#include using i64 = long long; using i64 = long long; template constexpr T power(T a, i64 b) { T res = 1; for (; b; b /= 2, a *= a) { if (b % 2) { res *= a; } } return res; } constexpr i64 mul(i64 a, i64 b, i64 p) { i64 res = a * b - i64(1.L * a * b / p) * p; res %= p; if (res < 0) { res += p; } return res; } template struct MLong { i64 x; constexpr MLong() : x{} {} constexpr MLong(i64 x) : x{norm(x % getMod())} {} static i64 Mod; constexpr static i64 getMod() { if (P > 0) { return P; } else { return Mod; } } constexpr static void setMod(i64 Mod_) { Mod = Mod_; } constexpr i64 norm(i64 x) const { if (x < 0) { x += getMod(); } if (x >= getMod()) { x -= getMod(); } return x; } constexpr i64 val() const { return x; } explicit constexpr operator i64() const { return x; } constexpr MLong operator-() const { MLong res; res.x = norm(getMod() - x); return res; } constexpr MLong inv() const { assert(x != 0); return power(*this, getMod() - 2); } constexpr MLong &operator*=(MLong rhs) &{ x = mul(x, rhs.x, getMod()); return *this; } constexpr MLong &operator+=(MLong rhs) &{ x = norm(x + rhs.x); return *this; } constexpr MLong &operator-=(MLong rhs) &{ x = norm(x - rhs.x); return *this; } constexpr MLong &operator/=(MLong rhs) &{ return *this *= rhs.inv(); } friend constexpr MLong operator*(MLong lhs, MLong rhs) { MLong res = lhs; res *= rhs; return res; } friend constexpr MLong operator+(MLong lhs, MLong rhs) { MLong res = lhs; res += rhs; return res; } friend constexpr MLong operator-(MLong lhs, MLong rhs) { MLong res = lhs; res -= rhs; return res; } friend constexpr MLong operator/(MLong lhs, MLong rhs) { MLong res = lhs; res /= rhs; return res; } friend constexpr std::istream &operator>>(std::istream &is, MLong &a) { i64 v; is >> v; a = MLong(v); return is; } friend constexpr std::ostream &operator<<(std::ostream &os, const MLong &a) { return os << a.val(); } friend constexpr bool operator==(MLong lhs, MLong rhs) { return lhs.val() == rhs.val(); } friend constexpr bool operator!=(MLong lhs, MLong rhs) { return lhs.val() != rhs.val(); } }; template<> i64 MLong<0LL>::Mod = i64(1E18) + 9; template struct MInt { int x; constexpr MInt() : x{} {} constexpr MInt(i64 x) : x{norm(x % getMod())} {} static int Mod; constexpr static int getMod() { if (P > 0) { return P; } else { return Mod; } } constexpr static void setMod(int Mod_) { Mod = Mod_; } constexpr int norm(int x) const { if (x < 0) { x += getMod(); } if (x >= getMod()) { x -= getMod(); } return x; } constexpr int val() const { return x; } explicit constexpr operator int() const { return x; } constexpr MInt operator-() const { MInt res; res.x = norm(getMod() - x); return res; } constexpr MInt inv() const { assert(x != 0); return power(*this, getMod() - 2); } constexpr MInt &operator*=(MInt rhs) &{ x = 1LL * x * rhs.x % getMod(); return *this; } constexpr MInt &operator+=(MInt rhs) &{ x = norm(x + rhs.x); return *this; } constexpr MInt &operator-=(MInt rhs) &{ x = norm(x - rhs.x); return *this; } constexpr MInt &operator/=(MInt rhs) &{ return *this *= rhs.inv(); } friend constexpr MInt operator*(MInt lhs, MInt rhs) { MInt res = lhs; res *= rhs; return res; } friend constexpr MInt operator+(MInt lhs, MInt rhs) { MInt res = lhs; res += rhs; return res; } friend constexpr MInt operator-(MInt lhs, MInt rhs) { MInt res = lhs; res -= rhs; return res; } friend constexpr MInt operator/(MInt lhs, MInt rhs) { MInt res = lhs; res /= rhs; return res; } friend constexpr std::istream &operator>>(std::istream &is, MInt &a) { i64 v; is >> v; a = MInt(v); return is; } friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) { return os << a.val(); } friend constexpr bool operator==(MInt lhs, MInt rhs) { return lhs.val() == rhs.val(); } friend constexpr bool operator!=(MInt lhs, MInt rhs) { return lhs.val() != rhs.val(); } }; template<> int MInt<0>::Mod = 998244353; template constexpr MInt

CInv = MInt

(V).inv(); constexpr int P = 1000000007; using Z = MInt

; using l64 = long double; void solve() { int k; std::cin >> k; //f[i] = p*(f[i+1]+1)+p*(f[i+2]+1)... ==> f[i] = 1 + sum/p f0/p*x std::vector f(k + 1), K(k + 1), b(k + 1); l64 p = 1.0 / 6; for (int i = k - 1; i >= 0; i--) { for (int j = i + 1, s = 1; s <= 6; s++, j++) { if (j <= k) { K[i] += p * K[j]; b[i] += p * b[j]; } else { K[i] += p; } } b[i] += 1; } //f0 = k0*f0+b0 l64 ans = b[0] / (1 - K[0]); std::cout << std::fixed << std::setprecision(10) << ans << "\n"; } signed main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int T = 1; //std::cin >> T; while (T--) solve(); return 0; }