#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=5e5+5,M=(1<<8)+5,K=1000+5,mod=998244353,Mod=mod-1;const db eps=1e-9;const int INF=1e9+7;mt19937 rnd(28382);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;
int n;
db p[N],dp[N];
using cp=complex<db>;
db slope(cp x,cp y){return (x.imag()-y.imag())*1.0/(x.real()-y.real());}
cp Q[N];int H,T;
void Solve(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%lf",&p[i]);
	dp[n]=n;H=1;T=0;
	for(int i=n-1;~i;i--){
		cp w=cp(p[i+1],p[i+1]*dp[i+1]);
		while(H<T&&slope(Q[T-1],Q[T])<slope(Q[T],w)) T--;
		Q[++T]=w;
		while(H<T&&slope(Q[H],Q[H+1])>i) H++;
		dp[i]=i-i*Q[H].real()+Q[H].imag();
		// for(int j=i+1;j<=n;j++) dp[i]=max(dp[i],(1-p[j])*i+p[j]*dp[j]);
	}
	printf("%.10lf\n",dp[0]);
}
int main(){
	int t=1;
	// scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}