#include // #include // using namespace atcoder; //using mint = modint1000000007; #include #include #include #define rep(i,n) for (int i = 0;i < (n); ++i) using namespace std; using ll = long long; using P = pair; #define chmax(x,y) x = max(x,y) using R=double; using ld = long double; int INF = 2*1e9; ll LINF = 1e18*9; int mod = 1000000007; int mod2 = 1; using graph = vector>; const double eps = 1e-10; template struct Matrix { vector > val; Matrix(int n, int m, T x = 0) : val(n, vector(m, x)) {} void init(int n, int m, T x = 0) {val.assign(n, vector(m, x));} size_t size() const {return val.size();} inline vector& operator [] (int i) {return val[i];} }; template int GaussJordan(Matrix &A,bool is_extended = false){ int n = A.size(), m = A[0].size(); int rank = 0; for(int col = 0;col < m;col++){ if(is_extended && col == m-1) break; int pivot = -1; T ma = eps; for(int row = rank;row < n;row++){ if(abs(A[row][col]) > ma){ ma = abs(A[row][col]); pivot = row; } } if(pivot == -1) continue; swap(A[pivot],A[rank]); auto fac = A[rank][col]; for(int col2 = 0;col2 < m;col2++) A[rank][col2] /= fac; for(int row = 0;row < n;row++){ if(row != rank && abs(A[row][col]) > eps){ auto fac = A[row][col]; for(int col2 = 0;col2 < m;col2++){ A[row][col2] -= A[rank][col2]*fac; } } } rank++; } return rank; } template vector LE(Matrix &A,vector &b){ int n = A.size(),m = A[0].size(); Matrix M(n,m+1); for(int i = 0;i < n;i++){ for(int j = 0;j < m;j++) M[i][j] = A[i][j]; M[i][m] = b[i]; } int rank = GaussJordan(M,true); vector res; for(int row = rank;row < n;row++) if(abs(M[row][m]) > eps) return res; res.assign(m,0); for(int i = 0;i < rank;i++) res[i] = M[i][m]; return res; } int main(){ int k;cin >> k; vector b(k,1); Matrix M(k,k); for(int i = k-1;i >= 0;i--){ M[i][i] = 1; for(int j = 1;j <= 6;j++){ if(i+j==k) continue; if(i+j < k) M[i][i+j] = -double(1)/6; else M[i][0] += -double(1)/6; } } // for(int i = 0;i < k;i++){ // for(int j = 0;j < k;j ++)cout << M[i][j] << " "; // cout << b[i] << endl; // } auto ans = LE(M,b); cout << ans[0] << endl; //for(int i = 0;i < k;i++) cout << ans[i] << endl; }