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

typedef long long ll;
typedef vector< int > vi;
typedef vector< vi > vvi;
typedef vector< ll > vl;
typedef vector< vl > vvl;
typedef pair< int, int > pii;
typedef vector< pii > vp;
typedef vector< double > vd;
typedef vector< vd > vvd;
typedef vector< string > vs;

template< class T1, class T2 >
int upmin( T1 &x, T2 v ){
  if( x > v ){
    x = v;
    return 1;
  }
  return 0;
}

template< class T1, class T2 >
int upmax( T1 &x, T2 v ){
  if( x < v ){
    x = v;
    return 1;
  }
  return 0;
}

const int INF = 0x3f3f3f3f;

int M;
vi S;

void init(){
  cin >> M;
  S = vi( 1 << M );
  for( int i = 0; i < 1 << M; ++i )
    cin >> S[ i ];
}

double dp[ 10 + 1 ][ ( 1 << 10 ) + 1 ];

double win( int i, int j ){
  return 1.0 * S[ i ] * S[ i ] / ( 1.0 * S[ i ] * S[ i ] + 1.0 * S[ j ] * S[ j ] );
}

void preprocess(){
  for( int i = 0; i < 1 << M; ++i )
    dp[ 0 ][ i ] = 1.0;
  for( int i = 0; i < M; ++i )
    for( int j = 0; j < 1 << M; j += 1 << i + 1 )
      for( int k = j; k < j + ( 1 << i ); ++k )
        for( int l = j + ( 1 << i ); l < j + ( 1 << i + 1 ); ++l )
          dp[ i + 1 ][ k ] += dp[ i ][ k ] * dp[ i ][ l ] * win( k, l ),
          dp[ i + 1 ][ l ] += dp[ i ][ l ] * dp[ i ][ k ] * win( l, k );
}

void solve(){
  cout << fixed << setprecision( 9 ) << dp[ M ][ 0 ] << endl;
}

signed main(){
  ios::sync_with_stdio( 0 );
  init();
  preprocess();
  solve();
  return 0;
}