#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) #if defined(_MSC_VER) || __cplusplus > 199711L #define aut(r,v) auto r = (v) #else #define aut(r,v) __typeof(v) r = (v) #endif #define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it) #define all(o) (o).begin(), (o).end() #define pb(x) push_back(x) #define mp(x,y) make_pair((x),(y)) #define mset(m,v) memset(m,v,sizeof(m)) #define INF 0x3f3f3f3f #define INFL 0x3f3f3f3f3f3f3f3fLL using namespace std; typedef vector vi; typedef pair pii; typedef vector > vpii; typedef long long ll; template inline void amin(T &x, U y) { if(y < x) x = y; } template inline void amax(T &x, U y) { if(x < y) x = y; } int main() { int K; while(cin >> K) { const int X = 6; vector > dp(K + 2); dp[K + 1] = make_pair(1., 0.); for(int i = K - 1; i >= 0; -- i) { double c1 = 0, c0 = 0; rer(j, 1, 6) { auto p = dp[min(K + 1, i + j)]; c1 += p.first / 6; c0 += (1 + p.second) / 6; } dp[i] = make_pair(c1, c0); } //c1 * x + c0 = x //x = c0 / (1 - c1) double ans = dp[0].second / (1 - dp[0].first); printf("%.10f\n", ans); } return 0; }