#include <bits/stdc++.h>
using namespace std;
 
typedef long long int ll;
typedef long double ld;
typedef double db; 
typedef string str; 
typedef bool bl;

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<ld,ld> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<ld> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 
typedef vector<vector<ll>> vvl;
typedef vector<bl> vbl;

#define mp make_pair 
#define ff first
#define ss second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
///#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (ll i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (ll i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const ll mod = 1e9 + 7; // 998244353;
const int MX = 2e5+5; 
const ll inf = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 

template<class T> bool ckmin(T& a, const T& b) { 
	return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
	return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); } 

namespace input {
	template<class T> void re(complex<T>& x);
	template<class T1, class T2> void re(pair<T1,T2>& p);
	template<class T> void re(vector<T>& a);
	template<class T, size_t SZ> void re(array<T,SZ>& a);

	template<class T> void re(T& x) { cin >> x; }
	void re(double& x) { string t; re(t); x = stod(t); }
	void re(ld& x) { string t; re(t); x = stold(t); }
	template<class T, class... Ts> void re(T& t, Ts&... ts) { 
		re(t); re(ts...); 
	}

	template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = {a,b}; }
	template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
	template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
	template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}

using namespace input;

namespace output {
	void pr(int x) { cout << x; }
	void pr(long x) { cout << x; }
	void pr(ll x) { cout << x; }
	void pr(unsigned x) { cout << x; }
	void pr(unsigned long x) { cout << x; }
	void pr(unsigned long long x) { cout << x; }
	void pr(float x) { cout << x; }
	void pr(double x) { cout << x; }
	void pr(ld x) { cout << x; }
	void pr(char x) { cout << x; }
	void pr(const char* x) { cout << x; }
	void pr(const string& x) { cout << x; }
	void pr(bool x) { pr(x ? "true" : "false"); }
	template<class T> void pr(const complex<T>& x) { cout << x; }
	
	template<class T1, class T2> void pr(const pair<T1,T2>& x);
	template<class T> void pr(const T& x);
	
	template<class T, class... Ts> void pr(const T& t, const Ts&... ts) { 
		pr(t); pr(ts...); 
	}
	template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
		pr("{",x.f,", ",x.s,"}"); 
	}
	template<class T> void pr(const T& x) { 
		pr("{"); // const iterator needed for vector<bool>
		bool fst = 1; for (const auto& a: x) pr(!fst?", ":"",a), fst = 0; 
		pr("}");
	}
	
	void ps() { pr("\n"); } // print w/ spaces
	template<class T, class... Ts> void ps(const T& t, const Ts&... ts) { 
		pr(t); if (sizeof...(ts)) pr(" "); ps(ts...); 
	}
	
	void pc() { pr("]\n"); } // debug w/ commas
	template<class T, class... Ts> void pc(const T& t, const Ts&... ts) { 
		pr(t); if (sizeof...(ts)) pr(", "); pc(ts...); 
	}
	#define dbg(x...) pr("[",#x,"] = ["), pc(x);
}

using namespace output;

namespace io {
	void setIn(string s) { freopen(s.c_str(),"r",stdin); }
	void setOut(string s) { freopen(s.c_str(),"w",stdout); }
	void setIO(string s = "") {
		ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
		// cin.exceptions(cin.failbit); 
		// throws exception when do smth illegal
		// ex. try to read letter into int
		if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
	}
}

using namespace io;

mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

inline ll mul(ll a, ll b)
{
    return ((a%mod)*(b%mod))%mod;
}
inline ll add(ll a, ll b)
{
	a+= mod;
	b += mod;
	return (a%mod + b% mod) % mod;
}
ll binpow(ll x, ll y)
{
    ll z = 1;
    while(y)
    {
        if(y & 1) z = mul(z, x);
        x = mul(x, x);
        y >>= 1;
    }
    return z;
}

inline ll inv(ll x)
{
    return binpow(x, mod - 2);
}
inline ll divide(ll x, ll y)
{
    return mul(x, inv(y));
}
inline ll lcm(ll a, ll b)
{
	return (a * b)/(__gcd(a, b));
}
inline ll gcd(ll a , ll b)
{
	return __gcd(a, b);
}
/*
unique(all(vec)); will remove all duplicate elements from the vector
find_by_order() - Returns an iterator to the k-th largest element (counting from zero) 
order_of_key()  - The number of items in a set that are strictly smaller than our item 
*max_element (first_iterator, last_iterator) – To find the maximum element of a vector.
*min_element (first_iterator, last_iterator) – To find the minimum element of a vector.
accumulate(first_iterator, last_iterator, initial value of sum) – Does the summation of vector elements
count(first_iterator, last_iterator,x) – To count the occurrences of x in vector.
find(first_iterator, last_iterator, x) – Points to last address of vector ((name_of_vector).end()) if element is not present in vector.
binary_search(first_iterator, last_iterator, x) – Tests whether x exists in sorted vector or not.
lower_bound(first_iterator, last_iterator, x) – returns an iterator pointing to the first element in the range [first,last) which has a value not less than ‘x’.
upper_bound(first_iterator, last_iterator, x) – returns an iterator pointing to the first element in the range [first,last) which has a value greater than ‘x’.
arr.erase(position to be deleted) – This erases selected element in vector and shifts and resizes the vector elements accordingly.
arr.erase(unique(arr.begin(),arr.end()),arr.end()) – This erases the duplicate occurrences in sorted vector in a single line.
next_permutation(first_iterator, last_iterator) – This modified the vector to its next permutation.
prev_permutation(first_iterator, last_iterator) – This modified the vector to its previous permutation.
 */

int main()
{
	ll n;re(n);vector<long double> p(n);
	FOR(i, 0, n)cin>>p[i];
	// atleast ceil(n/2) should be heads
	vector<vector<long double>> dp(n + 1, vector<long double> (n + 1, 0.0));
	dp[0][0] = 1.0;
	//pr(dp,"\n");
	FOR(i, 1, n + 1)dp[i][0] = p[i - 1] * dp[i - 1][0];
	FOR(i, 1, n + 1)dp[0][i] = (1.0 - p[i - 1]) * dp[0][i - 1];
	///pr(dp, "\n");
	for(ll i = 1;i<n + 1;i++)
	{
		//cout<<"i -===== "<<i<<endl;
		//cout<<"coming\n";
		for(ll j = 1;i + j<n + 1;j++)
		{
			//cout<<"j == "<<j<<endl;
			//cout<<",,,,,\n";
			dp[i][j] = p[i + j - 1] * dp[i - 1][j] + (1.0 - p[i + j - 1]) * dp[i][j - 1];
			//cout<<"ch\n";
		}
		//cout<<"na\n";
	} 
	///cout<<"sab thik hai\n";
	//trav(t, dp)pr(t, "\n");
	long double ans = 0;
	for(ll i = n;i >= (ll)ceil(n/2.0);i--)
	{
		ans += dp[i][n - i];
	}
	cout<<setprecision(15)<<ans<<endl;
}

Measured memory_bytes: 141056