#include #include #include #include using namespace std; template struct Matrix { Matrix(const int n) : Matrix{n, n} {} Matrix(const int r, const int c) : R{r}, C{c}, table(r, vector(c, static_cast(0))) {} vector& operator[](const int n) { return table[n]; } const vector& operator[](const int n) const { return table[n]; } Matrix& operator+=(const Matrix& mat) { assert(R == mat.R and C == mat.C); for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { table[i][j] += mat[i][j]; } } return *this; } Matrix& operator-=(const Matrix& mat) { assert(R == mat.R and C == mat.C); for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { table[i][j] -= mat[i][j]; } } return *this; } Matrix& operator*=(const T val) { for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { table[i][j] *= val; } } return *this; } Matrix& operator/=(const T val) { assert(val != 0); for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { table[i][j] /= val; } } return *this; } Matrix operator-() const { Matrix result(R, C); for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { result[i][j] = -table[i][j]; } } return result; } Matrix operator+(const Matrix& mat) { assert(R == mat.R and C == mat.C); Matrix result(R, C); for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { result[i][j] = table[i][j] + mat[i][j]; } } return result; } Matrix operator-(const Matrix& mat) { assert(R == mat.R and C == mat.C); Matrix result(R, C); for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { result.table[i][j] = table[i][j] - mat.table[i][j]; } } return result; } Matrix operator*(const T val) { Matrix result(R, C); for (int i = 0; i < R; i++) { for (int j = 0; j < C; j++) { result[i][j] = table[i][j] * val; } } return result; } Matrix operator*(const Matrix& mat) { assert(C == mat.R); Matrix result(R, mat.C); for (int i = 0; i < R; i++) { for (int j = 0; j < mat.C; j++) { T sum = 0; for (int k = 0; k < C; k++) { sum += table[i][k] * mat[k][j]; } result[i][j] = sum; } } return result; } Matrix transposed() const { Matrix result(C, R); for (int i = 0; i < C; i++) { for (int j = 0; j < R; j++) { result[i][j] = table[j][i]; } } return result; } Matrix& transpose() { if (R == C) { for (int i = 0; i < R; i++) { for (int j = i + 1; j < R; j++) { swap(table[i][j], table[j][i]); } } return *this; } else { return *this = transposed(); } } int R; int C; vector> table; }; template inline Matrix operator*(const T val, const Matrix& mat) { Matrix result(mat.R, mat.C); for (int i = 0; i < mat.R; i++) { for (int j = 0; j < mat.C; j++) { result[i][j] = val * mat[i][j]; } } return result; } template inline ostream& operator<<(ostream& os, const Matrix& mat) { os << "Mat<" << mat.R << "," << mat.C << ">" << endl; for (int i = 0; i < mat.R; i++) { os << "["; for (int j = 0; j < mat.C; j++) { os << mat[i][j] << ","; } os << "]" << endl; } return os; } // 縦ベクトル template struct Vector { Vector(const int n) : R(n), table(n, 0){}; T& operator[](const int n) { return table[n]; } const T& operator[](const int n) const { return table[n]; } Vector& operator+=(const Vector& v) { assert(R == v.R); for (int i = 0; i < R; i++) { table[i] += v[i]; } return *this; } Vector& operator-=(const Vector& v) { assert(R == v.R); for (int i = 0; i < R; i++) { table[i] -= v[i]; } return *this; } Vector& operator*=(const T& s) { for (int i = 0; i < R; i++) { table[i] *= s; } return *this; } Vector& operator/=(const T& s) { assert(s != 0.0); for (int i = 0; i < R; i++) { table[i] /= s; } return *this; } Vector operator+(const Vector& v) const { assert(R == v.R); Vector result(R); for (int i = 0; i < R; i++) { result[i] = table[i] + v[i]; } return result; } Vector operator-(const Vector& v) const { assert(R == v.R); Vector result(R); for (int i = 0; i < R; i++) { result[i] = table[i] - v[i]; } return result; } Vector operator*(const T& s) const { Vector result(R); for (int i = 0; i < R; i++) { result[i] = table[i] * s; } return result; } Vector operator/(const T& s) const { assert(s != 0.0); Vector result(R); for (int i = 0; i < R; i++) { result[i] = table[i] / s; } return result; } Vector operator-() const { Vector result(R); for (int i = 0; i < R; i++) { result[i] = -table[i]; } return result; } int R; vector table; }; template inline Vector operator*(const T& s, const Vector& v) { Vector result(v.R); for (int i = 0; i < v.R; i++) { result[i] = s * v[i]; } return result; } template inline Vector operator*(const Matrix& mat, const Vector& v) { assert(mat.C == v.R); Vector result(mat.R); for (int i = 0; i < v.R; i++) { for (int j = 0; j < mat.R; j++) { result[i] += mat[i][j] * v[j]; } } return result; } template inline ostream& operator<<(ostream& os, const Vector& v) { os << "Vec<" << v.R << ">" << endl; os << "["; for (int i = 0; i < v.R; i++) { os << v[i] << ","; } os << "]^T" << endl; return os; } template Vector GaussJordan(const Matrix& mat, const Vector& v) { assert(mat.R == mat.C); const int N = mat.R; Matrix A(N, N + 1); for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { A[i][j] = mat[i][j]; } } for (int i = 0; i < N; i++) { A[i][N] = v[i]; } for (int i = 0; i < N; i++) { int pivot = i; for (int j = i; j < N; j++) { if (abs(A[j][i]) > abs(A[pivot][i])) { pivot = j; } } assert(A[pivot][i]); swap(A[i], A[pivot]); for (int j = i + 1; j <= N; j++) { A[i][j] /= A[i][i]; } for (int j = 0; j < N; j++) { if (i != j) { for (int k = i + 1; k <= N; k++) { A[j][k] -= A[j][i] * A[i][k]; } } } } Vector res(N); for (int i = 0; i < N; i++) { res[i] = A[i][N]; } return res; } using ld = long double; int main() { int K; cin >> K; Matrix mat(K + 1, K + 1); for (int i = 0; i < K; i++) { mat[i][i] = 6; for (int j = 1; j <= 6; j++) { mat[i][(i + j <= K ? i + j : 0)]--; } } mat[K][K] = 1; Vector vec(K + 1); for (int i = 0; i < K; i++) { vec[i] = 6; } vec[K] = 0; cout << fixed << setprecision(15) << GaussJordan(mat, vec)[0] << endl; return 0; }