import java.util.Locale;

public class Euler645 {

    static double integrandValue(int days, double x) {
        if (x <= 0.0)
            return 0.0;
        if (x >= 1.0)
            return 1.0;

        double disc = Math.sqrt((1.0 - x) * (1.0 + 3.0 * x));
        double lambda1 = (1.0 - x + disc) * 0.5;
        double lambda2 = (1.0 - x - disc) * 0.5;

        double oneMinusLambda1Pow = 1.0;
        if (lambda1 > 0.0) {
            double logTerm = days * Math.log(lambda1);
            if (logTerm > -1e-4) {
                oneMinusLambda1Pow = -Math.expm1(logTerm);
            } else {
                oneMinusLambda1Pow = 1.0 - Math.exp(logTerm);
            }
        }

        double lambda2Pow = Math.pow(lambda2, days);
        double numerator = oneMinusLambda1Pow - lambda2Pow;
        return numerator / x;
    }

    static double simpsonIntegral(int days, int intervals) {
        double h = 1.0 / intervals;
        double sum = integrandValue(days, 0.0) + integrandValue(days, 1.0);
        for (int i = 1; i < intervals; ++i) {
            double x = i * h;
            int weight = (i % 2 != 0) ? 4 : 2;
            sum += weight * integrandValue(days, x);
        }
        return days * h * sum / 3.0;
    }

    static double computeExpectation(int days, int initialIntervals, int maxIntervals, double relativeTol) {
        int intervals = initialIntervals;
        double previous = simpsonIntegral(days, intervals);

        while (intervals < maxIntervals) {
            intervals *= 2;
            double current = simpsonIntegral(days, intervals);
            double delta = Math.abs(current - previous);
            double scale = Math.max(1.0, Math.abs(current));
            if (delta <= relativeTol * scale) {
                return current;
            }
            previous = current;
        }
        return previous;
    }

    public static String solve() {
        double ans = computeExpectation(10000, 4096, 1048576, 1e-12);
        return String.format(Locale.US, "%.4f", ans);
    }

    public static void main(String[] args) {
        System.out.println(solve());
    }
}