//@formatter:off #include #define rep(i,n) for (int i = 0; i < int(n); ++i) #define rrep(i,n) for (int i = int(n)-1; i >= 0; i--) #define rep2(i,s,n) for (int i = int(s); i < int(n); ++i) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define pb push_back #define eb emplace_back #define vi vector #define vvi vector> #define vl vector #define vvl vector> #define vd vector #define vvd vector> #define vs vector #define vc vector #define vvc vector> #define vb vector #define vvb vector> #define vp vector

#define vvp vector> using namespace std; using ll = long long; using P = pair; using LP = pair; template istream& operator>>(istream &is,pair &p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream &os,const pair &p) { return os<<'{'< istream& operator>>(istream &is,vector &v) { for(T &t:v){is>>t;} return is; } template ostream& operator<<(ostream &os,const vector &v) { os<<'[';rep(i,v.size())os< void fin(T a) { cout << a << endl; exit(0); } template bool chmin(T& a,T b) {if(a > b){a = b; return true;} return false;} template bool chmax(T& a,T b) {if(a < b){a = b; return true;} return false;} const int inf = 1001001001; const ll linf = 1001001001001001001; //@formatter:on //constexpr int mod = 1000000007; constexpr int mod = 998244353; struct mint { ll x; constexpr mint(ll x = 0) : x((x % mod + mod) % mod) {} constexpr mint operator-() const { return mint(-x); } constexpr mint &operator+=(const mint &a) { if ((x += a.x) >= mod) x -= mod; return *this; } constexpr mint &operator++() { return *this += mint(1); } constexpr mint &operator-=(const mint &a) { if ((x += mod - a.x) >= mod) x -= mod; return *this; } constexpr mint &operator--() { return *this -= mint(1); } constexpr mint &operator*=(const mint &a) { (x *= a.x) %= mod; return *this; } constexpr mint operator+(const mint &a) const { mint res(*this); return res += a; } constexpr mint operator-(const mint &a) const { mint res(*this); return res -= a; } constexpr mint operator*(const mint &a) const { mint res(*this); return res *= a; } constexpr mint pow(ll t) const { mint res = mint(1), a(*this); while (t > 0) { if (t & 1) res *= a; t >>= 1; a *= a; } return res; } // for prime mod constexpr mint inv() const { return pow(mod - 2); } constexpr mint &operator/=(const mint &a) { return *this *= a.inv(); } constexpr mint operator/(const mint &a) const { mint res(*this); return res /= a; } }; ostream &operator<<(ostream &os, const mint &a) { return os << a.x; } bool operator==(const mint &a, const mint &b) { return a.x == b.x; } bool operator!=(const mint &a, const mint &b) { return a.x != b.x; } bool operator==(const mint &a, const int &b) { return a.x == b; } bool operator!=(const mint &a, const int &b) { return a.x != b; } template< typename Mint > struct NumberTheoreticTransformFriendlyModInt { vector< int > rev; vector< Mint > rts; int base, max_base; Mint root; NumberTheoreticTransformFriendlyModInt() : base(1), rev{0, 1}, rts{0, 1} { assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(root.pow((mod - 1) >> 1) == 1) root += 1; assert(root.pow(mod - 1) == 1); root = root.pow((mod - 1) >> max_base); } void ensure_base(int nbase) { if(nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for(int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } assert(nbase <= max_base); while(base < nbase) { Mint z = root.pow(1 << (max_base - 1 - base)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; rts[(i << 1) + 1] = rts[i] * z; } ++base; } } void ntt(vector< Mint > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for(int i = 0; i < n; i++) { if(i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for(int k = 1; k < n; k <<= 1) { for(int i = 0; i < n; i += 2 * k) { for(int j = 0; j < k; j++) { Mint z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } void intt(vector< Mint > &a) { const int n = (int) a.size(); ntt(a); reverse(a.begin() + 1, a.end()); Mint inv_sz = Mint(1) / n; for(int i = 0; i < n; i++) a[i] *= inv_sz; } vector< Mint > multiply(vector< Mint > a, vector< Mint > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); Mint inv_sz = Mint(1) / sz; for(int i = 0; i < sz; i++) { a[i] *= b[i] * inv_sz; } reverse(a.begin() + 1, a.end()); ntt(a); a.resize(need); return a; } }; NumberTheoreticTransformFriendlyModInt ntt; vector pow(const vector &f, int k) { int n = f.size(); vector res(n, 0); res[0] = 1; vector now = f; while (k > 0) { if (k & 1) { res = ntt.multiply(res, now); if (res.size() > n) res.erase(res.begin() + n, res.end()); } now = ntt.multiply(now, now); if (now.size() > n) now.erase(now.begin() + n, now.end()); k >>= 1; } return res; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); int n; cin >> n; vector v(2 * n - 1, 0); mint now = 1; rep2(i, 1, n) { if (i > 1) now /= i - 1; v[i] = now * i; } auto ans = pow(v, n); now = 1; rep2(i, 1, n - 1) now *= i; cout << ans[2 * n - 2] * now / mint(n).pow(n - 2) << endl; }