#include #include #include #include #include #include #include #include #include #include using namespace std; typedef long long ll; const ll MOD = 998244353; class Prime { public: vector prime_list; const ll MAX_N = 1000000; Prime() { bool checked[MAX_N + 1]; memset(checked, false, sizeof(checked)); for (ll i = 2; i <= MAX_N; ++i) { if (!checked[i]) { prime_list.push_back(i); for (ll j = i * i; j <= MAX_N; j += i) { checked[j] = true; } } } } map prime_division(ll n) { map res; for (ll i = 0; prime_list[i] <= sqrt(n); ++i) { ll p = prime_list[i]; while (n % p == 0) { res[p]++; n /= p; } } if (n != 1) { res[n] = 1; } return res; } bool is_prime(ll n) { if (n <= 1) return false; for (int i = 0; i < prime_list.size(); ++i) { if (n % prime_list[i]) return false; } return true; } }; int main() { ll N; cin >> N; Prime prime; vector counter(N + 1, 0); map checked; for (ll i = 1; i <= N - 1; ++i) { ll a = i * (N - i); if (checked[a]) continue; checked[a] = true; map res1 = prime.prime_division(i); map res2 = prime.prime_division(N - i); map res; for (auto e : res1) { res[e.first] += e.second; } for (auto e : res2) { res[e.first] += e.second; } for (auto e : res) { counter[e.first] = max(counter[e.first], e.second); } } ll ans = 1; for (ll i = 1; i < N; ++i) { if (counter[i] == 0) continue; ll p = 1; for (int j = 0; j < counter[i]; ++j) { p *= i; p %= MOD; } ans *= p; ans %= MOD; } cout << ans << endl; return 0; }