import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	double[][] dp;
	double[][] p;

	double dp(int q, int k, int low, int high) {
		if (0 <= dp[q][k]) {
			return dp[q][k];
		}
		if (q == 0) {
			return 1.;
		}

		double res = 0;
		int mid = (low + high) / 2;
		for (int i = low; i < high; i++) {
			if (k < mid == i < mid) {
				continue;
			}
			if (k < mid) {
				res += dp(q - 1, k, low, mid) * dp(q - 1, i, mid, high) * p[k][i];
			} else {
				res += dp(q - 1, i, low, mid) * dp(q - 1, k, mid, high) * p[k][i];
			}
		}
		return dp[q][k] = res;
	}

	void run() {
		MyScanner sc = new MyScanner();

		int n = sc.nextInt();
		double[] a = new double[1 << n];
		for (int i = 0; i < 1 << n; i++) {
			a[i] = sc.nextInt();
		}
		p = new double[1 << n][1 << n];
		for (int i = 0; i < 1 << n; i++) {
			for (int j = 0; j < 1 << n; j++) {
				p[i][j] = (a[i] * a[i]) / (a[i] * a[i] + a[j] * a[j]);
			}
		}

		dp = new double[n + 1][1 << n];
		for (int i = 0; i < n + 1; i++) {
			Arrays.fill(dp[i], -1);
		}

		System.out.printf("%.7f\n", dp(n, 0, 0, 1 << n));
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");
		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}
		System.out.println("----------------------------" + '\n');
	}

	class MyScanner {
		int read() {
			try {
				return System.in.read();
			} catch (IOException e) {
				throw new InputMismatchException();
			}
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();
			return array;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();
			return array;
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();
			return array;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}