Language: C++


/*
	@・ω・@
*/

// Memo:https://scrapbox.io/hitsujirere-memo/

/*****/

/**/
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
/**/

#include <bits/stdc++.h>

//#define int long long

using namespace std;
using ll = long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template <class T>
using vec = vector<T>;
template <class T>
using grapth = vec<vec<T>>;

#define rep(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define rep1(i, n) for (ll i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep1(i, n) for (ll i = (n); i > 0; --i)
#define step(i, a, n) for (ll i = (a), i##_len = (a) + (n); i < i##_len; ++i)
#define rstep(i, a, n) for (ll i = (a) + (n)-1, i##_len = (a); i >= i##_len; --i)
#define range(i, a, b) for (ll i = (a), i##_len = (b); i < i##_len; ++i)
#define rrange(i, a, b) for (ll i = (b)-1, i##_len = (a); i >= i##_len; --i)

constexpr int INF = numeric_limits<int>::max();
constexpr ll INFL = numeric_limits<ll>::max();

std::string strMulti(const char c, const int n)
{
	std::string out = "";
	for (int i = 0; i < n; i++)
	{
		out += c;
	}
	return out;
}
std::string strMulti(const std::string t, const int n)
{
	std::string out = "";
	for (int i = 0; i < n; i++)
	{
		out += t;
	}
	return out;
}
std::string tab(const int n)
{
	return strMulti('\t', n);
}
std::string join(const vector<string> &v, const char *delim = 0)
{
	std::string s;
	if (!v.empty())
	{
		s += v[0];
		for (decltype(v.size()) i = 1, c = v.size(); i < c; ++i)
		{
			if (delim)
				s += delim;
			s += v[i];
		}
	}
	return s;
}

string to_string(string s) { return '"' + s + '"'; }
string to_string(char c) { return string({'\'', c, '\''}); }
template <size_t N>
string to_string(bitset<N> bs)
{
	return bs.to_string();
}
template <class T1, class T2>
string to_string(pair<T1, T2> p)
{
	return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class Tuple, size_t... I>
string _to_string_tuple(Tuple &&t, std::index_sequence<I...>)
{
	vector<string> texts = {to_string(std::get<I>(t))...};
	return "(" + join(texts, ", ") + ")";
}
template <class... Args>
string to_string(tuple<Args...> t)
{
	using Tuple = tuple<Args...>;
	return _to_string_tuple(std::forward<Tuple>(t),
							std::make_index_sequence<std::tuple_size<std::decay_t<Tuple>>::value>{});
}
template <class T>
string to_string(vector<T> ar)
{
	vector<string> texts(ar.size());
	for (size_t i = 0; i < ar.size(); ++i)
	{
		texts[i] = to_string(ar[i]);
	}
	return "{" + join(texts, ", ") + "}";
}
template <class T>
string to_string(initializer_list<T> il)
{
	vector<string> texts(il.size());
	size_t i = 0;
	for (T v : il)
	{
		texts[i] = to_string(v);
		i++;
	}
	return "{" + join(texts, ", ") + "}";
}

#ifdef DEBUG_BUILD
#define debugvar(x) debugln(#x, (x))
#define debugvartab(x, t) debugln(tab(t) + #x, (x))
void debug(string name)
{
	std::cerr << name;
}
void debugln(string name)
{
	std::cerr << name << '\n';
}
template <class T>
void debug(string name, T v)
{
	std::cerr << name << " = " << to_string(v);
}
template <class T>
void debugln(string name, T v)
{
	std::cerr << name << " = " << to_string(v) << '\n';
}
template <class T>
void debug(string name, initializer_list<T> il)
{
	std::cerr << name << " = " << to_string(il);
}
template <class T>
void debugln(string name, initializer_list<T> il)
{
	std::cerr << name << " = " << to_string(il) << '\n';
}
template <class... Args>
void debug(string name, Args... args)
{
	std::cerr << name << " = " << to_string(tuple<Args...>(args...));
}
template <class... Args>
void debugln(string name, Args... args)
{
	std::cerr << name << " = " << to_string(tuple<Args...>(args...)) << '\n';
}
#else
#define debugvar(x)
#define debugvartab(x, t)
void debug(string name)
{
}
void debugln(string name) {}
template <class T>
void debug(string name, T v) {}
template <class T>
void debugln(string name, T v) {}
template <class T>
void debug(string name, initializer_list<T> il) {}
template <class T>
void debugln(string name, initializer_list<T> il) {}
template <class... Args>
void debug(string name, Args... args) {}
template <class... Args>
void debugln(string name, Args... args) {}
#endif

