//squareさんのコード(epsf001-ex) #ifndef CLASS_FAST_MODINT #define CLASS_FAST_MODINT #include using singlebit = uint32_t; using doublebit = uint64_t; static constexpr int digit_level = 8 * sizeof(singlebit); static constexpr singlebit find_inv(singlebit n, int d = 6, singlebit x = 1) { return d == 0 ? x : find_inv(n, d - 1, x * (2 - x * n)); } template class fast_modint { // Fast Modulo Integer, Assertion: mod < 2^(bits of singlebit - 1) and mod is prime private: singlebit n; static constexpr singlebit r2 = (((doublebit(1) << digit_level) % mod) << digit_level) % mod; static constexpr singlebit ninv = singlebit(-1) * find_inv(mod); singlebit reduce(doublebit x) const { singlebit res = (x + doublebit(singlebit(x) * ninv) * mod) >> digit_level; return res < mod ? res : res - mod; } public: fast_modint() : n(0) {}; fast_modint(singlebit n_) { n = reduce(doublebit(n_) * r2); }; static constexpr singlebit get_mod() { return mod; } singlebit get() const { return reduce(n); } bool operator==(const fast_modint& x) const { return n == x.n; } bool operator!=(const fast_modint& x) const { return n != x.n; } fast_modint& operator+=(const fast_modint& x) { n += x.n; n -= (n < mod ? 0 : mod); return *this; } fast_modint& operator-=(const fast_modint& x) { n += mod - x.n; n -= (n < mod ? 0 : mod); return *this; } fast_modint& operator*=(const fast_modint& x) { n = reduce(doublebit(n) * x.n); return *this; } fast_modint operator+(const fast_modint& x) const { return fast_modint(*this) += x; } fast_modint operator-(const fast_modint& x) const { return fast_modint(*this) -= x; } fast_modint operator*(const fast_modint& x) const { return fast_modint(*this) *= x; } fast_modint inv() const { return binpow(mod - 2); } fast_modint binpow(singlebit b) const { fast_modint ans(1), cur(*this); while (b > 0) { if (b & 1) ans *= cur; cur *= cur; b >>= 1; } return ans; } }; #endif // CLASS_FAST_MODINT #ifndef CLASS_POLYNOMIAL_NTT #define CLASS_POLYNOMIAL_NTT #include #include template class polynomial_ntt { public: using modulo = fast_modint; static void fourier_transform(std::vector& v, bool inverse) { std::size_t s = v.size(); for (std::size_t i = 0, j = 1; j < s - 1; ++j) { for (std::size_t k = s >> 1; k > (i ^= k); k >>= 1); if (i < j) std::swap(v[i], v[j]); } std::size_t sc = 0, sz = 1; while (sz < s) sz *= 2, ++sc; modulo root = modulo(primroot).binpow((mod - 1) >> sc); std::vector pw(s + 1); pw[0] = 1; for (std::size_t i = 1; i <= s; i++) pw[i] = pw[i - 1] * root; std::size_t qs = s; for (std::size_t b = 1; b < s; b <<= 1) { qs >>= 1; for (std::size_t i = 0; i < s; i += b * 2) { for (std::size_t j = i; j < i + b; ++j) { modulo delta = pw[(inverse ? b * 2 - j + i : j - i) * qs] * v[j + b]; v[j + b] = v[j] - delta; v[j] += delta; } } } if (!inverse) return; modulo powinv = modulo((mod + 1) / 2).binpow(sc); for (std::size_t i = 0; i < s; ++i) { v[i] = v[i] * powinv; } } static std::vector convolve(std::vector v1, std::vector v2) { std::size_t s1 = v1.size(), s2 = v2.size(), s = 1; while (s < s1 || s < s2) s *= 2; v1.resize(s * 2); fourier_transform(v1, false); v2.resize(s * 2); fourier_transform(v2, false); for (singlebit i = 0; i < s * 2; ++i) v1[i] *= v2[i]; fourier_transform(v1, true); v1.resize(s1 + s2 - 1); return v1; } }; #endif // CLASS_POLYNOMIAL_NTT #include #include using namespace std; using ntt = polynomial_ntt<998244353, 23, 3>; using mint = ntt::modulo; mint factorial(int N) { // 1, 1, 2, 6, 24, 120, 720,... mint ans = 1; for (int i = 1; i <= N; ++i) { ans *= i; } return ans; } mint derangement(int N) { // 1, 0, 1, 2, 9, 44, 265,... mint ans = 1; for (int i = 1; i <= N; ++i) { ans *= i; if (i % 2 == 1) ans -= 1; else ans += 1; } return ans; } vector pow(vector poly, int b) { vector ans({ mint(1) }); while (b) { if (b & 1) ans = ntt::convolve(ans, poly); poly = ntt::convolve(poly, poly); b >>= 1; } return ans; } int main() { int N; cin >> N; vector poly = pow({ mint(1), mint(4), mint(2) }, N / 2); if (N % 2 == 1) poly = ntt::convolve(poly, { mint(1), mint(1) }); mint ans = 0, mul = 1; for (int i = 0; i <= N; ++i) { if ((N - i) % 2 == 0) ans += poly[N - i] * mul; else ans -= poly[N - i] * mul; mul *= i + 1; } cout << (ans + factorial(N) - derangement(N) * 2).get() << endl; return 0; }