# include <iostream>
# include <algorithm>
# include <vector>
# include <string>
# include <set>
# include <map>
# include <cmath>
# include <iomanip>
# include <functional>
# include <utility>
# include <stack>
# include <queue>
# include <list>
# include <bitset>
# include <complex>
#include<limits.h>
#include<unordered_map>
#include<unordered_set>
#include<deque>
#include<cstdio>
using namespace std;
typedef long long int ll;
const int N = 1000000;
const int mod = 1000000007;
const int INF = 1 << 30;
#define rep(i,n) for(int i=(ll)0;i<(ll)n;++i)
#define ALL(x) x.begin(),x.end()
#define pp pair<ll,ll>
#define fi first
#define se second
ll ppow(ll x, ll n) {
	ll ans = 1;
	while (n > 0) {
		if ((n & 1) == 1)ans = ans + x;
		x = x * x;
		n >>= 1;
		ans %= mod;
	}
	return ans;
}
string YN(bool b) { return(b ? "YES" : "NO"); }
string yn(bool b) { return(b ? "Yes" : "No"); }
ll n;
double v[2000], dp[2000][11];
int main() {
	cin >> n;
	cout  <<(1<< n) << endl;
	rep(i, 1 << n)cin >> v[i];
	rep(i, 1 << n)dp[i][0] = pow(v[i / 2 * 2 + i % 2],2) / (pow(v[i / 2 * 2],2) + pow(v[i / 2 * 2 + 1],2));
	for (int j = 1; j < n; ++j) {//j:回戦
		rep(i, 1 << n) {//i:ひと
			int p;
			if (i % (1 << j + 1) < (1 << j)) {
				p = (i / (1 << j) + 1)*(1 << j);
				for (int k = p; k < p + (1 << j); ++k) {
					dp[i][j] += (dp[i][j - 1] * dp[k][j - 1] * pow(v[i], 2) / (pow(v[i], 2) + pow(v[k], 2)));
				}
			}
			else {
				p = p = (i / (1 << j) - 1)*(1 << j);
				for (int k = p; k < p + (1 << j); ++k) {
					dp[i][j] += (dp[i][j - 1] * dp[k][j - 1] * pow(v[i], 2) / (pow(v[i], 2) + pow(v[k], 2)));
				}
			}
		}
	}
	cout << fixed << setprecision(15) << dp[0][n-1] << endl;
	return 0;
}