#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)...); } long long gcd(long long a,long long b) { if (a%b==0) return(b); else return(gcd(b,a%b)); } long long lcm(long long a,long long b){ long long g = gcd(a,b); return a / g * b; } struct Miller{ const vector v = { 2 , 7 , 61 }; // < 4,759,123,141 // x^k (mod m) long long modpow( long long x, long long k, long long m ){ long long res = 1; while( k ){ if( k & 1 ){ res = res * x % m; } k /= 2; x = x * x % m; } return res; } // check if n is prime bool check( long long n ){ if( n < 2 ){ return false; } long long d = n - 1; long long s = 0; while( d % 2 == 0 ){ d /= 2; s++; } for( long long a : v ){ if( a == n ){ return true; } if( modpow( a , d , n ) != 1 ){ bool ok = true; for( long long r = 0; r < s; r++ ){ if( modpow( a, d * (1LL << r), n ) == n-1 ){ ok = false; break; } } if( ok ){ return false; } } } return true; } }; struct Rho{ mt19937 mt; Miller miller; long long c; Rho(){ mt.seed( clock() ); } inline long long f( long long x, long long n ){ return ( x * x + c ) % n; } long long check( long long n ){ if( n == 4 ){ return 2; } c = mt() % n; long long x = mt() % n; long long y = x; long long d = 1; while( d == 1 ){ x = f(x, n); y = f(f(y,n),n); d = gcd( abs(x-y), n ); } if( d == n ){ return -1; } return d; } vector factor( long long n ){ if( n <= 1 ){ return {}; } if( miller.check( n ) ){ return { n }; } long long res = -1; while( res == -1 ){ res = check( n ); } vector fa = factor( res ); vector fb = factor( n / res ); fa.insert( fa.end() , fb.begin(), fb.end() ); return fa; } }; Rho rho; 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; int cnt = 1; map ma; map > mama; for (int i = n-1; i >= 1; --i) { if(mama[i].size() == 0) { auto tmp = rho.factor(i); map ma_tmp; for (int j = 0; j < tmp.size(); ++j) { ma_tmp[tmp[j]]++; } mama[i] = ma_tmp; } if(mama[n - i].size() == 0) { auto tmp = rho.factor(n - i); map ma_tmp; for (int j = 0; j < tmp.size(); ++j) { ma_tmp[tmp[j]]++; } mama[n - i] = ma_tmp; } map map1 = mama[i], map2 = mama[n - i]; map ma_tmp; for (auto p : map1) { ma_tmp[p.F] += p.S; } for (auto p : map2) { ma_tmp[p.F] += p.S; } for (auto p : ma_tmp) { chmax(ma[p.F], p.S); } } int ans = 1; for (auto p : ma) { ans *= mpow(p.F, p.S); ans %= MOD; } print(ans); }