#include #define rep(i,n) for(int i=0;i<(n);i++) using namespace std; template class matrix{ vector> a; public: matrix(int n):a(n,vector(n)){} matrix(int m,int n):a(m,vector(n)){} matrix& operator+=(const matrix& A){ assert(h()==A.h() && w()==A.w()); int m=h(),n=w(); rep(i,m) rep(j,n) (*this)[i][j]+=A[i][j]; return *this; } matrix& operator-=(const matrix& A){ assert(h()==A.h() && w()==A.w()); int m=h(),n=w(); rep(i,m) rep(j,n) (*this)[i][j]-=A[i][j]; return *this; } matrix& operator*=(const matrix& A){ assert(w()==A.h()); int m=h(),n=w(),l=A.w(); matrix B(m,l); rep(i,m) rep(j,l) rep(k,n) B[i][j]+=(*this)[i][k]*A[k][j]; swap(*this,B); return *this; } matrix operator+(const matrix& A)const{ return matrix(*this)+=A; } matrix operator-(const matrix& A)const{ return matrix(*this)-=A; } matrix operator*(const matrix& A)const{ return matrix(*this)*=A; } const vector& operator[](int i)const{ return a[i]; } vector& operator[](int i){ return a[i]; } vector operator*(const vector& v)const{ assert(w()==v.size()); int m=h(),n=w(); vector res(m); rep(i,m) rep(j,n) res[i]+=(*this)[i][j]*v[j]; return res; } int h()const{ return a.size(); } int w()const{ return a.empty()?0:a[0].size(); } static matrix identity(int n){ matrix I(n); rep(i,n) I[i][i]=R{1}; return I; } }; vector Gauss_Jordan(const matrix& A,const vector& b){ const double EPS=1e-8; assert(A.h()==A.w() && A.w()==b.size()); int n=A.h(); matrix B(n,n+1); rep(i,n){ rep(j,n) B[i][j]=A[i][j]; B[i][n]=b[i]; } rep(i,n){ int pivot=i; for(int j=i;jabs(B[pivot][i])) pivot=j; rep(j,n+1) swap(B[i][j],B[pivot][j]); assert(abs(B[i][i])>EPS); for(int j=i+1;j<=n;j++) B[i][j]/=B[i][i]; rep(j,n) if(i!=j) for(int k=i+1;k<=n;k++) B[j][k]-=B[j][i]*B[i][k]; } vector x(n); rep(i,n) x[i]=B[i][n]; return x; } int main(){ int n; scanf("%d",&n); matrix A(n); rep(i,n){ A[i][i]=1; for(int d=1;d<=6;d++){ if(i+dn) A[i][ 0 ]-=1.0/6; } } printf("%.9f\n",Gauss_Jordan(A,vector(n,1))[0]); return 0; }