#include<stdio.h>
#include<math.h>
#define rep(i,n) for(i=0;i<n;i++)
#define REP(i,a,b) for(i=a;i<b;i++)
#define EPS 1e-12

double x[11],y[11];
double t1,t2;
double ky[10][30]; int ky_size[10];
double sx,sy,ex,ey;
double d[110][110];
double mx[110],my[110];
int last_st;

double distv(int i,int j){
  double dx,dy;
  dx=x[i]-x[j];
  dy=y[i]-y[j];
  return sqrt(dx*dx+dy*dy);
}

double dist(double dx, double dy){
  return sqrt(dx*dx+dy*dy);
}

int d_eq(double a,double b){
  a-=b; if(a<0) a=-a;
  if(a<EPS) return 1;
  return 0;
}

int main(){
  int i,j,k,l,m,n;
  double a,b,c1,c2;
  double d1,d2;
  double nx,ny;
  double x1,x2,y1,y2;
  double bx,by;
  int nm;
  int st_v; double st_a;
  int t_v; double t_a;
  int k1,k2,k3;
  double tmp;
  
  for(;;){
    scanf("%d",&n); if(!n) break; nm=n-1;
    rep(i,n) scanf("%lf%lf",x+i,y+i);
    scanf("%lf%lf",&t1,&t2);
    scanf("%lf%lf",&sx,&sy);
    scanf("%lf%lf",&ex,&ey);
    x[n]=x[0]; y[n]=x[0];

    rep(i,n) ky_size[i]=2;
    rep(i,n) ky[i][0]=0.0, ky[i][1]=1.0;

    rep(k,n){
      a=0; b=1.0;
      while(b-a>1e-14){
        c1 = (a*2+b)/3.0;
        c2 = (a+b*2)/3.0;
        d1 = t1*c1*distv(k,k+1);
        nx=(1.0-c1) * x[k] + c1 * x[k+1];
        ny=(1.0-c1) * y[k] + c1 * y[k+1];
        d1 += t2*dist(ex-nx,ey-ny);
        d2 = t1*c2*distv(k,k+1);
        nx=(1.0-c1) * x[k] + c2 * x[k+1];
        ny=(1.0-c2) * y[k] + c2 * y[k+1];
        d2 += t2*dist(ex-nx,ey-ny);
        if(d1<d2) b=c2; else a=c1;
      }
      ky[k][ky_size[k]++]=a;
    }
    rep(k,n){
      a=0; b=1.0;
      while(b-a>1e-14){
        c1 = (a*2+b)/3.0;
        c2 = (a+b*2)/3.0;
        d1 = t1*c1*distv(k,(k+nm)%n);
        nx=(1.0-c1) * x[k] + c1 * x[(k+nm)%n];
        ny=(1.0-c1) * y[k] + c1 * y[(k+nm)%n];
        d1 += t2*dist(ex-nx,ey-ny);
        d2 = t1*c2*distv(k,(k+nm)%n);
        nx=(1.0-c1) * x[k] + c2 * x[(k+nm)%n];
        ny=(1.0-c2) * y[k] + c2 * y[(k+nm)%n];
        d2 += t2*dist(ex-nx,ey-ny);
        if(d1<d2) b=c2; else a=c1;
      }
      ky[(k+nm)%n][ky_size[(k+nm)%n]++]=1.0-a;
    }

    rep(k,n){
      x1=x[k]-sx; x2=x[k+1]-sx;
      y1=y[k]-sy; y2=y[k+1]-sy;
      x1 = x1*y2 - y1*x2;
      if(x1<0) x1=-x1;
      if(x1 < EPS) break;
    }
  

    if(d_eq(x[k],x[k+1])){
      y1=y[k+1] - y[k];
      a=sy-y[k]; a/=y1;
    } else {
      x1=x[k+1] - x[k];
      a=sx-x[k]; a/=x1;
    }
    
    st_v=k; st_a=a;

