#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<iostream>
#define ll long long
ll a[200005];
bool vis[2005][2005][2][2];
double f[2005][2005][2][2];
int n;
ll h;
double p;
int read(){int t=0,f=1;char ch=getchar();while (ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();}while ('0'<=ch&&ch<='9'){t=t*10+ch-'0';ch=getchar();}return t*f;
}
double dp(int l,int r,int sl,int sr){if (vis[l][r][sl][sr]) return f[l][r][sl][sr];vis[l][r][sl][sr]=1;f[l][r][sl][sr]=0;if (l==r){if (sl==1&&a[l-1]+h>a[l]){if (sr) return f[l][r][sl][sr]=std::min(h,a[l+1]-a[l]);else return f[l][r][sl][sr]=std::min(h,std::max(0LL,a[l+1]-a[l]-h));}elseif (sr==0&&a[r+1]-h<a[r]){if (sl==0) return f[l][r][sl][sr]=std::min(h,a[l]-a[l-1]);else return f[l][r][sl][sr]=std::min(h,std::max(0LL,a[l]-a[l-1]-h));}double ans=0;if (sl)ans+=p*std::min(h,std::max(0LL,a[l]-a[l-1]-h));elseans+=p*std::min(h,a[l]-a[l-1]);if (sr==0)ans+=(1.0-p)*std::min(h,std::max(0LL,a[l+1]-a[l]-h));elseans+=(1.0-p)*std::min(h,a[l+1]-a[l]);return f[l][r][sl][sr]=ans;}if (sl==1&&a[l-1]+h>a[l]) return f[l][r][sl][sr]=dp(l+1,r,1,sr)+std::min(h,a[l+1]-a[l]);elseif (sr==0&&a[r+1]-h<a[r])return f[l][r][sl][sr]=dp(l,r-1,sl,0)+std::min(h,a[r]-a[r-1]);double ans=0;ans+=0.5*(1-p)*(dp(l+1,r,1,sr)+std::min(h,a[l+1]-a[l]));ans+=0.5*(p)*(dp(l,r-1,sl,0)+std::min(a[r]-a[r-1],h));if (sl==1)ans+=0.5*p*(dp(l+1,r,0,sr)+std::min(h,std::max(0LL,a[l]-a[l-1]-h)));else ans+=0.5*(p)*(dp(l+1,r,0,sr)+std::min(h,a[l]-a[l-1]));if (sr==0)ans+=0.5*(1-p)*(dp(l,r-1,sl,1)+std::min(h,std::max(0LL,a[r+1]-a[r]-h)));else ans+=0.5*(1-p)*(dp(l,r-1,sl,1)+std::min(h,a[r+1]-a[r])); return f[l][r][sl][sr]=ans;
}
int main(){n=read();h=read();scanf("%lf",&p);for (int i=1;i<=n;i++) a[i]=read();std::sort(a+1,a+1+n);a[0]=a[1]-1e10;a[n+1]=a[n]+1e10;printf("%.9f\n",dp(1,n,0,1));
}