/* #region Head */ #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define endl '\n' #define sqrt sqrtl #define floor floorl #define log2 log2l constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #define DEBUG_ #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; string yes = "Yes", no = "No"; // string yes = "YES", no = "NO"; void yn(bool p) { cout << (p ? yes : no) << endl; } /* #endregion */ /* #region Mat */ // 行列,==, !=, [] あたりは vector と一緒 template class Mat : public vc> { public: // using vc>::vector; ll h, w; // コンストラクタ Mat(const ll h, ll w) : vc>(h, vc(w, 0)), h(h), w(w) {} Mat(const Mat &mt) : vc>(mt), h(mt.h), w(mt.w) {} // 行列に別の行列を足す Mat &operator+=(const Mat &another) { assert(this->h == another.h && this->w == another.w); REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] += another[i][j]; return *this; } // 行列から別の行列を引く Mat &operator-=(const Mat &another) { assert(this->h == another.h && this->w == another.w); REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] -= another[i][j]; return *this; } // 行列に別の行列を右から掛ける Mat &operator*=(const Mat &another) { assert(w == another.h); Mat ret(this->h, another.w); REP(i, 0, this->h) REP(j, 0, another.w) REP(k, 0, this->w) ret[i][j] += (*this)[i][k] * another[k][j]; *this = ret; return *this; } // 行列に別の行列を足す Mat operator+(const Mat &another) const { Mat ret(*this); return ret += another; } // 行列から別の行列を引く Mat operator-(const Mat &another) const { Mat ret(*this); return ret -= another; } // 行列に別の行列を右から掛ける Mat operator*(const Mat &another) const { Mat ret(*this); return ret *= another; } // 行列の n 乗を計算する Mat pow(ll n) const { assert(this->h == this->w); Mat ret(this->h, this->w); Mat a(*this); REP(i, 0, this->h) ret[i][i] = 1; while (n) { if (n & 1) ret = a * ret; a = a * a, n >>= 1; } return ret; } template Mat assign(T... nums) { vc num_list = vc{nums...}; assert(SIZE(num_list) == this->h * this->w); REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num_list[this->w * i + j]; return *this; } void fill(Num num) { REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num; } }; /* #endregion */ // Problem void solve() { ll k; cin >> k; using mat = Mat; mat t(7, 7); REP(i, 0, 5) t[1 + i][i] = 1; t[0][6] = t[6][6] = 1; auto m = [&t](ll ii) -> mat { mat ret = t; REP(j, 0, ii) ret[0][j] = 1.0L / 6.0L; if (ii <= 4) ret[0][ii] = ((5.0L - ii) / 6.0L); return ret; }; mat coef(7, 7); REP(i, 0, 7) coef[i][i] = 1; ll ptr = k; while (ptr > 0) { ll idx = k - ptr; if (idx >= 6) { coef = m(6).pow(ptr) * coef; break; } coef = m(idx) * coef; // dump(idx, m(idx)); ptr--; } cout << (coef[0][6] / (1.0L - coef[0][0])) << endl; } // entry point int main() { solve(); return 0; }