#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define REP(i, m, n) for (int i = (int)m; i < (int)n; i++)
#define rep(i, n) REP(i, 0, n)

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

using Real = double;
using Point = complex<Real>;
constexpr Real EPS = 1e-8;
constexpr Real PI = acos(-1.0);

inline bool eq(Real a, Real b) { return fabs(b - a) < EPS; }

Point operator*(const Point &p, const Real &d)
{
  return Point(real(p) * d, imag(p) * d);
}

istream &operator>>(istream &is, Point &p)
{
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}

ostream &operator<<(ostream &os, Point &p)
{
  return os << fixed << setprecision(20) << p.real() << " " << p.imag();
}

// 点 p を反時計回りに theta 回転
inline Point rotate(Real theta, const Point &p)
{
  return Point(cos(theta) * p.real() - sin(theta) * p.imag(), sin(theta) * p.real() + cos(theta) * p.imag());
}

Real radian_to_degree(Real r)
{
  return (r * 180.0 / PI);
}

Real degree_to_radian(Real d)
{
  return (d * PI / 180.0);
}

// a-b-c の角度のうち小さい方を返す
Real get_angle(const Point &a, const Point &b, const Point &c)
{
  const Point v(a - b), w(c - b);
  Real alpha = atan2(v.imag(), v.real()), beta = atan2(w.imag(), w.real());
  if (alpha > beta)
    swap(alpha, beta);
  Real theta = (beta - alpha);
  return min(theta, 2 * acos(-1) - theta);
}

namespace std
{
  bool operator<(const Point &a, const Point &b)
  {
    return a.real() != b.real() ? a.real() < b.real() : a.imag() < b.imag();
  }
} // namespace std

struct Line
{
  Point a, b;

  Line() = default;

  Line(Point a, Point b) : a(a), b(b) {}

  Line(Real A, Real B, Real C) // Ax + By = C
  {
    if (eq(A, 0))
      a = Point(0, C / B), b = Point(1, C / B);
    else if (eq(B, 0))
      b = Point(C / A, 0), b = Point(C / A, 1);
    else
      a = Point(0, C / B), b = Point(C / A, 0);
  }

  friend ostream &operator<<(ostream &os, Line &p)
  {
    return os << p.a << " to " << p.b;
  }

  friend istream &operator>>(istream &is, Line &a)
  {
    return is >> a.a >> a.b;
  }
};

void parameter(const Line &l, Real &A, Real &B, Real &C) // Ax + By = C
{
  A = imag(l.b) - imag(l.a);
  B = real(l.a) - real(l.b);
  C = real(l.a) * A + imag(l.a) * B;
}

struct Segment : Line
{
  Segment() = default;

  Segment(Point a, Point b) : Line(a, b) {}
};

struct Circle
{
  Point p;
  Real r;

  Circle() = default;

  Circle(Point p, Real r) : p(p), r(r) {}
};

using Points = vector<Point>;
using Polygon = vector<Point>;
using Segments = vector<Segment>;
using Lines = vector<Line>;
using Circles = vector<Circle>;

inline Real cross(const Point &a, const Point &b)
{
  return real(a) * imag(b) - imag(a) * real(b);
}

inline Real dot(const Point &a, const Point &b)
{
  return real(a) * real(b) + imag(a) * imag(b);
}

// 直線がx軸となす角 [0, π)
// to do: verify
inline Real get_angle(const Line &l)
{
  Real A, B, C;
  parameter(l, A, B, C);
  if (fabs(A) < EPS)
    return PI / 2.0;
  Real theta = atan(B / A);
  return theta < 0 ? theta + PI : theta;
}

