#pragma region template #pragma GCC optimize("Ofast") #include using namespace std; #ifdef __LOCAL #include #else #define debug(...) void(0) #endif using ll=long long; using ld=long double; using vi=vector; using vll=vector; using pi=pair; using pll=pair; #define overload2(a,b,c,...) c #define overload3(a,b,c,d,...) d #define overload4(a,b,c,d,e,...) e #define overload5(a,b,c,d,e,f,...) f #define TYPE1(T) template #define TYPE2(T,U) template #define TYPE(...) overload2(__VA_ARGS__,TYPE2,TYPE1)(__VA_ARGS__) #define TYPES1(T) template #define TYPES2(H,T) template #define TYPES(...) overload2(__VA_ARGS__,TYPES2,TYPES1)(__VA_ARGS__) #define REP4(i,s,n,d) for(int i=(s);i<(n);i+=(d)) #define REP3(i,s,n) REP4(i,s,n,1) #define REP2(i,n) REP3(i,0,n) #define REP1(n) REP2(tomato,n) #define REP(...) overload4(__VA_ARGS__,REP4,REP3,REP2,REP1)(__VA_ARGS__) #define RREP4(i,s,n,d) for(int i=(n)-1;i>=s;i-=d) #define RREP3(i,s,n) RREP4(i,s,n,1) #define RREP2(i,n) RREP3(i,0,n) #define RREP1(n) RREP2(tomato,n) #define RREP(...) overload4(__VA_ARGS__,RREP4,RREP3,RREP2,RREP1)(__VA_ARGS__) #define ALL(v) v.begin(),v.end() #define RALL(v) v.rbegin(),v.rend() #define SORT(v) sort(ALL(v)) #define RSORT(v) sort(RALL(v)) #define REVERSE(v) reverse(ALL(v)) #define UNIQUE(v) SORT(v),v.erase(unique(ALL(v)),v.end()) TYPES(T) void input(T&... a){ (cin>>...>>a); } #define DECLARE(T,...) T __VA_ARGS__;input(__VA_ARGS__); #define INT(...) DECLARE(int,__VA_ARGS__) #define STR(...) DECLARE(string,__VA_ARGS__) #define LL(...) DECLARE(long long,__VA_ARGS__) #define CHR(...) DECLARE(char,__VA_ARGS__) #define DBL(...) DECLARE(double,__VA_ARGS__) #define VI(n,v) vi v(n);cin>>v; #define VLL(n,v) vll v(n);cin>>v; TYPE(T) istream&operator>>(istream&is,vector&v){ for(auto&a:v)cin>>a; return is; } TYPE(T) ostream&operator<<(ostream&os,const vector&v){ if(&os==&cerr)os<<"["; REP(i,v.size()){ os<>(istream&is,pair&p){ cin>>p.first>>p.second; return is; } TYPE(T) using pq=priority_queue; TYPE(T) using pqg=priority_queue,greater>; TYPE(T) T pick(queue& que){assert(que.size()); T a=que.front();que.pop();return a;} TYPE(T) T pick(pq& que){assert(que.size()); T a=que.top();que.pop();return a;} TYPE(T) T pick(pqg& que){assert(que.size()); T a=que.top();que.pop();return a;} TYPE(T) T pick(stack& sta){assert(sta.size()); T a=sta.top();sta.pop();return a;} string YES(bool f=true){return (f?"YES":"NO");} string Yes(bool f=true){return (f?"Yes":"No");} string yes(bool f=true){return (f?"yes":"no");} constexpr int INF=1e9+7; constexpr ll LINF=ll(1e18)+7; constexpr ld EPS=1e-10; vi iota(int n){vi a(n);iota(ALL(a),0);return a;} TYPE(T) void fin(T a){cout<b&&(a=b,true));} TYPES(T,Ns) auto make_vector(T x,int n,Ns ...ns){ if constexpr(sizeof...(ns)==0)return vector(n,x); else return vector(n,make_vector(x,ns...)); } bool in(const ll S,const int a){return (S>>a)&1;} int popcount(const ll S){return __builtin_popcountll(S);} #pragma endregion template template struct r2{ T y,x; r2()=default; r2(T y,T x):y(y),x(x){} r2 operator+()const{ return *this; } r2 operator-()const{ return r2(-y,-x); } r2& operator++(){ y++;x++;return *this; } r2& operator--(){ y--;x--;return *this; } r2 operator++(int){ r2 a=*this; ++*this; return a; } r2 operator--(int){ r2 a=*this; --*this; return a; } r2& operator+=(const r2& v){ y+=v.y; x+=v.x; return *this; } r2& operator-=(const r2& v){ y-=v.y; x-=v.x; return *this; } r2& operator*=(const T& a){ y*=a; x*=a; return *this; } r2& operator/=(const T& a){ y/=a; x/=a; return *this; } friend r2 operator+(const r2& u,const r2& v){ return r2(u)+=v; } friend r2 operator-(const r2& u,const r2& v){ return r2(u)-=v; } friend r2 operator*(const r2&u,const T& a){ return r2(u)*=a; } friend r2 operator*(const T& a,const r2&u){ return r2(u)*=a; } friend r2 operator/(const r2&u,const T& a){ return r2(u)/=a; } bool operator<(const r2&v)const{ return y!=v.y ? y(const r2&v)const{ return y!=v.y ? y>v.y : x>v.x; } bool operator==(const r2&v)const{ return y==v.y and x==v.x; } bool operator!=(const r2&v)const{ return !(*this==v); } friend T dot(const r2&u,const r2& v){ return u.y*v.y + u.x*v.x; } T square_abs(){ return dot(*this,*this); } T abs(){ return sqrt(square_abs()); } friend istream&operator>>(istream&is,r2&v){ is>>v.x>>v.y; return is; } friend ostream&operator<<(ostream&os,const r2&v){ os<; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); INT(k); vector dp(k+1); dp[k]={0,0}; RREP(i,k){ R2 now(0,0); REP(j,1,7)now+=(i+j>k?R2(0,1):dp[i+j]); now/=6; now.y++; dp[i]=now; } ld ans=dp[0].y/(1.0-dp[0].x); cout<