#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=(n)-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define pb push_back
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define vtpl(x,y,z) vector<tuple<x,y,z>>
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
const ll dy[9]={0,0,1,-1,1,1,-1,-1,0};
const ll dx[9]={1,-1,0,0,1,-1,1,-1,0};
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
using vd=vector<double>;
pair<vd,vd> mergev(vd x,vd y,vd l,vd r){
    vd ret1,ret2;
    ll n=x.size();
    rep(i,n){
        double ret=0;
        rep(j,n){
            ret+=l[i]*r[j]*x[i]*x[i]/(x[i]*x[i]+y[j]*y[j]);
        }
        ret2.pb(ret);
    }
    rep(i,n){
        double ret=0;
        rep(j,n){
            ret+=r[i]*l[j]*y[i]*y[i]/(y[i]*y[i]+x[j]*x[j]);
        }
        ret2.pb(ret);
    }
    ret1=x;rep(i,n)ret1.pb(y[i]);
    return {ret1,ret2};
}
int main(){
    ll m;cin >> m;
    queue<pair<vd,vd>> que;
    rep(i,1<<m){
        double s;cin >> s;
        vd z={s};vd zz={1};
        que.push({z,zz});
    }
    CST(10);
    while(true){
        auto lz=que.front();que.pop();
        if(que.empty())cout << lz.se[0] <<endl,exit(0);
        auto rz=que.front();que.pop();
        auto nz=mergev(lz.fi,rz.fi,lz.se,rz.se);
        que.push(nz);
    }
}