#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native") // #pragma GCC target("avx512f,avx512dq,avx512cd,avx512bw,avx512vl") using ll = long long; constexpr int INF = 1001001001; // constexpr int mod = 1000000007; constexpr int mod = 998244353; template inline bool chmax(T& x, T y){ if(x < y){ x = y; return true; } return false; } template inline bool chmin(T& x, T y){ if(x > y){ x = y; return true; } return false; } struct mint { int x; mint() : x(0) {} mint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} mint& operator+=(const mint& p){ if((x += p.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint& p){ if((x -= p.x) < 0) x += mod; return *this; } mint& operator*=(const mint& p){ x = (int)(1LL * x * p.x % mod); return *this; } mint& operator/=(const mint& p){ *this *= p.inverse(); return *this; } mint operator-() const { return mint(-x); } mint operator+(const mint& p) const { return mint(*this) += p; } mint operator-(const mint& p) const { return mint(*this) -= p; } mint operator*(const mint& p) const { return mint(*this) *= p; } mint operator/(const mint& p) const { return mint(*this) /= p; } bool operator==(const mint& p) const { return x == p.x; } bool operator!=(const mint& p) const { return x != p.x; } mint pow(int64_t n) const { mint res = 1, mul = x; while(n > 0){ if(n & 1) res *= mul; mul *= mul; n >>= 1; } return res; } // x^(a^b) // warning : x と mod は互いに素 // x % mod == 0 かつ a > 0 はこれを呼び出さずに 0 を返すように処理 mint pow2(int64_t a, int64_t b) const { if(b == 0) return *this; if((a %= mod - 1) == 0) return mint(1); int64_t n = 1; while(b > 0){ if(b & 1) (n *= a) %= mod - 1; (a *= a) %= mod - 1; b >>= 1; } return pow(n); } mint inverse() const { return pow(mod - 2); } friend ostream& operator<<(ostream& os, const mint& p){ return os << p.x; } friend istream& operator>>(istream& is, mint& p){ int64_t val; is >> val; p = mint(val); return is; } }; struct ExtendedSieve{ vector table; const int n; ExtendedSieve(int n) : n(n) { table.assign(n + 1, 0); table[0] = table[1] = 1; for(int i = 2; i <= n; ++i){ if(table[i] > 0) continue; table[i] = i; for(int j = i + i; j <= n; j += i){ if(table[j] == 0) table[j] = i; } } } int operator[](const int& k){ return table[k]; } bool is_prime(int x){ if(x < 2) return false; return x == table[x]; } map prime_factorization(int x){ map res; while(x > 1){ ++res[table[x]]; x /= table[x]; } return res; } vector prime_factorization2(int x){ vector res; while(x > 1){ if(!res.size() || res.back() != table[x]){ res.emplace_back(table[x]); } x /= table[x]; } return res; } }; int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int N; cin >> N; ExtendedSieve sieve(N); map primes; for(int i = 1; i < N; ++i){ auto p1 = sieve.prime_factorization(i); auto p2 = sieve.prime_factorization(N - i); for(auto& [p, c] : p2){ chmax(primes[p], (p1[p] += c)); } } mint ans = 1; for(auto [p, c] : primes){ ans *= mint(p).pow(c); } cout << ans << endl; return 0; }