// 2直線がなす角 [0, π/2]
// to do: verify
inline Real get_angle(const Line &l1, const Line &l2)
{
  Real theta = get_angle(l1) - get_angle(l2);
  if (theta < 0)
    theta += PI;
  return theta >= PI / 2.0 ? theta - PI / 2.0 : theta;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
// 点の回転方向
int ccw(const Point &a, Point b, Point c)
{
  b = b - a, c = c - a;
  if (cross(b, c) > EPS)
    return +1; // "COUNTER_CLOCKWISE"
  if (cross(b, c) < -EPS)
    return -1; // "CLOCKWISE"
  if (dot(b, c) < 0)
    return +2; // "ONLINE_BACK"
  if (norm(b) < norm(c))
    return -2; // "ONLINE_FRONT"
  return 0;    // "ON_SEGMENT"
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 平行判定
inline bool parallel(const Line &a, const Line &b)
{
  return eq(cross(a.b - a.a, b.b - b.a), 0.0);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 垂直判定
inline bool orthogonal(const Line &a, const Line &b)
{
  return eq(dot(a.a - a.b, b.a - b.b), 0.0);
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A
// 射影
// 直線 l に p から垂線を引いた交点を求める
inline Point projection(const Line &l, const Point &p)
{
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}

inline Point projection(const Segment &l, const Point &p)
{
  double t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_B
// 反射
// 直線 l を対称軸として点 p  と線対称にある点を求める
inline Point reflection(const Line &l, const Point &p)
{
  return p + (projection(l, p) - p) * 2.0;
}

// pを通りlに垂直な直線
inline Line verticalline(const Line &l, const Point &p)
{
  Real a = imag(l.b) - imag(l.a);
  Real b = real(l.a) - real(l.b);
  return Line(b, -a, a * imag(p) - b * real(p));
}

inline bool intersect(const Line &l, const Point &p)
{
  return abs(ccw(l.a, l.b, p)) != 1;
}

inline bool intersect(const Line &l, const Line &m)
{
  return abs(cross(l.b - l.a, m.b - m.a)) > EPS || abs(cross(l.b - l.a, m.b - l.a)) < EPS;
}

inline bool intersect(const Segment &s, const Point &p)
{
  return ccw(s.a, s.b, p) == 0;
}

inline bool intersect(const Line &l, const Segment &s)
{
  return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
}

inline Real distance(const Line &l, const Point &p);

inline bool intersect(const Circle &c, const Line &l)
{
  return distance(l, c.p) <= c.r + EPS;
}

inline bool intersect(const Circle &c, const Point &p)
{
  return abs(abs(p - c.p) - c.r) < EPS;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B
bool intersect(const Segment &s, const Segment &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;
}

int intersect(const Circle &c, const Segment &l)
{
  if (norm(projection(l, c.p) - c.p) - c.r * c.r > EPS)
    return 0;
  auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
  if (d1 < c.r + EPS && d2 < c.r + EPS)
    return 0;
  if (d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS)
    return 1;
  const Point h = projection(l, c.p);
  if (dot(l.a - h, l.b - h) < 0)
    return 2;
  return 0;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_A&lang=jp
int intersect(Circle c1, Circle c2)
{
  if (c1.r < c2.r)
    swap(c1, c2);
  Real d = abs(c1.p - c2.p);
  if (c1.r + c2.r < d)
    return 4;
  if (eq(c1.r + c2.r, d))
    return 3;
  if (c1.r - c2.r < d)
    return 2;
  if (eq(c1.r - c2.r, d))
    return 1;
  return 0;
}

inline Real distance(const Point &a, const Point &b)
{
  return abs(a - b);
}

inline Real distance(const Line &l, const Point &p)
{
  return abs(p - projection(l, p));
}

inline Real distance(const Line &l, const Line &m)
{
  return intersect(l, m) ? 0 : distance(l, m.a);
}

inline Real distance(const Segment &s, const Point &p)
{
  Point r = projection(s, p);
  if (intersect(s, r))
    return abs(r - p);
  return min(abs(s.a - p), abs(s.b - p));
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_D
Real distance(const Segment &a, const Segment &b)
{
  if (intersect(a, b))
    return 0;
  return min({distance(a, b.a), distance(a, b.b), distance(b, a.a), distance(b, a.b)});
}

Real distance(const Line &l, const Segment &s)
{
  if (intersect(l, s))
    return 0;
  return min(distance(l, s.a), distance(l, s.b));
}

