#include "bits/stdc++.h" using namespace std; //#include "atcoder/all" //using namespace atcoder; #define int long long #define REP(i, n) for (int64_t i = 0; i < (int)n; ++i) #define RREP(i, n) for (int64_t i = (int)n - 1; i >= 0; --i) #define FOR(i, s, n) for (int64_t i = s; i < (int)n; ++i) #define RFOR(i, s, n) for (int64_t i = (int)n - 1; i >= s; --i) #define ALL(a) a.begin(), a.end() #define IN(a, x, b) (a <= x && x < b) templateistream&operator >>(istream&is,vector&vec){for(T&x:vec)is>>x;return is;} templateinline void out(T t){cout << t << "\n";} templateinline void out(T t,Ts... ts){cout << t << " ";out(ts...);} templateinline bool CHMIN(T&a,T b){if(a > b){a = b;return true;}return false;} templateinline bool CHMAX(T&a,T b){if(a < b){a = b;return true;}return false;} constexpr int64_t INF = 1000000000000000000; // 10^18 vector > prime_factorize(long long n) { //計算量は√N!!! vector > res; for (long long p = 2; p * p <= n; ++p) { if (n % p != 0) continue; int num = 0; while (n % p == 0) { ++num; n /= p; } res.push_back(make_pair(p, num)); } if (n != 1) res.push_back(make_pair(n, 1)); return res; } // a^b long long modpow(long long a, long long n, long long mod) { long long res = 1; while (n > 0) { if (n & 1) res = res * a % mod; a = a * a % mod; n >>= 1; } return res; } // a^-1 long long modinv(long long a, long long m) { long long b = m, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= m; if (u < 0) u += m; return u; } // a^x ≡ b (mod. m) となる最小の正の整数 x を求める long long modlog(long long a, long long b, int m) { a %= m, b %= m; // calc sqrt{M} long long lo = -1, hi = m; while (hi - lo > 1) { long long mid = (lo + hi) / 2; if (mid * mid >= m) hi = mid; else lo = mid; } long long sqrtM = hi; // {a^0, a^1, a^2, ..., a^sqrt(m)} map apow; long long amari = 1; for (long long r = 0; r < sqrtM; ++r) { if (!apow.count(amari)) apow[amari] = r; (amari *= a) %= m; } // check each A^p long long A = modpow(modinv(a, m), sqrtM, m); amari = b; for (long long q = 0; q < sqrtM; ++q) { if (apow.count(amari)) { long long res = q * sqrtM + apow[amari]; if (res > 0) return res; } (amari *= A) %= m; } // no solutions return -1; } signed main() { int N; cin >> N; vector primes(N + 1); FOR(i, 1, N + 1) { for(auto[val, cnt]: prime_factorize(i)) { CHMAX(primes[val], cnt); } } int flg = true; int ans = 1; int MOD = 998244353; RREP(i, N + 1) { if(flg && primes[i]) flg = false; else if(primes[i]) { ans *= modpow(i, primes[i], MOD); ans %= MOD; } } out(ans); }