pub mod io { pub fn scan(r: &mut R) -> Vec { let mut res = Vec::new(); loop { let buf = match r.fill_buf() { Ok(buf) => buf, Err(e) if e.kind() == std::io::ErrorKind::Interrupted => continue, Err(e) => panic!(e), }; let (done, used, buf) = { match buf.iter().position(u8::is_ascii_whitespace) { Some(i) => (i > 0 || res.len() > 0, i + 1, &buf[..i]), None => (buf.is_empty(), buf.len(), buf), } }; res.extend_from_slice(buf); r.consume(used); if done { return res; } } } #[macro_export] macro_rules! scan { ($r:expr, [$t:tt; $n:expr]) => { (0..$n).map(|_| scan!($r, $t)).collect::>() }; ($r:expr, ($($t:tt),*)) => { ($(scan!($r, $t)),*) }; ($r:expr, Usize1) => { scan!($r, usize) - 1 }; ($r:expr, Bytes) => { io::scan($r) }; ($r:expr, String) => { String::from_utf8(scan!($r, Bytes)).unwrap() }; ($r:expr, $t:ty) => { scan!($r, String).parse::<$t>().unwrap() }; } #[macro_export] macro_rules! input { ($r:expr, $($($v:ident)* : $t:tt),* $(,)?) => { $(let $($v)* = scan!($r, $t);)* }; } } const MOD: usize = 998_244_353; pub fn pow_mod(mut a: usize, mut n: usize, m: usize) -> usize { let mut res = 1; while n > 0 { if n & 1 > 0 { res = res * a % m; } a = a * a % m; n >>= 1; } res } pub fn get_primes(n: usize) -> Vec { let mut primes = Vec::new(); let mut is_prime = vec![true; n + 1]; for p in 2..=n { if !is_prime[p] { continue; } primes.push(p); let mut q = 2 * p; while q <= n { is_prime[q] = false; q += p; } } primes } fn run(reader: &mut R, writer: &mut W) { let n = scan!(reader, usize); let primes = get_primes(n - 1); let mut count = vec![0; primes.len()]; for i in 1..n { let mut x = i; let mut y = n - i; for (count, p) in count.iter_mut().zip(primes.iter()) { if p * p > x.max(y) { break; } let mut c = 0; while x % p == 0 { x /= p; c += 1; } while y % p == 0 { y /= p; c += 1; } *count = (*count).max(c); } if x > 1 { let k = primes.binary_search(&x).unwrap(); count[k] = count[k].max(if x == y { 2 } else { 1 }); } if x != y && y > 1 { let k = primes.binary_search(&y).unwrap(); count[k] = count[k].max(1); } } let mut ans = 1; for (count, p) in count.into_iter().zip(primes.into_iter()) { ans *= pow_mod(p, count, MOD); ans %= MOD; } writeln!(writer, "{}", ans).ok(); } fn main() { let (stdin, stdout) = (std::io::stdin(), std::io::stdout()); let ref mut reader = std::io::BufReader::new(stdin.lock()); let ref mut writer = std::io::BufWriter::new(stdout.lock()); run(reader, writer); }