// >>> TEMPLATES #include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define double ld #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define rep1(i,n) for (int i = 1; i <= (int)(n); i++) #define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = (int)(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x,l,r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define mp make_pair #define fst first #define snd second template <class Int> auto constexpr inf = numeric_limits<Int>::max()/2-1; auto constexpr INF32 = inf<int32_t>; auto constexpr INF64 = inf<int64_t>; auto constexpr INF = inf<int>; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } }; template <class T> using pque_max = pque<T, less<T>>; template <class T> using pque_min = pque<T, greater<T>>; template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template <class T, class S> ostream& operator<<(ostream& os, pair<T,S> const& p) { return os << "(" << p.first << ", " << p.second << ")"; } template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template <class F> struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward<F>(f)) {} template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); } }; struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template <class T, size_t d> struct vec_impl { using type = vector<typename vec_impl<T,d-1>::type>; template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); } }; template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } }; template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type; template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); } template <class T> void quit(T const& x) { cout << x << endl; exit(0); } template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); } template <class T> int sz(T const& x) { return x.size(); } template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } const int dx[] = { 1,0,-1,0 }; const int dy[] = { 0,1,0,-1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } // [a,b] template <class Int> Int rand(Int a, Int b) { static mt19937_64 mt{random_device{}()}; return uniform_int_distribution<Int>(a,b)(mt); } i64 irand(i64 a, i64 b) { return rand<i64>(a,b); } u64 urand(u64 a, u64 b) { return rand<u64>(a,b); } // <<< int32_t main() { int n; cin >> n; vector<int> a(n); cin >> a; vector<int> pow3(n+1); pow3[0] = 1; rep (i,n) pow3[i+1] = pow3[i]*3; auto kth = [&](int s, int k) { return s/pow3[k]%3; }; vector<int> calc(pow3[n]); vector<pair<ld,ld>> dp(pow3[n]); def (solve, int s) -> pair<ld,ld> { if (calc[s]) return dp[s]; calc[s] = true; auto &[p,q] = dp[s]; vector<int> rest; rep (i,n) if (kth(s,i) == 0) rest.eb(i); if (rest.empty()) { int sum[3] = {}; rep (i,n) sum[kth(s,i)] += a[i]; if (sum[1] > sum[2]) p = q = 1; else p = q = 0; return {p,q}; } p = q = 0; while (true) { // repR (k,300) { ld ma = 0, mi = 1; for (int i : rest) { ld r = ld(1)/a[i]; chmax(ma, r * solve(s+pow3[i]*1).snd + (1-r) * q); chmin(mi, r * solve(s+pow3[i]*2).fst + (1-r) * p); } const ld eps = 1e-9; if (abs(p-ma) < eps && abs(q-mi) < eps) { break; // if (k == 0) { // assert(abs(p-ma) < 1e-7); // assert(abs(q-mi) < 1e-7); } else { p = ma; q = mi; } } return {p,q}; }; auto [p,q] = solve(0); cout << p << endl; // dump(as_mat(dp)); }