#include #include template struct ModInt { using lint = long long; int val; // constructor ModInt(lint v = 0) : val(v % MOD) { if (val < 0) val += MOD; }; // unary operator ModInt operator+() const { return ModInt(val); } ModInt operator-() const { return ModInt(MOD - val); } ModInt inv() const { return this->pow(MOD - 2); } // arithmetic ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; } ModInt pow(lint n) const { auto x = ModInt(1); auto b = *this; while (n > 0) { if (n & 1) x *= b; n >>= 1; b *= b; } return x; } // compound assignment ModInt& operator+=(const ModInt& x) { if ((val += x.val) >= MOD) val -= MOD; return *this; } ModInt& operator-=(const ModInt& x) { if ((val -= x.val) < 0) val += MOD; return *this; } ModInt& operator*=(const ModInt& x) { val = lint(val) * x.val % MOD; return *this; } ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); } // compare bool operator==(const ModInt& b) const { return val == b.val; } bool operator!=(const ModInt& b) const { return val != b.val; } bool operator<(const ModInt& b) const { return val < b.val; } bool operator<=(const ModInt& b) const { return val <= b.val; } bool operator>(const ModInt& b) const { return val > b.val; } bool operator>=(const ModInt& b) const { return val >= b.val; } // I/O friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { lint v; is >> v; x = v; return is; } friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; } }; template struct NumberTheoreticalTransform { using mint = ModInt; using mints = std::vector; std::vector zetas; explicit NumberTheoreticalTransform() { int exp = MOD - 1; while (true) { mint zeta = mint(Root).pow(exp); zetas.push_back(zeta); if (exp % 2 != 0) break; exp /= 2; } } void bitrev(mints& f) const { int n = f.size(); for (int i = 0; i < n; ++i) { int ti = i, ni = 0; for (int k = 0; (1 << k) < n; ++k) { int b = (ti & 1); ti >>= 1; ni <<= 1; ni += b; } if (i < ni) { std::swap(f[i], f[ni]); } } } void udft(mints& f, bool isinv) const { if (f.size() <= 1) return; int l = 1; int k = 1 << l; int n = f.size(); while (k <= n) { mint zeta = zetas[l]; if (isinv) zeta = zeta.inv(); for (int r = 0; r < n / k; ++r) { mint zetapow = 1; for (int j = 0; j < k / 2; ++j) { int b = r * k + j; mint t = zetapow * f[b + k / 2]; f[b + k / 2] = f[b] - t; f[b] = f[b] + t; zetapow *= zeta; } } ++l; k <<= 1; } } void dft(mints& f, bool isinv) const { bitrev(f); udft(f, isinv); } mints ntt(mints f, mints g) const { int fdeg = f.size(), gdeg = g.size(); int k = 0; while ((1 << k) < fdeg + gdeg) ++k; int n = (1 << k); f.resize(n, mint(0)); g.resize(n, mint(0)); dft(f, false); dft(g, false); mints h(n); for (int i = 0; i < n; ++i) h[i] = f[i] * g[i]; dft(h, true); h.resize(fdeg + gdeg - 1); for (auto& x : h) x /= n; return h; } }; template struct Combination { int max_n; std::vector f, invf; explicit Combination(int n) : max_n(n), f(n + 1), invf(n + 1) { f[0] = 1; for (int i = 1; i <= n; ++i) { f[i] = f[i - 1] * i; } invf[max_n] = f[max_n].inv(); for (int i = max_n - 1; i >= 0; --i) { invf[i] = invf[i + 1] * (i + 1); } } T fact(int n) const { return n < 0 ? T(0) : f[n]; } T invfact(int n) const { return n < 0 ? T(0) : invf[n]; } T perm(int a, int b) const { return a < b || b < 0 ? T(0) : f[a] * invf[a - b]; } T binom(int a, int b) const { return a < b || b < 0 ? T(0) : f[a] * invf[a - b] * invf[b]; } }; constexpr int MOD = 998244353; using mint = ModInt; const Combination C(200000); const NumberTheoreticalTransform NTT; std::vector pow(std::vector xs, int n) { std::vector ret{1}; while (n > 0) { if (n & 1) ret = NTT.ntt(ret, xs); n >>= 1; xs = NTT.ntt(xs, xs); } return ret; } void solve() { int n; std::cin >> n; std::vector bs{1, 4, 2}; bs = pow(bs, n / 2); if (n % 2 == 1) bs = NTT.ntt(bs, {1, 1}); mint ans = C.fact(n); for (int k = 0; k <= n; ++k) { ans -= mint(-1).pow(k) * C.binom(n, k) * C.fact(n - k) * 2; } for (int k = 0; k <= n; ++k) { ans += mint(-1).pow(k) * bs[k] * C.fact(n - k); } std::cout << ans << "\n"; } int main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); solve(); return 0; }