#include #include using namespace std; using namespace atcoder; #define rep(i,n)for (int i = 0; i < int(n); ++i) #define rrep(i,n)for (int i = int(n)-1; i >= 0; --i) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() template void chmax(T& a, const T& b) {a = max(a, b);} template void chmin(T& a, const T& b) {a = min(a, b);} using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; std::pair,std::vector> primes_lpf(const int n) { std::pair,std::vector> rv; std::vector& primes = rv.first; std::vector& lpf = rv.second; primes.reserve(n / 10); lpf.resize(n + 1); for(int i = 2; i <= n; i += 2) lpf[i] = 2; for(int i = 3; i <= n; i += 6) lpf[i] = 3; if (2 <= n) primes.push_back(2); if (3 <= n) primes.push_back(3); // 5 * x <= n, x <= floor(n / 5) const int n5 = n / 5; int x = 5; bool one_mod6 = false; // x_1 <= n5, x_2 = x_1 + 2 <= n5 + 2 <= n for(; x <= n5; one_mod6 = !one_mod6, x += (one_mod6 ? 2 : 4)) { if (lpf[x] == 0) { lpf[x] = x; primes.push_back(x); } int px = lpf[x]; for(int i = 2;; ++i) { int q = primes[i]; int y = q * x; if (y > n) break; lpf[y] = q; if (q == px) break; } } for(; x <= n; one_mod6 = !one_mod6, x += (one_mod6 ? 2 : 4)) { if (lpf[x] == 0) { lpf[x] = x; primes.push_back(x); } } return rv; } auto [primes, lpf] = primes_lpf(1000000); // global variable lpf must be defined std::vector> factorize(int n) { std::vector> fs; while(n > 1) { int p = lpf[n]; int cnt = 0; do {n /= p; cnt++;} while(n % p == 0); fs.emplace_back(p, cnt); } return fs; } int main() { ios::sync_with_stdio(false); cin.tie(0); int n; cin >> n; map d; for(int i = 1; i <= n - 1; i++) { map mp; for(int x: {i, n - i}) { for(auto [p, cnt]: factorize(x)) { mp[p] += cnt; } } for(auto [p, cnt]: mp) { chmax(d[p], cnt); } } mint ans = 1; for(auto [p, cnt]: d) ans *= mint::raw(p).pow(cnt); cout << ans.val() << '\n'; }