#include <bits/stdc++.h>
#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define FORR(i,a,b) for (int i=(a);i>=(b);i--)
#define pb push_back
#define pcnt __builtin_popcount
#define show(x) cout<<#x<<" = "<<x<<endl;
#define maxs(x,y) x = max(x,y)
#define mins(x,y) x = min(x,y)
#define fi first
#define se second
#define rng(a) a.begin(),a.end()
#define each(it,c) for(__typeof((c).begin()) it=(c).begin();it!=(c).end();it++)
#define sz(x) (int)(x).size()

using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<pii> vpii;
typedef set<int> si;
typedef pair<ll,ll> pll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<pll> vpll;
typedef set<ll> sl;
template<typename T>string join(vector<T>&v)
{stringstream s;FOR(i,0,sz(v))s<<' '<<v[i];return s.str().substr(1);}
ll gcd(ll a,ll b){if(a>b)swap(a,b);for(;a>0;b%=a,swap(a,b));return b;}
int modpow(ll a,ll n,int m){if(a==0)return a;ll p=1;for(;n>0;n/=2,a=a*a%m)if(n&1)p=p*a%m;return(int)p;}
void dout(double d){printf("%.12f\n",d);}

const int iinf = 1e9;
const ll linf = 1e18;
const int mod = 1e9+7;
const double eps = 1e-10;

int m, s[1024], pm;
double w[1024][1024];
double dp[1024], dpn[1024];
main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> m;
  pm = 1<<m;
  FOR(i, 0, pm){
    cin >> s[i];
  }
  FOR(i, 0, pm)FOR(j, 0, pm) w[i][j] = 1.0 * s[i]*s[i] / (s[i]*s[i] + s[j]*s[j]);
  FOR(i, 0, pm) dp[i] = 1.0;
  int id, iid;
  FOR(i, 1, m+1){
    FOR(j, 0, pm){
      double d = 0.0;
      id = (j>>i);
      FOR(k, 0, 1<<i){
        iid = id + k;
        if(iid == j)continue;
        d += dp[id] * w[j][iid];
      }
      dpn[j] = d * dp[j];
    }
    swap(dp, dpn);
  }
  dout(dp[0]);
}