#include<stdio.h>
#include<algorithm>
#include<math.h>
#include<vector>
#include<queue>
using namespace std;
const double EPS = 1e-10;
const double INF = 1e+10;
const double PI = acos(-1);
int sig(double r) { return (r < -EPS) ? -1 : (r > +EPS) ? +1 : 0; }
inline double ABS(double a){return max(a,-a);}
struct Pt {
    double x, y;
    Pt() {}
    Pt(double x, double y) : x(x), y(y) {}
    Pt operator+(const Pt &a) const { return Pt(x + a.x, y + a.y); }
    Pt operator-(const Pt &a) const { return Pt(x - a.x, y - a.y); }
    Pt operator*(const Pt &a) const { return Pt(x * a.x - y * a.y, x * a.y + y * a.x); }
    Pt operator-() const { return Pt(-x, -y); }
    Pt operator*(const double &k) const { return Pt(x * k, y * k); }
    Pt operator/(const double &k) const { return Pt(x / k, y / k); }
    double ABS() const { return sqrt(x * x + y * y); }
    double abs2() const { return x * x + y * y; }
    double arg() const { return atan2(y, x); }
    double dot(const Pt &a) const { return x * a.x + y * a.y; }
    double det(const Pt &a) const { return x * a.y - y * a.x; }
};
double tri(const Pt &a, const Pt &b, const Pt &c) { return (b - a).det(c - a); }
int iSP(Pt a, Pt b, Pt c) {
    int s = sig((b - a).det(c - a));
    if (s) return s;
    if (sig((b - a).dot(c - a)) < 0) return -2; // c-a-b
    if (sig((a - b).dot(c - b)) < 0) return +2; // a-b-c
    return 0;
}
Pt pLL(Pt a, Pt b, Pt c, Pt d) {
    b = b - a; d = d - c; return a + b * (c - a).det(d) / b.det(d);
}
Pt hLP(Pt a,Pt b,Pt c){
    return pLL(a,b,c,c+(b-a)*Pt(0,1));
}
//inside: +1 on: 0 outside: -1
int sGP(int n, Pt p[], Pt a) {
    int side = -1, i;
    p[n] = p[0];
    for (i = 0; i < n; ++i) {
        Pt p0 = p[i] - a, p1 = p[i + 1] - a;
        if (sig(p0.det(p1)) == 0 && sig(p0.dot(p1)) <= 0) return 0;
        if (p0.y > p1.y) swap(p0, p1);
        if (sig(p0.y) <= 0 && 0 < sig(p1.y) && sig(p0.det(p1)) > 0) side = -side;
    }
    return side;
}
 
Pt p[20000];
Pt h[20000];
double ijk[1100000];
int v[1100000];
int main(){
    int a;
    while(scanf("%d",&a),a){
        double tg,tw;
        for(int i=0;i<a;i++){
            double X,Y;
            scanf("%lf%lf",&X,&Y);
            p[i]=Pt(X,Y);
        }
        p[a]=p[0];
        scanf("%lf%lf",&tg,&tw);
        Pt s,t;
        double X,Y;
        scanf("%lf%lf",&X,&Y);
        s=Pt(X,Y);
        scanf("%lf%lf",&X,&Y);
        t=Pt(X,Y);
        double th=asin(tg/tw);
        for(int i=0;i<a;i++){
            h[i]=hLP(p[i],p[i+1],t);
        }
        vector<Pt> hb;
        hb.push_back(s);
        hb.push_back(t);
        for(int i=0;i<a;i++){
            hb.push_back(p[i]);
        }
        for(int j=0;j<a;j++){
            Pt tmp=hLP(p[j],p[j+1],t);
            double dist=(tmp-t).ABS();
            double len=dist*tan(th);
            Pt vec=p[j+1]-p[j];
            vec=vec/(vec.ABS())*len;
            Pt t1=tmp+vec;
            Pt t2=tmp-vec;
            if(iSP(p[j],t1,p[j+1])==2)hb.push_back(t1);
            if(iSP(p[j],t2,p[j+1])==2)hb.push_back(t2);
        }
        for(int j=0;j<a;j++){
            Pt tmp=hLP(p[j],p[j+1],s);
            double dist=(tmp-s).ABS();
            double len=dist*tan(th);
            Pt vec=p[j+1]-p[j];
            vec=vec/(vec.ABS())*len;
            Pt t1=tmp+vec;
            Pt t2=tmp-vec;
            if(iSP(p[j],t1,p[j+1])==2)hb.push_back(t1);
            if(iSP(p[j],t2,p[j+1])==2)hb.push_back(t2);
        }
        int sz=hb.size();
        for(int i=0;i<sz;i++){
            v[i]=0;
            ijk[i]=999999999;
        }
        ijk[0]=0;
        for(int i=0;i<sz;i++){
            int at=0;
            double tmp=999999999;
            for(int j=0;j<sz;j++){
                if(!v[j]&&tmp>ijk[j]){
                    at=j;tmp=ijk[j];
                }
            }
            v[at]=1;
            for(int j=0;j<sz;j++){
                if(v[j])continue;
                Pt M=(hb[at]+hb[j])/2;
                double toc=ijk[at];
                if(sGP(a,p,M)==0)toc+=(hb[at]-hb[j]).ABS()*tg;
                else toc+=(hb[at]-hb[j]).ABS()*tw;
                ijk[j]=min(ijk[j],toc);
            }
        }
        //for(int i=0;i<sz;i++)printf("(%f %f): %f\n",hb[i].x,hb[i].y,ijk[i]);
        printf("%.12f\n",ijk[1]);
    }
}



Measured memory_bytes: 2852