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atcoder_dp_I.cpp
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atcoder_dp_I.cpp
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#include<bits/stdc++.h>
using namespace std;
#define vi vector<int>
#define vll vector<ll>
#define vpll vector<pair<ll ,ll>>
#define vvi vector<vector<int>>
#define vvll vector<vector<ll>>
#define map map<ll ,ll>
#define umap unordered_map<ll , ll>
#define endl "\n"
#define set set<ll>
#define setC set<char>
#define all(x) x.begin() , x.end()
#define fast ios::sync_with_stdio(0); cin.tie(0);
#define fastcout ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define testcases int tt = 1 ; cin >> tt ; for(int i = 1 ; i <= tt ; ++i)
#define codejam cout << "Case #"<<i <<": ";
#define FOR(i,a,n) for(int i = a ; i <= n ; ++i)
#define FORback(i,a,n) for(int i = n ; i >= a ; --i)
#define ll long long int
const ll INF = 1e13+7;
const ll mod = 1e9+7;
// double dp[3001][3001] ;
vector<vector<double>> dp;
double doSome(vector<double>&arr , int i , int curr ){
if( curr == 0){
return 1;
}
if(i < 0){
return 0;
}
if(dp[i][curr] > -.9) return dp[i][curr];
double x = arr[i] * doSome(arr , i-1 , curr-1);
double y = (1 - arr[i]) * doSome(arr , i-1 , curr);
return dp[i][curr] = x+y;
}
void solv(){
ll n;
cin >> n ;
vector<double> arr(n);
FOR(i , 0 , n-1){
cin >> arr[i];
arr[i] = arr[i] * 1.000000000;
}
dp.assign(n+1 , vector<double>(n+1 , -1));
ll target = (n+1)/2 ;
// FOR(i , 0 , n){
// FOR(j , 0 , n){
// cout << dp[i][j] << " ";
// }
// cout << endl;
// }
double ans = doSome(arr , n , target);
cout << setprecision(10) << ans << endl;
}
int main(){
fast ;
// testcases{
// codejam ;
solv();
// }
}