#include "bits/stdc++.h"

using namespace std;

using ld = long double;
using Point = std::complex<ld>;

const ld eps = 1e-9, pi = acos(-1.0);

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();
}
} // namespace std

Point input_point()
{
    ld x, y;
    std::cin >> x >> y;
    return Point(x, y);
}

bool eq(ld a, ld b)
{
    return (abs(a - b) < eps);
}

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

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

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

class Line
{
public:
    Point a, b;
    Line() : a(Point(0, 0)), b(Point(0, 0)) {}
    Line(Point a, Point b) : a(a), b(b) {}
};

ld dot(Line l, Line m)
{
    return dot((l.a - l.b), (m.a - m.b));
}

// l:line, m:line が交点を持つか
bool isis_ll(Line l, Line m)
{
    return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// l:line, s:segment
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);
}

// s:segment, t:segment
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;
}

// p が l:line 上に存在するか
bool isis_lp(Line l, Point p)
{
    return (abs(cross(l.b - p, l.a - p)) < eps);
}

bool isis_sp(Line s, Point p)
{
    return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// p から l に下ろした足との交点
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);
}

// l:line, t:line の交点
Point is_ll(Line l, Line m)
{
    Point lv = l.b - l.a, mv = m.b - m.a;
    assert(cross(lv, mv) != 0);
    return l.a + lv * cross(mv, m.a - l.a) / cross(mv, lv);
}

// p, l:line の距離
ld dist_lp(Line l, Point p)
{
    return abs(p - proj(l, p));
}

ld dist_ll(Line l, Line m)
{
    return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(Line l, Line s)
{
    return isis_ls(l, s) ? 0 : std::min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(Line s, Point p)
{
    Point r = proj(s, p);
    return isis_sp(s, r) ? abs(r - p) : std::min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(Line s, Line t)
{
    if (isis_ss(s, t))
        return 0;
    return std::min({dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b)});
}

using Polygon = std::vector<Point>;

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

bool is_counter_clockwise(const Polygon &poly)
{
    ld angle = 0;
    int n = poly.size();
    for (int i = 0; i < n; i++)
    {
        Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
        angle += arg((c - b) / (b - a));
    }
    return angle > eps;
}

// 0 => out
// 1 => on
// 2 => in
int is_in_polygon(const Polygon &poly, Point p)
{
    ld angle = 0;
    int n = poly.size();
    for (int i = 0; i < n; i++)
    {
        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(std::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;
}

using namespace std;

ld dist_pp(const Polygon &ps, Point p)
{
    int sz = ps.size();
    if (is_in_polygon(ps, p))
        return 0;
    ld mi = 1e15;
    for (int i = 0; i < sz; i++)
    {
        Line s(ps[i], ps[(i + 1) % sz]);
        mi = min(mi, dist_sp(s, p));
    }
    return mi;
}

ld dist_pp(const Polygon &p1, const Polygon &p2)
{
    int sz1 = p1.size(), sz2 = p2.size();
    assert(sz1 > 1 && sz2 > 1);
    ld ret = 1e15;
    for (int i = 0; i < sz1; i++)
    {
        Line s1(p1[i], p1[(i + 1) % sz1]);
        for (int j = 0; j < sz2; j++)
        {
            Line s2(p2[j], p2[(j + 1) % sz2]);
            ret = min(ret, dist_ss(s1, s2));
        }
    }
    return ret;
}

Point from_sun(ld x, ld y, ld h, ld phi, ld shita)
{
    ld p = phi / 180.0 * pi, s = shita / 180.0 * pi;
    return Point(x - h * cos(s) / tan(p), y - h * sin(s) / tan(p));
}

int main()
{
    int n;
    while (cin >> n, n)
    {
        vector<Polygon> polys(n);
        vector<ld> hs(n);
        for (int i = 0; i < n; i++)
        {
            int nv;
            cin >> nv >> hs[i];
            Polygon ps;
            for (int j = 0; j < nv; j++)
            {
                ps.push_back(input_point());
            }
            polys[i] = ps;
        }
        ld phi, shita;
        cin >> shita >> phi;
        Point s = input_point(), t = input_point();
        for (int i = 0; i < n; i++)
        {
            int sz = polys[i].size();
            for (int j = 0; j < sz; j++)
            {
                ld x = polys[i][j].real(), y = polys[i][j].imag();
                polys[i].push_back(from_sun(x, y, hs[i], phi, shita));
            }
            polys[i] = convex_hull(polys[i]);
        }
        vector<vector<ld>> dist(n + 2, vector<ld>(n + 2, 1e15));
        for (int i = 0; i < n + 2; i++)
            dist[i][i] = 0;
        for (int i = 0; i < n; i++)
        {
            for (int j = i + 1; j < n; j++)
            {
                dist[i][j] = dist[j][i] = dist_pp(polys[i], polys[j]);
            }
            dist[i][n] = dist[n][i] = dist_pp(polys[i], s);
            dist[i][n + 1] = dist[n + 1][i] = dist_pp(polys[i], t);
        }
        dist[n][n + 1] = dist[n + 1][n] = abs(s - t);
        for (int k = 0; k < n + 2; k++)
        {
            for (int i = 0; i < n + 2; i++)
            {
                for (int j = 0; j < n + 2; j++)
                {
                    dist[i][j] = min(dist[i][j], dist[i][k] + dist[k][j]);
                }
            }
        }
        cout << fixed << setprecision(10) << dist[n][n + 1] << endl;
    }
}



Measured memory_bytes: 3752