#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; constexpr int INF = 1001001001; // constexpr int mod = 1000000007; constexpr int mod = 998244353; template inline bool chmax(T& x, T y){ if(x < y){ x = y; return true; } return false; } template inline bool chmin(T& x, T y){ if(x > y){ x = y; return true; } return false; } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int K; cin >> K; vector coeff(K + 1, -1), bias(K + 1, -1); auto func = [&](auto&& self, int x) -> pair { if(coeff[x] != -1) return {coeff[x], bias[x]}; if(x == K) return {coeff[x] = 0, bias[x] = 0}; double a = 0, b = 0; for(int i = 1; i <= 6; ++i){ if(x + i > K) a += 1.0 / 6; else{ auto [aa, bb] = self(self, x + i); a += aa / 6, b += bb / 6; } } b += 1; return {coeff[x] = a, bias[x] = b}; }; auto [a, b] = func(func, 0); double ans = b / (1 - a); cout << fixed << setprecision(10); cout << ans << endl; return 0; }