#include <bits/stdc++.h> //#include <chrono> //#pragma GCC optimize("O3") using namespace std; #define reps(i,s,n) for(int i = s; i < n; i++) #define rep(i,n) reps(i,0,n) #define Rreps(i,n,e) for(int i = n - 1; i >= e; --i) #define Rrep(i,n) Rreps(i,n,0) #define ALL(a) a.begin(), a.end() using ll = long long; using vec = vector<ll>; using mat = vector<vec>; ll N,M,H,W,Q,K,A,B; string S; using P = pair<ll, ll>; const ll INF = (1LL<<60); template<class T> bool chmin(T &a, const T &b){ if(a > b) {a = b; return true;} else return false; } template<class T> bool chmax(T &a, const T &b){ if(a < b) {a = b; return true;} else return false; } template <unsigned long long mod > class modint{ public: ll x; constexpr modint(){x = 0;} constexpr modint(ll _x) : x((_x < 0 ? ((_x += (LLONG_MAX / mod) * mod) < 0 ? _x + (LLONG_MAX / mod) * mod : _x) : _x)%mod){} constexpr modint set_raw(ll _x){ //_x in [0, mod) x = _x; return *this; } constexpr modint operator-(){ return x == 0 ? 0 : mod - x; } constexpr modint& operator+=(const modint& a){ if((x += a.x) >= mod) x -= mod; return *this; } constexpr modint operator+(const modint& a) const{ return modint(*this) += a; } constexpr modint& operator-=(const modint& a){ if((x -= a.x) < 0) x += mod; return *this; } constexpr modint operator-(const modint& a) const{ return modint(*this) -= a; } constexpr modint& operator*=(const modint& a){ (x *= a.x)%=mod; return *this; } constexpr modint operator*(const modint& a) const{ return modint(*this) *= a; } constexpr modint pow(unsigned long long pw) const{ modint res(1), comp(*this); while(pw){ if(pw&1) res *= comp; comp *= comp; pw >>= 1; } return res; } //以下、modが素数のときのみ constexpr modint inv() const{ if(x == 2) return (mod + 1) >> 1; return modint(*this).pow(mod - 2); } constexpr modint& operator/=(const modint &a){ (x *= a.inv().x)%=mod; return *this; } constexpr modint operator/(const modint &a) const{ return modint(*this) /= a; } }; #define mod1 998244353 using mint = modint<mod1>; ostream& operator<<(ostream& os, const mint& a){ os << a.x; return os; } using vm = vector<mint>; class NTT{ static int root; static vm root_pow; static vector<int> id; static void make_root_pow(int n){ if(n + 1 == (int)root_pow.size()) return; root_pow.resize(n + 1); mint new_root = mint(root).pow((mod1 - 1) / n); root_pow[0].x = 1; rep(i,n){ root_pow[i + 1] = root_pow[i] * new_root; } } static void make_bit_reverse(int n){ if(n == (int)id.size()) return; id.resize(n); iota(ALL(id), 0); for(int i = 1; (1<<i) <= n; ++i){ int l = 1<<(i - 1), r = 1<<i; int plus = n >> i; for(int j = l; j < r; ++j){ int temp = id[j - l] + plus; if(j < temp) swap(id[j], id[temp]); } } } static void dft(int n, vm &f, bool inv){ vm g(n); rep(i,n) g[i] = f[id[i]]; swap(f, g); for(int l = n / 2, len = 1; l >= 1; l /= 2, len *= 2){ for(int i = 0; i < n; i += len * 2){ rep(j, len){ mint z_f = (inv ? root_pow[n - l * j] : root_pow[l * j]) * f[i + len + j]; g[i + j] = f[i + j] + z_f; g[i + len + j] = f[i + j] - z_f; } } swap(f, g); } if(inv) { mint n_inv = mint(n).inv(); rep(i, n) f[i] *= n_inv; } } public: NTT(int _x = 3) { root = _x; } void dft_2D(int n, int m, vector<vm> &a, bool inv){ //簡単に、書き換える形で //aがn×mサイズであることや、n,mが2冪であることは仮定 make_root_pow(m); make_bit_reverse(m); rep(i, n) dft(m, a[i], inv); make_root_pow(n); make_bit_reverse(n); rep(j, m){ vm temp(n); rep(i, n) temp[i] = a[i][j]; dft(n, temp, inv); rep(i, n) a[i][j] = temp[i]; } } static vm convolution(vm &a, vm &b, int size_a = INT_MAX, int size_b = INT_MAX){ if(size_a > (int)a.size()) size_a = (int)a.size(); if(size_b > (int)b.size()) size_b = (int)b.size(); int sz = size_a + size_b - 1, n = 1; while(sz > n) n *= 2; vm g(n), h(n), gh(n); copy(a.begin(), a.begin() + size_a, g.begin()); copy(b.begin(), b.begin() + size_b, h.begin()); make_root_pow(n); make_bit_reverse(n); dft(n, g, false); dft(n, h, false); rep(i, n) gh[i] = g[i] * h[i]; dft(n, gh, true); //gh.resize(sz); gh.resize(size_a); return gh; } static vm simple_pow(vm &a, int pw){ int sz = a.size(), n = 1; while(sz > n) n <<= 1; n <<= 1; make_root_pow(n); make_bit_reverse(n); vm res(n, 0), cpy(n, 0); res[0] = 1; copy(ALL(a), cpy.begin()); while(pw){ dft(n, cpy, false); if(pw&1){ dft(n, res, false); rep(i, n) res[i] *= cpy[i]; dft(n, res, true); reps(i, n / 2, n) res[i] = 0; } rep(i, n) cpy[i] *= cpy[i]; dft(n, cpy, true); reps(i, n / 2, n) cpy[i] = 0; pw >>= 1; } return res; } }; int NTT::root; vm NTT::root_pow; vector<int> NTT::id; const ll MAX_N = ll(4e+5) + 10; vm fact(MAX_N, mint(1)), fact_inv(MAX_N, mint(1)), n_inv(MAX_N, mint(1)); void makefact(){ mint tmp; reps(i,2,MAX_N) fact[i] = fact[i-1] * tmp.set_raw(i); fact_inv[MAX_N - 1] = fact[MAX_N - 1].inv(); Rreps(i, MAX_N - 1, 1){ fact_inv[i] = fact_inv[i + 1] * tmp.set_raw(i + 1); n_inv[i + 1] = fact[i] * fact_inv[i + 1]; } } mint nCm(ll n, ll m){ return fact[n] * fact_inv[n-m] * fact_inv[m]; } mint nCm_inv(ll n, ll m){ return fact[n-m] * fact[m] * fact_inv[n]; } int main(){ makefact(); cin>>N; vm pol(N - 1); rep(i, N - 1) pol[i] = fact_inv[i] * (i + 1); NTT ntt; cout<<fact[N - 2] * mint(N).pow(N - 2).inv() * NTT::simple_pow(pol, N)[N - 2]<<endl; }