atDPI.cpp

/*
 * Contest : AtCoder Educational DP Contest
 * Problem : I - Coins
 * Link    : https://atcoder.jp/contests/dp/tasks/dp_i
 */

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#define fastio ios::sync_with_stdio(0); cin.tie(0);

int main() {
  fastio

  int n; cin >> n;
  vector<double> p(n);
  for (int i = 0; i < n; ++i) cin >> p[i];

  vector<double> dp(n + 1); // prob de i heads
  dp[0] = 1;
  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j >= 0; --j) {
      dp[j] = dp[j] * (1 - p[i]);
      if (j) dp[j] += dp[j - 1] * p[i];
    }
  }
  double ans = 0;
  for (int heads = 0; heads <= n; ++heads) {
    int tails = n - heads;
    if (heads > tails) ans += dp[heads];
  }
  cout << fixed << setprecision(10) << ans << '\n';

  return 0;
}