#include using namespace std; #define int long long #define rep(i, n) for(int (i)=0;(i)<(n);(i)++) #define rrep(i, n) for(int (i)=((n)-1);(i)>=0;(i)--) #define itn int #define miele(v) min_element(v.begin(), v.end()) #define maele(v) max_element(v.begin(), v.end()) #define SUM(v) accumulate(v.begin(), v.end(), 0LL) #define lb(a, key) lower_bound(a.begin(),a.end(),key) #define ub(a, key) upper_bound(a.begin(),a.end(),key) #define COUNT(a, key) count(a.begin(), a.end(), key) #define BITCOUNT(x) __builtin_popcount(x) #define pb push_back #define all(x) (x).begin(),(x).end() #define F first #define S second using P = pair; using WeightedGraph = vector>; using UnWeightedGraph = vector>; using Real = long double; using Point = complex; //Point and Vector2d is the same! // p.real() or real(p) -> x軸, p.imag() or imag(p) -> y軸 using Vector2d = complex; const int MOD = 998244353; const long long INF = 1LL << 60; const double EPS = 1e-15; const double PI = 3.14159265358979323846; template int getIndexOfLowerBound(vector &v, T x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); } template int getIndexOfUpperBound(vector &v, T x) { return upper_bound(v.begin(), v.end(), x) - v.begin(); } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } #define repi(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) istream &operator>>(istream &is, Point &p) { Real a, b; is >> a >> b; p = Point(a, b); return is; } template istream &operator>>(istream &is, pair &p_var) { is >> p_var.first >> p_var.second; return is; } template istream &operator>>(istream &is, vector &vec) { for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, pair &pair_var) { os << pair_var.first << ' ' << pair_var.second; return os; } template ostream &operator<<(ostream &os, vector &vec) { for (int i = 0; i < vec.size(); i++) os << vec[i] << ' '; return os; } template ostream &operator<<(ostream &os, vector> &vec) { for (int i = 0; i < vec.size(); i++) os << vec[i] << '\n'; return os; } template ostream &operator<<(ostream &os, vector> &df) { for (auto &vec : df) os << vec; return os; } template ostream &operator<<(ostream &os, map &map_var) { repi(itr, map_var) { os << *itr << ' '; itr++; itr--; } return os; } template ostream &operator<<(ostream &os, set &set_var) { repi(itr, set_var) { os << *itr << ' '; itr++; itr--; } return os; } void print() { cout << endl; } template void print(Head &&head, Tail &&... tail) { cout << head; if (sizeof...(tail) != 0) cout << " "; print(forward(tail)...); } vector primes(1000010,1) ; void Eratosthenes(int n){ for(int i = 2; i <= sqrt(n); i++){ if(primes[i]){ for(int j = 0; i * (j + 2) <= n; j++){ primes[i *(j + 2)] = 0; } } } primes[0] = 0; primes[1] = 0; } int mpow(int x, int n) { int ret = 1; while(n > 0) { if(n & 1) (ret *= x) %= MOD; (x *= x) %= MOD; n >>= 1; } return ret; } signed main(void) { cin.tie(0); ios::sync_with_stdio(false); int n; cin>>n; Eratosthenes(n+1); int ans = 1; for (int i = 2; i <= n-1; ++i) { if(!primes[i]) continue; if(n % i == 0) { int num = n; int t=0; int cnt = 0; while(num % i == 0) { num /= i; cnt++; } t = num; if(t == 1) { ans *= mpow(i, cnt+cnt-2); } else { //print(i, "tが1ではない"); int cnt_t = 0; int _num = 1; while(_num * i <= t-1) { _num *= i; cnt_t++; } //print(cnt, cnt_t); ans *= mpow(i, cnt+cnt+cnt_t); } ans %= MOD; } else { int num = i; while(num * i <= n-1) { num *= i; } ans %= MOD; ans *= (num%MOD); ans %= MOD; } //print(i, ans); } print(ans); }