import java.util.*;

public class Euler930 {

    static double F(int n, int m) {
        double[][] binom = new double[m + 1][m + 1];
        for (int i = 0; i <= m; ++i) {
            binom[i][0] = 1.0;
            binom[i][i] = 1.0;
            for (int j = 1; j < i; ++j) {
                binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
            }
        }

        double twoPi = 2.0 * Math.PI;
        double[] cosine = new double[n];
        for (int r = 0; r < n; ++r) {
            cosine[r] = Math.cos(twoPi * r / n);
        }

        double[] total = new double[1];
        dfs(0, m, 0, 0, 0.0, 1.0, n, m, binom, cosine, total);
        return total[0];
    }

    static void dfs(int idx, int rem, int modSum, int countZero, double cosSum, double ways, int n, int m,
            double[][] binom, double[] cosine, double[] total) {
        if (idx == n - 1) {
            int x = rem;
            if ((modSum + idx * x) % n != 0)
                return;
            if (countZero == m)
                return;

            double finalCos = cosSum + x * cosine[idx];
            double denom = 1.0 - finalCos / m;
            if (denom > 0.0) {
                total[0] += ways / denom;
            }
            return;
        }

        for (int x = 0; x <= rem; ++x) {
            int nextCountZero = countZero;
            if (idx == 0) {
                nextCountZero = x;
            }
            dfs(idx + 1, rem - x, (modSum + idx * x) % n, nextCountZero,
                    cosSum + x * cosine[idx], ways * binom[rem][x], n, m, binom, cosine, total);
        }
    }

    static double G(int N, int M) {
        double total = 0.0;
        for (int n = 2; n <= N; ++n) {
            for (int m = 2; m <= M; ++m) {
                total += F(n, m);
            }
        }
        return total;
    }

    public static String solve() {
        double answer = G(12, 12);
        String s = String.format(Locale.US, "%.12e", answer);
        return s.replace("e+", "e");
    }

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