#pragma GCC optimize("Ofast") #include #include #include using namespace std; using namespace __gnu_pbds; using ll = long long; using u64 = uint_fast64_t; using pii = pair; using pll = pair; #define rep(i, n) for(int i = 0; i < (n); ++i) #define all(x) (x).begin(),(x).end() constexpr char ln = '\n'; constexpr long long MOD = 1000000007; //constexpr long long MOD = 998244353; template inline bool chmax(T1 &a, T2 b) { if (a < b) { a = b; return true;} return false; } template inline bool chmin(T1 &a, T2 b) { if (a > b) { a = b; return true;} return false; } inline int popcount(int x) {return __builtin_popcount(x);} inline int popcount(long long x) {return __builtin_popcountll(x);} void print() { cout << "\n"; } template void print(const T &x, const Args &... args) { cout << x << " "; print(args...); } /////////////////////////////////////////////////////////////////////////////////////////////////////////////// template struct ModInt { using u64 = uint_fast64_t; u64 a; constexpr ModInt(const long long x = 0) noexcept : a(x >= 0 ? x % Modulus : (Modulus - (-x) % Modulus) % Modulus) {} constexpr u64 &value() noexcept {return a;} constexpr const u64 &value() const noexcept {return a;} constexpr ModInt operator+(const ModInt rhs) const noexcept {return ModInt(*this) += rhs;} constexpr ModInt operator-(const ModInt rhs) const noexcept {return ModInt(*this) -= rhs;} constexpr ModInt operator*(const ModInt rhs) const noexcept {return ModInt(*this) *= rhs;} constexpr ModInt operator/(const ModInt rhs) const noexcept {return ModInt(*this) /= rhs;} constexpr ModInt operator^(const long long rhs) const noexcept {return ModInt(*this) ^= rhs;} constexpr bool operator==(const ModInt &rhs) const noexcept {return a == rhs.a;} constexpr bool operator!=(const ModInt &rhs) const noexcept {return a != rhs.a;} constexpr ModInt &operator+=(const ModInt rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr ModInt &operator-=(const ModInt rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr ModInt &operator*=(const ModInt rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr ModInt &operator/=(ModInt rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp&1) *this *= rhs; exp >>= 1; rhs *= rhs; } return *this; } constexpr ModInt &operator^=(long long exp) noexcept { ModInt rhs = a; a = 1; while (exp) { if (exp&1) *this *= rhs; exp >>= 1; rhs *= rhs; } return *this; } friend ostream &operator<<(ostream& os, const ModInt& rhs) noexcept {return os << rhs.a;} friend istream &operator>>(istream& is, ModInt& rhs) noexcept {long long a; is >> a; rhs = a; return is;} }; using mint = ModInt; template struct Matrix { array, sz> A; int N; Matrix() : N(sz) {} Matrix(int N) : N(N) {} inline const array &operator[](int k) const {return A[k];} inline array &operator[](int k) {return A[k];} static Matrix I(int N) { Matrix mat(N); for(int i = 0; i < N; ++i) mat[i][i] = 1; return mat; } Matrix &operator+=(const Matrix &B) noexcept { for(int i = 0; i < N; ++i) { for(int j = 0; j < N; ++j) { (*this)[i][j] += B[i][j]; } } return *this; } Matrix &operator-=(const Matrix &B) noexcept { for(int i = 0; i < N; ++i) { for(int j = 0; j < N; ++j) { (*this)[i][j] -= B[i][j]; } } return *this; } Matrix &operator*=(const Matrix &B) noexcept { Matrix C(N); for(int i = 0; i < N; ++i) { for(int k = 0; k < N; ++k) { for(int j = 0; j < N; ++j) { C[i][j] += (*this)[i][k] * B[k][j]; } } } for (int i = 0; i < N; ++i) { for (int j = 0; j < N; ++j) { swap(A[i][j],C.A[i][j]); } } return *this; } Matrix &operator^=(long long k) noexcept { Matrix B = Matrix::I(N); while(k) { if(k & 1) B *= *this; *this *= *this; k >>= 1; } for (int i = 0; i < N; ++i) { for (int j = 0; j < N; ++j) { swap(A[i][j],B.A[i][j]); } } return *this; } Matrix operator+(const Matrix &B) const noexcept {return (Matrix(*this) += B);} Matrix operator-(const Matrix &B) const noexcept {return (Matrix(*this) -= B);} Matrix operator*(const Matrix &B) const noexcept {return (Matrix(*this) *= B);} Matrix operator^(const long long k) const noexcept {return (Matrix(*this) ^= k);} }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); ll N; cin >> N; Matrix mat(6); mint b = mint(1)/6; rep(i,6) mat[0][i] = b; rep(i,5) mat[i+1][i] = 1; mat^= N; cout << mat[0][0] << ln; }