Point crosspoint(const Line &l, const Line &m)
{
  Real A = cross(l.b - l.a, m.b - m.a);
  Real B = cross(l.b - l.a, l.b - m.a);
  if (eq(abs(A), 0.0) && eq(abs(B), 0.0))
    return m.a;
  return m.a + (m.b - m.a) * B / A;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C
Point crosspoint(const Segment &l, const Segment &m)
{
  return crosspoint(Line(l), Line(m));
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D
pair<Point, Point> crosspoint(const Circle &c, const Line l)
{
  Point pr = projection(l, c.p);
  Point e = (l.b - l.a) / abs(l.b - l.a);
  if (eq(distance(l, c.p), c.r))
    return {pr, pr};
  double base = sqrt(c.r * c.r - norm(pr - c.p));
  return {pr - e * base, pr + e * base};
}

pair<Point, Point> crosspoint(const Circle &c, const Segment &l)
{
  Line aa = Line(l.a, l.b);
  if (intersect(c, l) == 2)
    return crosspoint(c, aa);
  auto ret = crosspoint(c, aa);
  if (dot(l.a - ret.first, l.b - ret.first) < 0)
    ret.second = ret.first;
  else
    ret.first = ret.second;
  return ret;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_E
pair<Point, Point> crosspoint(const Circle &c1, const Circle &c2)
{
  Real d = abs(c1.p - c2.p);
  Real a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
  Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());
  Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r);
  Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r);
  return {p1, p2};
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_F
// 点 p を通る円 c の接線
pair<Point, Point> tangent(const Circle &c1, const Point &p2)
{
  return crosspoint(c1, Circle(p2, sqrt(norm(c1.p - p2) - c1.r * c1.r)));
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_G
// 円 c1, c2 の共通接線
Lines tangent(Circle c1, Circle c2)
{
  Lines ret;
  if (c1.r < c2.r)
    swap(c1, c2);
  Real g = norm(c1.p - c2.p);
  if (eq(g, 0))
    return ret;
  Point u = (c2.p - c1.p) / sqrt(g);
  Point v = rotate(PI * 0.5, u);
  for (int s : {-1, 1})
  {
    Real h = (c1.r + s * c2.r) / sqrt(g);
    if (eq(1 - h * h, 0))
    {
      ret.emplace_back(c1.p + u * c1.r, c1.p + (u + v) * c1.r);
    }
    else if (1 - h * h > 0)
    {
      Point uu = u * h, vv = v * sqrt(1 - h * h);
      ret.emplace_back(c1.p + (uu + vv) * c1.r, c2.p - (uu + vv) * c2.r * s);
      ret.emplace_back(c1.p + (uu - vv) * c1.r, c2.p - (uu - vv) * c2.r * s);
    }
  }
  return ret;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B
// 凸性判定
bool is_convex(const Polygon &p)
{
  int n = (int)p.size();
  for (int i = 0; i < n; i++)
  {
    if (ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == -1)
      return false;
  }
  return true;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_4_A
// 凸包
Polygon convex_hull(Polygon &p)
{
  int n = (int)p.size(), k = 0;
  if (n <= 2)
    return p;
  sort(p.begin(), p.end());
  vector<Point> ch(2 * n);
  for (int i = 0; i < n; ch[k++] = p[i++])
  {
    while (k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS)
      --k;
  }
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--])
  {
    while (k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < EPS)
      --k;
  }
  ch.resize(k - 1);
  return ch;
}

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C
// 多角形と点の包含判定
enum
{
  OUT,
  ON,
  IN
};

int contains(const Polygon &Q, const Point &p)
{
  bool in = false;
  for (int i = 0; i < Q.size(); i++)
  {
    Point a = Q[i] - p, b = Q[(i + 1) % Q.size()] - p;
    if (a.imag() > b.imag())
      swap(a, b);
    if (a.imag() <= 0 && 0 < b.imag() && cross(a, b) < 0)
      in = !in;
    if (cross(a, b) == 0 && dot(a, b) <= 0)
      return ON;
  }
  return in ? IN : OUT;
}

double theta;
void update(Polygon &p, double k)
{
  int sz = p.size();
  rep(i, sz)
  {
    Point q = p[i] - Point(cos(theta) * k, sin(theta) * k);
    p.push_back(q);
  }
  p = convex_hull(p);
}

