#include<iostream>
#include<cstdio>
#include<vector>
#include<complex>
#include<algorithm>
#include<deque>
#include<cstring>
#include<cassert>
#include<climits>
#include<map>
#include<queue>
#include<set>
#include<unordered_set>

#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define EPS (1e-8)
#define equals(a,b) (fabs((a)-(b))<EPS)
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0

using namespace std;

// -- BEGIN --
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(a*x,a*y);}
  Point operator / (double a){return Point(x/a,y/a);}
  Point operator * (Point a){ return Point(x * a.x - y * a.y, x * a.y + y * a.x); }

  bool operator < (const Point& p) const{ return !equals(x,p.x)?x<p.x:(!equals(y,p.y)&&y<p.y); }

  bool operator == (const Point& p)const{ return fabs(x-p.x) < EPS && fabs(y-p.y) < EPS; }

};

struct Segment{
  Point p1,p2;
  Segment(Point p1 = Point(),Point p2 = Point()):p1(p1),p2(p2){}
  bool operator <  (const Segment& s) const { return ( p2 == s.p2 ) ? p1 < s.p1 : p2 < s.p2; }
  bool operator == (const Segment& s) const { return ( s.p1 == p1 && s.p2 == p2 ) || ( s.p1 == p2 && s.p2 == p1 ); }

};

typedef Point Vector;
typedef Segment Line;
typedef vector<Point> Polygon;

ostream& operator << (ostream& os,const Point& a){ return os << "(" << a.x << "," << a.y << ")"; }

ostream& operator << (ostream& os,const Segment& a){ return os << "( " << a.p1 << " , " << a.p2 << " )"; }

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

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

double norm(Point a){ return a.x*a.x+a.y*a.y; }

double abs(Point a){ return sqrt(norm(a)); }

//rad ????§???????????????¢?????§?????????????????¨
Point rotate(Point a,double rad){ return Point(cos(rad)*a.x - sin(rad)*a.y,sin(rad)*a.x + cos(rad)*a.y); }

// ??????????????¢????????????
double toRad(double agl){ return agl*M_PI/180.0; }

// a => prev, b => cur, c=> next
// prev ?????? cur ????????£??? next ????????????????§????????±???????
double getArg(Point a,Point b,Point c){
  double arg1 = atan2(b.y-a.y,b.x-a.x);
  double arg2 = atan2(c.y-b.y,c.x-b.x);
  double arg = fabs( arg1 - arg2 );
  while( arg > M_PI ) arg -= 2.0 * M_PI;
  return fabs(arg);
}

int ccw(Point p0,Point p1,Point p2){
  Point a = p1-p0;
  Point 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(norm(a) < norm(b))return ONLINE_FRONT;
  return ON_SEGMENT;
}

Polygon andrewScan(Polygon s) {
  Polygon u,l;
  if((int)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<(int)s.size();i++) {
    for(int n=(int)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=(int)s.size()-3; i>=0 ; i--) {
    for(int n=(int)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 = (int)u.size()-2; i >= 1; i--) l.push_back(u[i]);

  return l;
}


//cross product of pq and pr
double cross3p(Point p,Point q,Point r) { return (r.x-q.x) * (p.y -q.y) - (r.y - q.y) * (p.x - q.x); }
  
//returns true if point r is on the same line as the line pq
bool collinear(Point p,Point q,Point r) { return fabs(cross3p(p,q,r)) < EPS; }
  
//returns true if point t is on the left side of line pq
bool ccwtest(Point p,Point q,Point r){
  return cross3p(p,q,r) > 0; //can be modified to accept collinear points
}
 
bool onSegment(Point p,Point q,Point r){
  return collinear(p,q,r) && equals(sqrt(pow(p.x-r.x,2)+pow(p.y-r.y,2)) + sqrt(pow(r.x-q.x,2) + pow(r.y-q.y,2) ),sqrt(pow(p.x-q.x,2)+pow(p.y-q.y,2)) ) ;
}
  

bool isConvex(vector<Point> p) {
  int sz = (int)p.size();
  if(sz < 3)return false;//boundary case, we treat a point or a line as not convex
  bool isLeft = ccwtest(p[0],p[1],p[2]);
  for(int i=1; i<(int)p.size();i++)
    if(ccwtest(p[i],p[(i+1)%sz],p[(i+2)%sz]) != isLeft) return false;
  return true;
}


double angle(Point a,Point b,Point c) {
  double ux = b.x - a.x, uy = b.y - a.y;
  double vx = c.x - a.x, vy = c.y - a.y;
  return acos((ux*vx + uy*vy)/sqrt((ux*ux + uy*uy) * (vx*vx + vy*vy)));
}  
  