#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)

template <class T>
bool chmax(T &a, const T b)
{
	if (a < b)
	{
		a = b;
		return true;
	}
	return false;
}
template <class T>
bool chmin(T &a, const T b)
{
	if (a > b)
	{
		a = b;
		return true;
	}
	return false;
}
template <class T>
T divup(const T a, const T b)
{
	if (a % b == 0)
	{
		return a / b;
	}
	return a / b + 1;
}
template <class T>
bool cmp_2nd(pair<T, T> a, pair<T, T> b)
{
	if (a.second != b.second)
	{
		return a.second < b.second;
	}
	return a.first < b.first;
}
ll modpow(ll x, ll n, const ll &p)
{
	ll ret = 1;
	while (n > 0)
	{
		if (n & 1)
		{
			(ret *= x) %= p;
		}
		(x *= x) %= p;
		n >>= 1;
	}
	return ret;
}
template <class T>
T modinv(T a, const T &p)
{
	T b = p, u = 1, v = 0;
	while (b)
	{
		T t = a / b;
		a -= t * b;
		swap(a, b);
		u -= t * v;
		swap(u, v);
	}
	u %= p;
	if (u < 0)
	{
		u += p;
	}
	return u;
}
template <class T>
T math_P(T m, T n)
{
	T ret = 1;
	for (T i = m; i > m - n; i--)
	{
		ret *= i;
	}
	return ret;
}
template <class T>
T math_C(T m, T n)
{
	T ret = math_P(m, n);
	for (T i = 2; i <= n; i++)
	{
		ret /= i;
	}
	return ret;
}
ll extended_euclidean(ll u, ll v)
{
	ll r0 = u;
	ll r1 = v;
	ll s0 = 1;
	ll s1 = 0;
	ll t0 = 0;
	ll t1 = 1;
	while (r1 != 0)
	{
		ll q = r0 / r1;
		ll r = r0 - q * r1;
		ll s = s0 - q * s1;
		ll t = t0 - q * t1;
		r0 = r1;
		s0 = s1;
		t0 = t1;
		r1 = r;
		s1 = s;
		t1 = t;
	}
	if (t0 < 0)
	{
		return t0 + u;
	}
	else
	{
		return t0;
	}
}
ll math_C_mod(ll n, ll c, const ll &p)
{
	ll upe = 1;
	ll dow = 1;
	for (ll i = 1; i < c + 1; ++i)
	{
		upe = upe * n % p;
		dow = dow * i % p;
		n -= 1;
	}
	return (upe * extended_euclidean(p, dow)) % p;
}
template <class T>
T math_gcd(T a, T b)
{
	if (b == 0)
	{
		return a;
	}
	else
	{
		return math_gcd(b, a % b);
	}
}
template <class T>
T math_lcm(T a, T b) { return a / math_gcd(a, b) * b; }
template <class T>
T SumStep(T a, T n, T d) { return n * (2 * a + (n - 1) * d) / 2; }
template <class T>
T SumRange(T a, T b, T d) { return SumStep(a, (b - a) / d, d); }

constexpr ll MOD = 1000000007; // 10^9+7

/*****/

void Main()
{
	int N;
	cin >> N;
	vec<ld> P(N);
	rep(i, N) cin >> P[i];

	vec<vec<ld>> dp(N + 1, vec<ld>(N + 1));
	dp[0][0] = 1.0;
	rep(i, N)
	{
		rep(j, N)
		{
			dp[i + 1][j] += dp[i][j] * P[i];
			dp[i + 1][j + 1] += dp[i][j] * (1.0 - P[i]);
		}
	}

	debugvar(dp);

	ld ret = 0.0;
	rep(i, N / 2 + 1)
	{
		ret += dp[N][i];
	}

	cout << ret << endl;
}

/*****/

int main()
{
	std::ios::sync_with_stdio(false);
	std::cin.tie(0);

	std::cout << std::fixed << std::setprecision(10);

	Main();
	std::cerr << flush;
	std::cout << flush;

	return 0;
}


Compiler output:
In file included from /usr/include/c++/14/string:43,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52,
                 from a.cc:16:
/usr/include/c++/14/bits/allocator.h: In destructor 'std::__cxx11::basic_string<char>::_Alloc_hider::~_Alloc_hider()':
/usr/include/c++/14/bits/allocator.h:182:7: error: inlining failed in call to 'always_inline' 'std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = char]': target specific option mismatch
  182 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/14/string:54:
/usr/include/c++/14/bits/basic_string.h:186:14: note: called from here
  186 |       struct _Alloc_hider : allocator_type // TODO check __is_final
      |              ^~~~~~~~~~~~