#include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define pi M_PI
#define R cin>>
#define Z class
#define ll long long
#define ln cout<<'\n'
#define in(a) insert(a)
#define pb(a) push_back(a)
#define pd(a) printf("%.10f\n",a)
#define mem(a) memset(a,0,sizeof(a))
#define all(c) (c).begin(),(c).end()
#define iter(c) __typeof((c).begin())
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;i--)
#define REP(i,m,n) for(int i=(int)(m);i<(int)(n);i++)
#define rep(i,n) REP(i,0,n)
#define tr(it,c) for(iter(c) it=(c).begin();it!=(c).end();it++)
template<Z A>void pr(A a){cout<<a;ln;}
template<Z A,Z B>void pr(A a,B b){cout<<a<<' ';pr(b);}
template<Z A,Z B,Z C>void pr(A a,B b,C c){cout<<a<<' ';pr(b,c);}
template<Z A,Z B,Z C,Z D>void pr(A a,B b,C c,D d){cout<<a<<' ';pr(b,c,d);}
template<Z A>void PR(A a,ll n){rep(i,n){if(i)cout<<' ';cout<<a[i];}ln;}
ll check(ll n,ll m,ll x,ll y){return x>=0&&x<n&&y>=0&&y<m;}
const ll MAX=1000000007,MAXL=1LL<<61,dx[4]={-1,0,1,0},dy[4]={0,1,0,-1};
typedef pair<int,int> P;

double dp[11][1111];

void Main() {
  int m;
  cin >> m;
  int n=1<<m;
  double a[n];
  rep(i,n) cin >> a[i];
  rep(i,n) dp[m][i]=1;
  ll k=1;
  rrep(i,m) {
    rep(j,n) {
      ll t=j/k;
      if(j/k%2) REP(l,(t-1)*k,t*k) dp[i][j]+=dp[i+1][j]*dp[i+1][l]*a[j]*a[j]/(a[j]*a[j]+a[l]*a[l]);
      else REP(l,(t+1)*k,(t+2)*k) dp[i][j]+=dp[i+1][j]*dp[i+1][l]*a[j]*a[j]/(a[j]*a[j]+a[l]*a[l]);
    }
    k*=2;
  }
  pd(dp[0][0]);
}

int main(){ios::sync_with_stdio(0);cin.tie(0);Main();return 0;}