//????§???¢poly?????????????????????????????????p????????¨??????????????????????????????  
bool inPolygon(Polygon &poly,Point p){
  if((int)poly.size() == 0)return false;
  rep(i,(int)poly.size()) if(onSegment(poly[i],poly[(i+1)%poly.size()],p))return true;
  double sum = 0;
  for(int i=0; i < (int)poly.size() ;i++) {
    if( equals(cross(poly[i]-p,poly[(i+1)%poly.size()]-p),0.0) ) continue; // ????????????????????¨angle???nan?????????sum???nan??????????????¬
    if( cross3p(p,poly[i],poly[(i+1)%poly.size()]) < 0 ) sum -= angle(p,poly[i],poly[(i+1)%poly.size()]);
    else                                                 sum += angle(p,poly[i],poly[(i+1)%poly.size()]);
  }
  // ?????????????????????????????????????????¨?????????????????§??\????????????????????? 
  const double eps = 1e-5;
  return (fabs(sum - 2*M_PI) < eps || fabs(sum + 2*M_PI) < eps);
}  


bool intersectLL(Line l, Line m) {
  return abs(cross(l.p2-l.p1, m.p2-m.p1)) > EPS || // non-parallel
         abs(cross(l.p2-l.p1, m.p1-l.p1)) < EPS;   // same line
}
bool intersectLS(Line l, Line s) {
  return cross(l.p2-l.p1, s.p1-l.p1)*       // s[0] is left of l
         cross(l.p2-l.p1, s.p2-l.p1) < EPS; // s[1] is right of l
}
bool intersectLP(Line l,Point p) {
  return abs(cross(l.p2-p, l.p1-p)) < EPS;
}
bool intersectSS(Line s, Line t) {
  return ccw(s.p1,s.p2,t.p1)*ccw(s.p1,s.p2,t.p2) <= 0 &&
         ccw(t.p1,t.p2,s.p1)*ccw(t.p1,t.p2,s.p2) <= 0;
}
bool intersectSP(Line s, Point p) {
  return abs(s.p1-p)+abs(s.p2-p)-abs(s.p2-s.p1) < EPS; // triangle inequality
}

Point projection(Line l,Point p) {
  double t = dot(p-l.p1, l.p1-l.p2) / norm(l.p1-l.p2);
  return l.p1 + (l.p1-l.p2)*t;
}
Point reflection(Line l,Point p) {
  return p + (projection(l, p) - p) * 2;
}
double distanceLP(Line l, Point p) {
  return abs(p - projection(l, p));
}
double distanceLL(Line l, Line m) {
  return intersectLL(l, m) ? 0 : distanceLP(l, m.p1);
}

double distanceLS(Line l, Line s) {
  if (intersectLS(l, s)) return 0;
  return min(distanceLP(l, s.p1), distanceLP(l, s.p2));
}
double distanceSP(Line s, Point p) {
  Point r = projection(s, p);
  if (intersectSP(s, r)) return abs(r - p);
  return min(abs(s.p1 - p), abs(s.p2 - p));
}

double distanceSS(Line s, Line t) {
  if (intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t.p1), distanceSP(s, t.p2)),
             min(distanceSP(t, s.p1), distanceSP(t, s.p2)));
}

Point crosspoint(Line l,Line m){
  double A = cross(l.p2-l.p1,m.p2-m.p1);
  double B = cross(l.p2-l.p1,l.p2-m.p1);
  if(abs(A) < EPS && abs(B) < EPS){
    vector<Point> vec;
    vec.push_back(l.p1),vec.push_back(l.p2),vec.push_back(m.p1),vec.push_back(m.p2);
    sort(vec.begin(),vec.end());
    assert(vec[1] == vec[2]); //???????????°??????????????????
    return vec[1];
    //return m.p1;
  }
  if(abs(A) < EPS)assert(false);
  return m.p1 + (m.p2-m.p1)*(B/A);
}