Real distance(const Polygon &p, const Point &a)
{
  if (contains(p, a) != OUT)
    return 0;
  Real Min = 4e18;
  int sz = p.size();
  rep(i, sz)
  {
    Segment sg(p[i], p[(i + 1) % sz]);
    Min = min(Min, distance(sg, a));
  }
  return Min;
}

Real distance(const Polygon &p1, const Polygon &p2)
{
  int sz1 = p1.size(), sz2 = p2.size();
  Real Min = 4e18;
  rep(i, sz1)
  {
    if (contains(p2, p1[i]) != OUT)
      return 0;
  }
  rep(i, sz2)
  {
    if (contains(p1, p2[i]) != OUT)
      return 0;
  }
  rep(i, sz1) rep(j, sz2)
  {
    Segment sg1(p1[i], p1[(i + 1) % sz1]), sg2(p2[j], p2[(j + 1) % sz2]);
    Min = min(Min, distance(sg1, sg2));
  }
  return Min;
}

template <typename T>
struct dijkstra
{
  int V;
  T INF_d;
  struct edge
  {
    int to;
    T cost;
  };
  vector<vector<edge>> E;
  vector<T> d;
  using pt = pair<T, int>;
  dijkstra(int V_) : V(V_)
  {
    E.resize(V);
    d.resize(V);
    INF_d = 4e18;
  }

  void add_E(int a, int b, T c = 1, bool directed = true)
  {
    E[a].emplace_back(edge{b, c});
    if (!directed)
      E[b].emplace_back(edge{a, c});
  }

  void calc(int s)
  {
    priority_queue<pt, vector<pt>, greater<pt>> que;
    fill(d.begin(), d.end(), INF_d);
    que.emplace(T(0), s);
    d[s] = 0;
    while (!que.empty())
    {
      pt p = que.top();
      que.pop();
      int v = p.second;
      if (d[v] < p.first)
        continue;
      for (auto &&e : E[v])
      {
        if (d[e.to] > d[v] + e.cost)
        {
          d[e.to] = d[v] + e.cost;
          que.emplace(d[e.to], e.to);
        }
      }
    }
  }
};

void solve(int n)
{
  vector<Polygon> v(n);
  vector<double> h(n);
  rep(i, n)
  {
    int p;
    cin >> p;
    cin >> h[i];
    rep(pi, p)
    {
      Real x, y;
      cin >> x >> y;
      v[i].push_back(Point(x, y));
    }
  }
  double phi;
  cin >> theta >> phi;
  theta = theta * PI / 180.0;
  phi = phi * PI / 180.0;
  vector<double> k(n);
  rep(i, n) k[i] = h[i] / tan(phi);
  rep(i, n) update(v[i], k[i]);
  dijkstra<double> ds(n + 2);
  double sx, sy, gx, gy;
  cin >> sx >> sy >> gx >> gy;
  Point start(sx, sy), goal(gx, gy);
  rep(i, n) REP(j, i + 1, n)
  {
    double d = distance(v[i], v[j]);
    ds.add_E(i, j, d, false);
  }
  rep(i, n)
  {
    double d = distance(v[i], start);
    ds.add_E(i, n, d, false);
  }
  rep(i, n)
  {
    double d = distance(v[i], goal);
    ds.add_E(i, n + 1, d, false);
  }
  ds.add_E(n, n + 1, distance(start, goal), false);

  ds.calc(n);
  cout << ds.d[n + 1] << "\n";
}

int main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(30) << setiosflags(ios::fixed);
  while (1)
  {
    int n;
    cin >> n;
    if (n == 0)
      break;
    solve(n);
  }
}



Measured memory_bytes: 3812