#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #define COLOR(s) ("\x1b[" s "m") //////////////////////////////////////////////////////////////////////////////// template struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 998244353; using Mint = ModInt; using Pair = pair; Pair operator+(const Pair &a, const Pair &b) { return make_pair(a.first + b.first, a.second + b.second); } Pair operator-(const Pair &a, const Pair &b) { return make_pair(a.first - b.first, a.second - b.second); } Pair operator*(const Pair &a, const Pair &b) { return make_pair(a.first * b.first, a.first * b.second + a.second * b.first); } Pair operator*(const Pair &a, Mint k) { return make_pair(a.first * k, a.second * k); } Pair operator*(Mint k, const Pair &a) { return make_pair(k * a.first, k * a.second); } Pair &operator+=(Pair &a, const Pair &b) { return a = a + b; } Pair &operator-=(Pair &a, const Pair &b) { return a = a - b; } Pair &operator*=(Pair &a, const Pair &b) { return a = a * b; } Pair &operator*=(Pair &a, Mint k) { return a = a * k; } constexpr Pair ZERO(0, 0); constexpr int U = 5; struct Mat { Pair a[U][U]; Mat() : a{} {} }; Mat operator*(const Mat &a, const Mat &b) { const int n = U; Mat c; for (int i = 0; i < n; ++i) for (int k = 0; k < n; ++k) for (int j = 0; j < n; ++j) { c.a[i][j] += a.a[i][k] * b.a[k][j]; } return c; } Mat A; Mat power(int e) { if (e == 0) { Mat ret; for (int u = 0; u < U; ++u) ret.a[u][u] = Pair(1, 0); return ret; } Mat res = power(e >> 1); res = res * res; if (e & 1) { return res * A; } else { return res; } } int main() { for (int u = 0; u < 5; ++u) { int denom = 0; for (int v = 0; v < 5; ++v) if (abs(u - v) <= 1) ++denom; for (int v = 0; v < 5; ++v) if (abs(u - v) <= 1) A.a[u][v] = Mint(denom).inv() * Pair(1, (1 <= v && v <= 3) ? 1 : 0); } int N; for (; ~scanf("%d", &N); ) { const Mat B = power(N - 1); Pair ans = ZERO; for (int u = 0; u < U; ++u) for (int v = 0; v < U; ++v) { ans += Mint(5).inv() * Pair(1, ((1 <= u && u <= 3) ? 1 : 0)) * B.a[u][v]; } printf("%u\n", ans.second.x); } return 0; }