    ky[st_v][ky_size[st_v]++] = st_a;
    rep(i,n){
      k1=st_v+i; k2=k1+1; k3=k2+1;
      k1 %= n; k2 %= n; k3 %= n;
      
      a = ky[k1][ky_size[k1]-1];
      bx = (1-a)*x[k1] + a*x[k2];
      by = (1-a)*y[k1] + a*y[k2];

      a=0; b=1;      
      while(b-a>1e-14){
        c1 = (a*2+b)/3.0;
        c2 = (a+b*2)/3.0;
        
        nx = (1-c1)*x[k2] + c1*x[k3];
        ny = (1-c1)*y[k2] + c1*y[k3];
        d1 = dist(bx-nx,by-ny) * t2;
        d1+= dist(x[k3]-nx,y[k3]-ny) * t1;

        nx = (1-c2)*x[k2] + c2*x[k3];
        ny = (1-c2)*y[k2] + c2*y[k3];
        d2 = dist(bx-nx,by-ny) * t2;
        d2+= dist(x[k3]-nx,y[k3]-ny) * t1;

        if(d1<d2) b=c2; else a=c1;
      }
      ky[k2][ky_size[k2]++]=a;
    }
    
    ky[st_v][ky_size[st_v]++] = st_a;
    rep(i,n){
      k1=st_v-i+n; k2=k1-1+n; k3=k1+1;
      k1 %= n; k2 %= n;
      
      a = ky[k1][ky_size[k1]-1];
      bx = (1-a)*x[k1] + a*x[k3];
      by = (1-a)*y[k1] + a*y[k3];

      a=0; b=1;      
      while(b-a>1e-14){
        c1 = (a*2+b)/3.0;
        c2 = (a+b*2)/3.0;
        
        nx = (1-c1)*x[k2] + c1*x[k1];
        ny = (1-c1)*y[k2] + c1*y[k1];
        d1 = dist(bx-nx,by-ny) * t2;
        d1+= dist(x[k2]-nx,y[k2]-ny) * t1;

        nx = (1-c2)*x[k2] + c2*x[k1];
        ny = (1-c2)*y[k2] + c2*y[k1];
        d2 = dist(bx-nx,by-ny) * t2;
        d2+= dist(x[k2]-nx,y[k2]-ny) * t1;

        if(d1<d2) b=c2; else a=c1;
      }
      ky[k2][ky_size[k2]++]=a;
    }
    
    rep(i,110) rep(j,110) d[i][j]=1e100;
    m=0;
    rep(i,n) rep(j,ky_size[i]){
      a = ky[i][j];
      nx = (1-a)*x[i] + a*x[i+1];
      ny = (1-a)*y[i] + a*y[i+1];
      //      printf("point %d %d [%d] %lf %lf\n",i,j,m,nx,ny);
      if(d_eq(nx,sx) && d_eq(ny,sy)) last_st=m;
      mx[m]=nx; my[m]=ny;
      rep(k,j) d[m-1-k][m]=d[m][m-1-k] = dist(mx[m]-mx[m-1-k],my[m]-my[m-1-k])*t1;
      m++;
    }
    mx[m]=ex; my[m]=ey; m++;
    mx[m]=sx; my[m]=sy; m++;

    //printf("first point %d\n",last_st);
    //printf("m %d\n",m);

    rep(i,m) rep(j,m){
      a=dist(mx[i]-mx[j],my[i]-my[j]);
      a *= t2;
      if(d[i][j] > a) d[i][j] = a;
    }

    rep(k,m) rep(i,m) rep(j,m){
      if(d[i][j] > d[i][k] + d[k][j]) d[i][j] = d[i][k]+d[k][j];
    }

    //printf("dist 0 2 = %lf\n",d[0][2]);
    //rep(i,m) REP(j,m-1,m) printf("dist %d %d = %lf\n",i,j,d[i][j]);

    printf("%.15lf\n",d[m-2][m-1]);
  }
}