#include <cstdint>
#include <iomanip>
#include <iostream>
#include <vector>

#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>

using boost::multiprecision::cpp_int;
using boost::multiprecision::cpp_dec_float_100;

static cpp_int factorial(int n) {
    cpp_int r = 1;
    for (int i = 2; i <= n; ++i) r *= i;
    return r;
}

int main() {
    constexpr int N = 52;

    std::vector<cpp_int> fact(N + 1);
    fact[0] = 1;
    for (int i = 1; i <= N; ++i) fact[i] = fact[i - 1] * i;

    auto comb = [&](int n, int k) -> cpp_int {
        if (k < 0 || k > n) return 0;
        return fact[n] / (fact[k] * fact[n - k]);
    };

    std::vector<cpp_int> f(N + 1);
    f[0] = 1;
    for (int b = 1; b <= N; ++b) {
        cpp_int fb = 0;
        for (int r = 0; r <= b - 1; ++r) {
            const cpp_int term = comb(b - 1, r) * fact[b - r];
            if (r & 1)
                fb -= term;
            else
                fb += term;
        }
        f[b] = fb;
    }

    std::vector<std::vector<cpp_dec_float_100>> P(N + 1);
    for (int m = 1; m <= N; ++m) {
        P[m].assign(m + 1, cpp_dec_float_100(0));
        const cpp_dec_float_100 denom = cpp_dec_float_100(fact[m]);
        for (int b = 1; b <= m; ++b) {
            const cpp_int cnt = comb(m - 1, b - 1) * f[b];
            P[m][b] = cpp_dec_float_100(cnt) / denom;
        }
    }

    std::vector<cpp_dec_float_100> E(N + 1);
    E[1] = 0;
    for (int m = 2; m <= N; ++m) {
        cpp_dec_float_100 num = 1;
        for (int b = 1; b < m; ++b) num += P[m][b] * E[b];
        E[m] = num / (cpp_dec_float_100(1) - P[m][m]);
    }

    auto S = [&](int n) -> cpp_dec_float_100 {
        cpp_dec_float_100 s = 0;
        for (int b = 1; b <= n; ++b) s += P[n][b] * E[b];
        return s;
    };

    {
        const auto s1 = S(1);
        if (s1 != 0) {
            std::cerr << "Validation failed: S(1)\n";
            return 1;
        }
        const auto s2 = S(2);
        if (s2 != 1) {
            std::cerr << "Validation failed: S(2)\n";
            return 1;
        }
        const auto s5 = S(5);
        const cpp_dec_float_100 target = cpp_dec_float_100(4213) / cpp_dec_float_100(871);
        if (abs(s5 - target) > cpp_dec_float_100("1e-60")) {
            std::cerr << "Validation failed: S(5)\n";
            return 1;
        }
    }

    const auto ans = S(52);
    std::cout << std::fixed << std::setprecision(8) << ans << "\n";
    return 0;
}