// -- END -- 

const bool debug = false;

struct Edge {
  int dst;
  double cost;
};

bool LT(double a,double b) { return !equals(a,b) && a < b; }
bool LTE(double a,double b) { return equals(a,b) || a < b; }

int N,VN[110];
double Hs[110];
Polygon polies[110];
Point ep[2];

bool check(Segment &seg,int skip1=-1,int skip2=-1) {
  rep(i,N) {
    if( i == skip1 || i == skip2 ) continue;
    rep(j,VN[i]) {
      Segment ururu_beam = Segment(polies[i][j],polies[i][(j+1)%VN[i]]);
      if( equals(cross(seg.p1-seg.p2,ururu_beam.p1-ururu_beam.p2),0) ) continue;
      if( intersectSS(seg,ururu_beam) ) return false;
    }
  }
  return true;
}

Segment nearestSS(Segment &seg1,Segment &seg2) {
  Segment seg = Segment(seg1.p1,seg2.p1);
  double mini = abs(seg1.p1-seg2.p1);
  /*
  if( LT(abs(seg1.p1-seg2.p2),mini) ) {
    mini = abs(seg1.p1-seg2.p2);
    seg = Segment(seg1.p1,seg2.p2);
  }
  if( LT(abs(seg1.p2-seg2.p1),mini) ) {
    mini = abs(seg1.p2-seg2.p1);
    seg = Segment(seg1.p2,seg2.p1);
  }
  if( LT(abs(seg1.p2-seg2.p2),mini) ) {
    mini = abs(seg1.p2-seg2.p2);
    seg = Segment(seg1.p2,seg2.p2);
  }
  */
  Point proj = projection(seg2,seg1.p1);
  if( onSegment(seg2.p1,seg2.p2,proj) && LT(abs(seg1.p1-proj),mini) ) {
    mini = abs(seg1.p1-proj);
    seg = Segment(seg1.p1,proj);
  }
  proj = projection(seg2,seg1.p2);
  if( onSegment(seg2.p1,seg2.p2,proj) && LT(abs(seg1.p2-proj),mini) ) {
    mini = abs(seg1.p2-proj);
    seg = Segment(seg1.p2,proj);
  }
  proj = projection(seg1,seg2.p1);
  if( onSegment(seg1.p1,seg1.p2,proj) && LT(abs(seg2.p1-proj),mini) ) {
    mini = abs(seg2.p1-proj);
    seg = Segment(seg2.p1,proj);
  }
  proj = projection(seg1,seg2.p2);
  if( onSegment(seg1.p1,seg1.p2,proj) && LT(abs(seg2.p2-proj),mini) ) {
    mini = abs(seg2.p2-proj);
    seg = Segment(seg2.p2,proj);
  }
  return seg;
}

struct Data {
  int cur;
  double w;
  bool operator < ( const Data &data ) const {
    if( !equals(w,data.w) ) return LT(data.w,w);
    return cur > data.cur;
  }
};

vector<Edge> G[110];
double dijkstra(int V) {
  vector<double> mini(V,1e8);
  mini[0] = 0;
  priority_queue<Data> Q;
  Q.push((Data){0,0});
  while( !Q.empty() ) {
    Data data = Q.top(); Q.pop();
    if( data.cur == 1 ) return data.w;
    rep(i,(int)G[data.cur].size()) {
      Edge &e = G[data.cur][i];
      if( LT(data.w+e.cost,mini[e.dst]) ) {
	mini[e.dst] = data.w+e.cost;
	Q.push((Data){e.dst,mini[e.dst]});
      }
    }
  }
  return mini[1];
}

void compute(int N,double theta,double phi) {
  double ans = abs(ep[0]-ep[1]);
  // ??±?????????????????´????????????
  rep(i,N) {
    vector<Point> ps;
    Vector v = Vector(cos(theta),sin(theta));
    rep(j,VN[i]) {
      ps.push_back(polies[i][j]);
      ps.push_back(polies[i][j]-v*Hs[i]/tan(phi));
    }
    polies[i] = andrewScan(ps);
    VN[i] = (int)polies[i].size();
    
    if( debug ) {
      puts("");
      cout << i << "-th polygon" << endl;
      rep(j,(int)polies[i].size()) {
	cout << polies[i][j] << endl;
      }
    }

