Problem: Andrey needs one more problem to conduct a programming contest. He has n friends who are always willing to help. He can ask some of them to come up with a contest problem. Andrey knows one value for each of his fiends — the probability that this friend will come up with a problem if Andrey asks him.

Help Andrey choose people to ask. As he needs only one problem, Andrey is going to be really upset if no one comes up with a problem or if he gets more than one problem from his friends. You need to choose such a set of people that maximizes the chances of Andrey not getting upset.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of Andrey's friends. The second line contains n real numbers pi (0.0 ≤ pi ≤ 1.0) — the probability that the i-th friend can come up with a problem. The probabilities are given with at most 6 digits after decimal point.

Output

Print a single real number — the probability that Andrey won't get upset at the optimal choice of friends. The answer will be considered valid if it differs from the correct one by at most 10 - 9.

Examples

Input

4
0.1 0.2 0.3 0.8


Output

0.800000000000


Input

2
0.1 0.2


Output

0.260000000000

Note

In the first sample the best strategy for Andrey is to ask only one of his friends, the most reliable one.

In the second sample the best strategy for Andrey is to ask all of his friends to come up with a problem. Then the probability that he will get exactly one problem is 0.1·0.8 + 0.9·0.2 = 0.26.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
bool deb_mode = 0;
class debugger {
  vector<string> vars;

 public:
  template <typename T>
  debugger &operator,(const T v) {
    stringstream ss;
    ss << v, vars.push_back(ss.str());
    return *this;
  }
  void printall() {
    int j = 0, l = vars.size();
    for (int i = 0; i < (l - 1); i++) {
      if (i) cout << ", ";
      for (j; j < vars[l - 1].size(); j++) {
        if (vars[l - 1][j] == ',') {
          j++;
          break;
        }
        cout << vars[l - 1][j];
      }
      cout << " = " << vars[i];
    }
    vars.clear();
  }
} Dbug;
template <typename T1, typename T2>
inline ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  return os << "(" << p.first << "," << p.second << ")";
}
template <typename T>
inline ostream &operator<<(ostream &os, const vector<T> &v) {
  bool first = true;
  os << "{";
  for (unsigned int i = 0; i < v.size(); i++) {
    if (!first) os << ",";
    os << v[i];
    first = false;
  }
  return os << "}";
}
template <typename T>
inline ostream &operator<<(ostream &os, const set<T> &v) {
  bool first = true;
  os << "{";
  for (typename set<T>::const_iterator ii = v.begin(); ii != v.end(); ++ii) {
    if (!first) os << ",";
    os << *ii;
    first = false;
  }
  return os << "}";
}
template <typename T1, typename T2>
inline ostream &operator<<(ostream &os, const map<T1, T2> &v) {
  bool first = true;
  os << "{";
  for (typename map<T1, T2>::const_iterator ii = v.begin(); ii != v.end();
       ++ii) {
    if (!first) os << ",";
    os << *ii;
    first = false;
  }
  return os << "}";
}
template <typename T>
void getarray(T a[], int b, int e) {
  for (int i = b; i < e + b; i++) cin >> a[i];
}
template <typename T>
void printarray(T a[], int b, int e) {
  for (int i = b; i < e - 1 + b; i++) cout << a[i] << " ";
  if (e - 1 + b >= 0) cout << a[e - 1 + b] << endl;
}
template <typename T>
void printV(vector<T> v) {
  int sz = v.size();
  if (sz) cout << v[0];
  for (int i = 1; i < sz; i++) cout << " " << v[i];
  puts("");
}
template <typename T>
T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <typename T>
T BigMod(T b, T p, T m) {
  if (p == 0) return 1;
  if (p % 2 == 0) {
    T s = BigMod(b, p / 2, m);
    return ((s % m) * (s % m)) % m;
  }
  return ((b % m) * (BigMod(b, p - 1, m) % m)) % m;
}
template <typename T>
T ModInv(T b, T m) {
  return BigMod(b, m - 2, m);
}
template <class T>
inline void read(T &x) {
  bool Minus = 0;
  char c;
  for (c = getchar(); c <= 32; c = getchar())
    ;
  if (c == '-') Minus = 1, c = getchar();
  for (x = 0; c > 32; c = getchar()) x = x * 10 + c - '0';
  if (Minus) x = -x;
}
char getc() {
  char c;
  for (c = getchar(); c <= 32; c = getchar())
    ;
  return c;
}
int CI(int &_x) { return scanf("%d", &_x); }
int CI(int &_x, int &_y) { return scanf("%d %d", &_x, &_y); }
int CI(int &_x, int &_y, int &_z) { return scanf("%d %d %d", &_x, &_y, &_z); }
int CI(int &_a, int &_b, int &_c, int &_d) {
  return scanf("%d %d %d %d", &_a, &_b, &_c, &_d);
}
template <class T>
string toString(T n) {
  ostringstream oss;
  oss << n;
  return oss.str();
}
int toInt(string s) {
  int r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
long long int toLong(string s) {
  long long int r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
bool isVowel(char ch) {
  ch = tolower(ch);
  if (ch == 'a' || ch == 'e' || ch == 'i' || ch == 'o' || ch == 'u')
    return true;
  return false;
}
bool isUpper(char c) { return c >= 'A' && c <= 'Z'; }
bool isLower(char c) { return c >= 'a' && c <= 'z'; }
int dr8[8] = {+1, -1, +0, +0, +1, -1, -1, +1};
int dc8[8] = {+0, +0, -1, +1, +1, +1, -1, -1};
int dr4[4] = {+0, +0, +1, -1};
int dc4[4] = {-1, +1, +0, +0};
int kn8r[8] = {+1, +2, +2, +1, -1, -2, -2, -1};
int kn8c[8] = {+2, +1, -1, -2, -2, -1, +1, +2};
const double EPS = 1e-9;
const int INF = (1 << 30) - 1;
const long long int LINF = (1ll << 62) - 1;
const int mod = (int)1e9 + 7;
const int MAX = (int)1e5;
int main() {
  if (deb_mode) srand(int(time(NULL)));
  int i, j, k, l, n, m, q, a, b, c;
  double probability[110];
  cin >> n;
  for (i = 0; i < n; i++) cin >> probability[i];
  sort(probability, probability + n);
  reverse(probability, probability + n);
  double ans = 0;
  for (i = 1; i <= n; i++) {
    double pr = 0;
    for (j = 0; j < i; j++) {
      double curr = 1;
      for (k = 0; k < i; k++)
        curr *= (j == k) ? probability[k] : 1 - probability[k];
      pr += curr;
    }
    ans = max(ans, pr);
  }
  cout << fixed << setprecision(10) << ans << "\n";
  if (deb_mode) cerr << "TIME = " << clock() << " ms" << endl;
  return 0;
}