// ---------- begin Run Length Encoding ---------- fn run_length_encoding(a: &[T]) -> Vec<(T, usize)> { let mut a = a.iter().map(|a| (a.clone(), 1)).collect::>(); a.dedup_by(|a, b| { a.0 == b.0 && { b.1 += a.1; true } }); a } // ---------- end Run Length Encoding ---------- // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- fn run() { input! { n: usize, } let mut f = (0..=n).collect::>(); for i in (2..).take_while(|p| p * p <= n) { if i == f[i] { for j in i..=(n / i) { f[j * i] = i; } } } let mut cnt = vec![0; n + 1]; for i in 1..n { let mut p = vec![]; for n in [i, n - i].iter() { let mut n = *n; while n > 1 { let v = f[n]; p.push(v); n /= v; } } p.sort(); for (p, c) in run_length_encoding(&p) { cnt[p] = cnt[p].max(c); } } const MOD: usize = 998_244_353; let mut ans = 1; for (i, &c) in cnt.iter().enumerate() { for _ in 0..c { ans = ans * i % MOD; } } println!("{}", ans); } fn main() { run(); }