#include #define rep(i,a,b) for(int i=a;i=b;i--) #define fore(i,a) for(auto &i:a) #pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } //--------------------------------------------------------------------------------------------------- template int gaussianElimination(vector> &A, int var = -1) { int N = A.size(), M = A[0].size(); if (var < 0) { var = N; assert(N <= M); } int k = 0, rank = var; rep(i, 0, var) { int v = -1; for (int j = k; j < N && v == -1; j++) if (A[j][i] != 0) v = j; if (v == -1) { rank--; continue; } //a[i] = k; swap(A[k], A[v]); T x = T(1) / A[k][i]; rep(j, 0, M) A[k][j] = A[k][j] * x; rep(j, 0, N) if(j != k) { T y = A[j][i]; for (int h = M - 1; h >= i; h--) A[j][h] = A[j][h] - A[k][h] * y; } k++; } return rank; } template void print(vector> &A) { int N = A.size(), M = A[0].size(); rep(y, 0, N) { rep(x, 0, M) cout << A[y][x] << "\t"; cout << endl; }cout << endl;} template struct ModInt { static const int Mod = MOD; unsigned x; ModInt() : x(0) { } ModInt(signed sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; } ModInt(signed long long sig) { x = sig < 0 ? sig % MOD + MOD : sig % MOD; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if ((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if ((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { long long a = x, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } return ModInt(u); } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; template ostream& operator<<(ostream& st, const ModInt a) { st << a.get(); return st; }; template ModInt operator^(ModInt a, unsigned long long k) { ModInt r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r; } typedef ModInt<5> mint; typedef ModInt<1000000007> mint2; /*---------------------------------------------------------------------------------------------------             ∧_∧       ∧_∧  (´<_` )  Welcome to My Coding Space!      ( ´_ゝ`) /  ⌒i     /   \    | |     /   / ̄ ̄ ̄ ̄/  |   __(__ニつ/  _/ .| .|____      \/____/ (u ⊃ ---------------------------------------------------------------------------------------------------*/ int K; //--------------------------------------------------------------------------------------------------- void _main() { cin >> K; vector> A(K, vector(K + 1, 0)); rep(i, 0, K) { rep(j, 1, 7) { int next = (i + j > K) ? 0 : i + j; A[i][K] -= 1.0 / 6; if (i + j != K) A[i][next] += 1.0 / 6; } A[i][i] -= 1; } //print(A); gaussianElimination(A); //print(A); double ans = A[0][K]; printf("%.10f\n", ans); }