, greater<ll> > pqlll;
typedef priority_queue<P, vector<P>, greater<P> > pqlP;
typedef pair<int, pair<int, int> > Edge;
typedef vector<Edge> vE;
typedef priority_queue<Edge, vector<Edge>, greater<Edge> > pqlE;

#define equals(a,b)(fabs((a)-(b))<EPS)

static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

class Point {
public:
	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(x * a, y * a); }
	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;

typedef vector<Point> Polygon;

class Segment {
public:
	Point p1, p2;
	Segment(Point p1 = Point(), Point p2 = Point()) :p1(p1), p2(p2) {}
};

typedef Segment Line;

class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0) :c(c), r(r) {}
};

double dot(Vector a, Vector b) {
	return a.x*b.x + a.y*b.y;
}

double cross(Vector a, Vector b) {
	return a.x*b.y - a.y*b.x;
}

bool isOrthogonal(Vector a, Vector b) {
	return equals(dot(a, b), 0.0);
}

bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
	return isOrthogonal(a1 - a2, b1 - b2);
}

bool isOrthogonal(Segment s1, Segment s2) {
	return equals(dot(s1.p1 - s1.p2, s2.p2 - s2.p1), 0.0);
}

bool isParallel(Vector a, Vector b) {
	return equals(cross(a, b), 0.0);
}

bool isParallel(Point a1, Point a2, Point b1, Point b2) {
	return isParallel(a1 - a2, b1 - b2);
}

bool isParallel(Segment s1, Segment s2) {
	return equals(cross(s1.p1 - s1.p2, s2.p2 - s2.p1), 0.0);
}

Point project(Segment s, Point p) {
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / base.norm();
	return s.p1 + base*r;
}

// ??????s???????§°?????¨?????????p???????§°???
Point reflect(Segment s, Point p) {
	return p + (project(s, p) - p)*2.0;
}

double getDistance(Point a, Point b) {
	return (a - b).abs();
}

double getDistanceLP(Line l, Point p) {
	return abs(cross(l.p2 - l.p1, p - l.p1) / (l.p2 - l.p1).abs());
}

double getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0)return (p - s.p1).abs();
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0)return (p - s.p2).abs();
	return getDistanceLP(s, p);
}

// ????????????(p0,p1)???????????????p2?????????
int ccw(Point p0, Point p1, Point p2) {
	Vector a = p1 - p0;
	Vector b = p2 - p0;
	if (cross(a, b) > EPS)return COUNTER_CLOCKWISE;
	if (cross(a, b) < -EPS)return CLOCKWISE;
	if (dot(a, b) < -EPS)return ONLINE_BACK;
	if (a.norm() < b.norm())return ONLINE_FRONT;
	return ON_SEGMENT;
}

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(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}

double getDistance(Segment s1, Segment s2) {
	if (intersect(s1, s2))return 0.0;
	return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
		min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

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;
}

pair<Point, Point> getCrossPoints(Circle c, Line l) {
	Vector pr = project(l, c.c);
	Vector e = (l.p2 - l.p1) / (l.p2 - l.p1).abs();
	double base = sqrt(c.r*c.r - (pr - c.c).norm());
	return make_pair(pr + e*base, pr - e*base);
}

double arg(Vector p) {
	return atan2(p.y, p.x);
}

// ?????¢a???????§?r
Vector polar(double a, double r) {
	return Point(cos(r)*a, sin(r)*a);
}

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
	double d = (c1.c - c2.c).abs();
	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));
}

// IN:2, ON:1, OUT:0
int contain(Polygon g, Point p) {
	int n = g.size();
	bool x = false;
	for (int i = 0; i < n; i++) {
		Point a = g[i] - p;
		Point b = g[(i + 1) % n] - p;
		if (abs(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)x = !x;
	}
	return (x ? 2 : 0);
}

// ??????
Polygon andrewScan(Polygon s) {
	Polygon u, l;
	if (s.size() < 3)return s;
	sort(s.begin(), s.end());

	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]) != CLOCKWISE; n--) {
			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]) != CLOCKWISE; n--) {
			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;
}

// ??£??\??????ver
void Dijkstra(vvd graph, int start, vd &cost, int V) {
	vi prev(V);
	priority_queue<pair<double, int>, vector<pair<double, int>>, greater<pair<double, int>>> Q;

	fill(cost.begin(), cost.end(), INF);
	cost[start] = 0;

	Q.push(mp(0, start));	// (cost, index)

	while (!Q.empty()) {
		pair<double, int> _pos = Q.top();
		double d = _pos.first;
		int pos = _pos.second;
		Q.pop();
		rep(i, V) {
			if (i == pos)continue;
			if (cost[i] > cost[pos] + graph[pos][i]) {
				cost[i] = cost[pos] + graph[pos][i];
				Q.push(mp(cost[i], i));
			}
		}
	}
}

int main() {
	cout << fixed << setprecision(14);

	while (true) {
		int N;
		cin >> N;
		if (N == 0)break;
		vector<Polygon> poly(N);
		vd h(N);
		vi nv(N);

		rep(i, N) {
			cin >> nv[i] >> h[i];
			poly[i] = Polygon(2 * nv[i]);
			rep(j, nv[i]) {
				double x, y;
				cin >> x >> y;
				poly[i][2 * j] = Point(x, y);
			}
		}
		double theta, phi;
		cin >> theta >> phi;
		theta *= PI / 180;
		phi *= PI / 180;
		double sx, sy, tx, ty;
		cin >> sx >> sy >> tx >> ty;
		Point start(sx, sy), goal(tx, ty);

		vector<Polygon> hull(N);

		rep(i, N) {
			Vector shadow = polar(h[i] / tan(phi), theta + PI);
			rep(j, nv[i]) {
				poly[i][2 * j + 1] = poly[i][2 * j] + shadow;
			}
			hull[i] = andrewScan(poly[i]);
		}

		vvd graph(N + 2, vd(N + 2, INF));
		rep(i, N) {
			repl(j, i + 1, N) {
				double dist = INF;
				rep(p1, hull[i].size()) {
					Segment s1(hull[i][p1], hull[i][(p1+1)%hull[i].size()]);
					rep(p3, hull[j].size()) {
						Segment s2(hull[j][p3], hull[j][(p3+1)%hull[j].size()]);
						dist = min(dist, getDistance(s1, s2));
					}
				}
				graph[i][j] = dist;
				graph[j][i] = dist;
			}
		}
		rep(i, N) {
			if (contain(hull[i], start) != 0) {
				graph[i][N] = 0;
				graph[N][i] = 0;
			}
			else {
				double dist = INF;
				rep(p1, hull[i].size()) {
					Segment s1(hull[i][p1], hull[i][(p1 + 1) % hull[i].size()]);
					dist = min(dist, getDistanceSP(s1, start));
				}
				graph[i][N] = dist;
				graph[N][i] = dist;
			}

			if (contain(hull[i], goal) != 0) {
				graph[i][N + 1] = 0;
				graph[N + 1][i] = 0;
			}
			else {
				double dist = INF;
				rep(p1, hull[i].size()) {
					Segment s1(hull[i][p1], hull[i][(p1 + 1) % hull[i].size()]);
					dist = min(dist, getDistanceSP(s1, goal));
				}
				graph[i][N + 1] = dist;
				graph[N + 1][i] = dist;
			}
		}

		graph[N][N + 1] = getDistance(start, goal);
		graph[N + 1][N] = getDistance(start, goal);

		vd cost(N + 2);
		Dijkstra(graph, N, cost, N + 2);

		cout << cost[N + 1] << endl;
	}


	return 0;
}

Measured memory_bytes: 3788