#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => { read_value!($next, usize) - 1 }; ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); (0..len).map(|_| read_value!($next, $t)).collect::>() }}; ($next:expr, $t:ty) => { $next().parse::<$t>().expect("Parse error") }; } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } /// Verified by https://atcoder.jp/contests/arc093/submissions/3968098 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl ::std::fmt::Debug for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { let (mut a, mut b, _) = red(self.x, M::m()); if b < 0 { a = -a; b = -b; } write!(f, "{}/{}", a, b) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } // Finds the simplest fraction x/y congruent to r mod p. // The return value (x, y, z) satisfies x = y * r + z * p. fn red(r: i64, p: i64) -> (i64, i64, i64) { if r.abs() <= 10000 { return (r, 1, 0); } let mut nxt_r = p % r; let mut q = p / r; if 2 * nxt_r >= r { nxt_r -= r; q += 1; } if 2 * nxt_r <= -r { nxt_r += r; q -= 1; } let (x, z, y) = red(nxt_r, r); (x, y - q * z, z) } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 1012924417; define_mod!(P, MOD); type ModInt = mod_int::ModInt

; /// FFT (in-place, verified as NTT only) /// R: Ring + Copy /// Verified by: https://codeforces.com/contest/1096/submission/47672373 mod fft { use std::ops::*; /// n should be a power of 2. zeta is a primitive n-th root of unity. /// one is unity /// Note that the result should be multiplied by 1/sqrt(n). pub fn transform(f: &mut [R], zeta: R, one: R) where R: Copy + Add + Sub + Mul { let n = f.len(); assert!(n.is_power_of_two()); { let mut i = 0; for j in 1 .. n - 1 { let mut k = n >> 1; loop { i ^= k; if k <= i { break; } k >>= 1; } if j < i { f.swap(i, j); } } } let mut zetapow = Vec::new(); { let mut m = 1; let mut cur = zeta; while m < n { zetapow.push(cur); cur = cur * cur; m *= 2; } } let mut m = 1; while m < n { let base = zetapow.pop().unwrap(); let mut r = 0; while r < n { let mut w = one; for s in r .. r + m { let u = f[s]; let d = f[s + m] * w; f[s] = u + d; f[s + m] = u - d; w = w * base; } r += 2 * m; } m *= 2; } } } // Depends on ModInt.rs fn fact_init(w: usize) -> (Vec, Vec) { let mut fac = vec![ModInt::new(1); w]; let mut invfac = vec![0.into(); w]; for i in 1 .. w { fac[i] = fac[i - 1] * i as i64; } invfac[w - 1] = fac[w - 1].inv(); for i in (0 .. w - 1).rev() { invfac[i] = invfac[i + 1] * (i as i64 + 1); } (fac, invfac) } fn rec(lo: usize, hi: usize, dp: &mut [ModInt], ep: &mut [ModInt], fac: &[ModInt], invfac: &[ModInt]) { let n = hi - lo; debug_assert!(n.is_power_of_two()); if (lo, hi) == (0, 2) { dp[0] += 1; dp[1] += 1; ep[0] += 1; ep[1] += 1; return; } if n == 1 { return; } let mid = (lo + hi) / 2; rec(lo, mid, dp, ep, fac, invfac); if n <= 80 { for i in lo..mid { for j in mid - i - 1..hi - i - 1 { let tmp = ep[i] * ep[j] * if lo != 0 { 2 } else { 1 }; let tmp = tmp * fac[i + j]; dp[i + j + 1] += tmp; } } for i in mid..hi { ep[i] = dp[i] * invfac[i] * invfac[2]; } } else { // FFT let zeta = ModInt::new(5).pow((MOD - 1) / n as i64); let mut tmp = vec![ModInt::new(0); n]; let mut tmp2 = vec![ModInt::new(0); n]; for i in lo..mid { tmp[i - lo] = ep[i]; } // Difference can be anything in [1, n - 1]. for i in 0..n { tmp2[i] = ep[i]; } fft::transform(&mut tmp, zeta, 1.into()); fft::transform(&mut tmp2, zeta, 1.into()); let mut invn = ModInt::new(n as i64).inv(); // If not overlapping, multiply by two. if lo != 0 { invn *= 2; } for i in 0..n { tmp[i] = tmp[i] * tmp2[i] * invn; } fft::transform(&mut tmp, zeta.inv(), 1.into()); for i in mid..hi { dp[i] += tmp[i - lo - 1] * fac[i - 1]; ep[i] += tmp[i - lo - 1] * fac[i - 1] * invfac[i] * invfac[2]; } } rec(mid, hi, dp, ep, fac, invfac); } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (write!(out,$($format)*).unwrap()); } input!(n: usize); const W: usize = 1 << 18; let (fac, invfac) = fact_init(W); let mut dp = vec![ModInt::new(0); W]; let mut ep = vec![ModInt::new(0); W]; rec(0, W, &mut dp, &mut ep, &fac, &invfac); //debugln!("{:?}", dp); //debugln!("{:?}", ep); puts!("{}\n", dp[n]); } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }