/* -*- coding: utf-8 -*-
 *
 * 66.cc: No.66 輝け☆全国たこやき杯 - yukicoder
 */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<functional>
 
using namespace std;

/* constant */

const int MAX_M = 10;
const int MAX_N = 1 << MAX_M;

/* typedef */

/* global variables */

int s2s[MAX_N];
double dp[MAX_M + 1][MAX_N];

/* subroutines */

/* main */

int main() {
  int m;
  cin >> m;

  int n = 1 << m;
  for (int i = 0; i < n; i++) {
    cin >> s2s[i];
    s2s[i] *= s2s[i];
    dp[0][i] = 1.0;
  }

  for (int i = 1; i <= m; i++) {
    int l = 1 << i, b = l >> 1;
    for (int j = 0; j < n; j++) {
      int j0 = (j >> i) << i;
      if (((j >> (i - 1)) & 1) == 0) j0 |= b;
      //printf("i=%d, j=%d, j0=%d\n", i, j, j0);

      dp[i][j] = 0.0;
      for (int k = j0; k < j0 + b; k++)
	dp[i][j] += dp[i - 1][k] * s2s[j] / (s2s[j] + s2s[k]);
      dp[i][j] *= dp[i - 1][j];
    }

    //printf("%d:", i);
    //for (int j = 0; j < n; j++) printf(" %lf", dp[i][j]); putchar('\n');
  }

  printf("%.7lf\n", dp[m][0]);
  return 0;
}