  }
  
  // ?§??????????+??±?????????????????´?????????????????§?§??????§??????????????§??????????????±??????????????¢????±??????°?????????
  rep(i,N+2) G[i].clear();
  rep(i,2) { //?§??????????????????±??????????????´??????????????¢
    rep(j,N) {
      if( inPolygon(polies[j],ep[i]) ) {
	G[i].push_back((Edge){2+j,0});
	G[2+j].push_back((Edge){i,0});
      } else {
	double mini = 1e8;

	rep(k,VN[j]) {
	  Segment seg = Segment(ep[i],polies[j][k]);
	  if( LTE(ans,abs(seg.p1-seg.p2)) ) continue;
	  if( LT(abs(seg.p1-seg.p2),mini) && check(seg,j) ) {
	    mini = abs(seg.p1-seg.p2);
	  }
	}
	rep(k,VN[j]) {
	  Point p = projection(Line(polies[j][k],polies[j][(k+1)%VN[j]]),ep[i]);
	  if( !onSegment(polies[j][k],polies[j][(k+1)%VN[j]],p) ) continue;
	  Segment seg = Segment(ep[i],p);
	  if( LTE(ans,abs(seg.p1-seg.p2)) ) continue;
	  if( LT(abs(seg.p1-seg.p2),mini) && check(seg,j) ) {
	    mini = abs(seg.p1-seg.p2);
	  }
	}
	//if( !equals(mini,1e8) ) {
	if( LT(mini,ans) ) {
	  G[i].push_back((Edge){2+j,mini});
	  G[2+j].push_back((Edge){i,mini});
	}
      }
    }
  }
  rep(i,N) { //??±??????????????´???i????????±??????????????´???j???????????¢
    REP(j,i+1,N) {
      double mini = 1e8;
      
      rep(k,VN[i]) {
	Segment seg1 = Segment(polies[i][k],polies[i][(k+1)%VN[i]]);
	rep(l,(int)polies[j].size()) {
	  Segment seg2 = Segment(polies[j][l],polies[j][(l+1)%VN[j]]);
	  
	  if( equals(cross(seg1.p1-seg1.p2,seg2.p1-seg2.p2),0.0) && ( onSegment(seg1.p1,seg1.p2,seg2.p1) || onSegment(seg1.p1,seg1.p2,seg2.p2) )  ) {
	    mini = 0;
	    goto Skip;
	  } else if( !equals(cross(seg1.p1-seg1.p2,seg2.p1-seg2.p2),0.0) && intersectSS(seg1,seg2) ) {
	    mini = 0;
	    goto Skip;
	  } else {
	    Segment seg = nearestSS(seg1,seg2);
	    if( LTE(ans,abs(seg.p1-seg.p2)) ) continue;
	    if( LT(abs(seg.p1-seg.p2),mini) && check(seg,i,j) ) {
	      mini = abs(seg.p1-seg.p2);
	    }
	  }
	}
      }
    Skip:;
      //if( !equals(mini,1e8) ) {
      if( LT(mini,ans) ) {
	G[2+i].push_back((Edge){2+j,mini});
	G[2+j].push_back((Edge){2+i,mini});
      }
    }
  }
  
  if( debug ) {
    rep(i,2+N) {
      puts("");
      if( i < 2 ) cout << "(" << i << ")" << " From : " << ep[i] << endl;
      else        cout << "(" << i << ")" << " From : " << "polygon " << i-2 << " (" << polies[i-2][0] << ")" << endl;
      rep(j,(int)G[i].size()) {
	cout << "  To : " << G[i][j].dst << ", Weight : " << G[i][j].cost << endl;
      }
    } 
  }

  // dijkstra
  ans = min(ans,dijkstra(N+2));
  printf("%.10f\n",ans);
  //printf("%.10f\n",dijkstra(N+2));
  
}

int main(){
  while( cin >> N, N ) {
    rep(i,N) {
      cin >> VN[i] >> Hs[i];
      polies[i].resize(VN[i]);
      rep(j,VN[i]) cin >> polies[i][j].x >> polies[i][j].y;
    }
    double theta, phi;
    cin >> theta >> phi;
    rep(i,2) cin >> ep[i].x >> ep[i].y;
    compute(N,toRad(theta),toRad(phi));
  }
  return 0;
}

Measured memory_bytes: 3664