// -*- coding: utf-8-unix -*- #![allow(dead_code, unused_imports, unused_macros, unused_variables)] use std::cmp::{max, min, Ordering, Reverse}; use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque}; use std::fmt::Debug; use std::io::{self, Read}; use std::str::FromStr; const INF_I32: i32 = 1_i32 << 30; const INF_I64: i64 = 1_i64 << 60; const INF_I128: i128 = 1_i128 << 120; const INF_USIZE: usize = usize::MAX / 4; const INF: i64 = INF_I64; const UINF: usize = INF_USIZE; const INF128: i128 = INF_I128; const MOD1: i64 = 1_000_000_007; const MOD9: i64 = 998_244_353; const MOD: i64 = MOD9; const UMOD: usize = MOD as usize; // ============================================================================= // Input // ========================================================================= #[allow(dead_code)] fn read() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } #[allow(dead_code)] fn read_vec() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } #[allow(dead_code)] fn read_mat(n: usize) -> Vec> { (0..n).map(|_| read_vec()).collect() } macro_rules! sc { ($($x:ident),+ $(,)?) => { sc!(@read usize; $($x),+); }; ($($x:ident : $t:ty),+ $(,)?) => { let values = read_vec::(); let mut iter = values.into_iter(); $( let mut $x = iter.next() .expect("入力不足") .parse::<$t>() .expect("パース失敗"); )+ }; (@read $t:ty; $($x:ident),+) => { let values = read_vec::<$t>(); let mut iter = values.into_iter(); $( let mut $x = iter.next() .expect("入力不足"); )+ }; } macro_rules! vsc { ($x:ident $(,)?) => { vsc!(@read usize; $x); }; ($x:ident : char $(,)?) => { let mut $x: Vec = read::().chars().collect(); }; ($x:ident : $t:ty $(,)?) => { vsc!(@read $t; $x); }; (@read $t:ty; $x:ident) => { let mut $x = read_vec::<$t>(); }; } // ============================================================================= // Output / Debug // ============================================================================= macro_rules! p { () => { println!(); }; ($value:expr $(,)?) => { println!("{}", $value); }; ($fmt:literal, $($arg:tt)*) => { println!($fmt, $($arg)*); }; } macro_rules! join { ($iter:expr, $separator:expr $(,)?) => { ($iter) .into_iter() .map(|x| x.to_string()) .collect::>() .join($separator) }; } macro_rules! vp { ($iter:expr $(,)?) => { println!("{}", join!($iter, " ")); }; ($iter:expr, $separator:expr $(,)?) => { println!("{}", join!($iter, $separator)); }; } macro_rules! yesno { ($condition:expr $(,)?) => { println!("{}", if $condition { "Yes" } else { "No" }); }; ($condition:expr, $yes:expr, $no:expr $(,)?) => { println!("{}", if $condition { $yes } else { $no }); }; } macro_rules! d { ($($value:expr),+ $(,)?) => { #[cfg(debug_assertions)] { eprint!("[{}:{}]", file!(), line!()); $( eprint!(" {} = {:?}", stringify!($value), &$value); )+ eprintln!(); } }; } // ============================================================================= // Scalar / Vec utilities // ============================================================================= macro_rules! chmin { ($base:expr, $($value:expr),+ $(,)?) => {{ let mut updated = false; $( let value = $value; if $base > value { $base = value; updated = true; } )+ updated }}; } macro_rules! chmax { ($base:expr, $($value:expr),+ $(,)?) => {{ let mut updated = false; $( let value = $value; if $base < value { $base = value; updated = true; } )+ updated }}; } macro_rules! min { // collection: Vec、配列、スライスなど ($iter:expr $(,)?) => {{ ($iter) .iter() .min() .cloned() .expect("min! called on an empty iterator") }}; // 複数の値 ($first:expr, $($rest:expr),+ $(,)?) => {{ let mut answer = ($first).clone(); $( chmin!(answer, ($rest).clone()); )+ answer }}; } macro_rules! max { // collection: Vec、配列、スライスなど ($iter:expr $(,)?) => {{ ($iter) .iter() .max() .cloned() .expect("max! called on an empty iterator") }}; // 複数の値 ($first:expr, $($rest:expr),+ $(,)?) => {{ let mut answer = ($first).clone(); $( chmax!(answer, ($rest).clone()); )+ answer }}; } macro_rules! ndvec { ($value:expr; $len:expr) => { vec![$value; $len] }; ($value:expr; $len:expr, $($rest:expr),+ $(,)?) => { vec![ndvec![$value; $($rest),+]; $len] }; } macro_rules! prefix_sum { ($values:expr $(,)?) => {{ fn prefix_sum_impl(values: &[T]) -> Vec where T: Copy + Default + std::ops::Add, { let mut prefix = Vec::with_capacity(values.len() + 1); prefix.push(T::default()); for &value in values { let next = *prefix.last().unwrap() + value; prefix.push(next); } prefix } prefix_sum_impl(&$values) }}; } // 数学的な floor(a / b)。b != 0。 macro_rules! div_floor { ($a:expr, $b:expr $(,)?) => {{ let a = $a; let b = $b; let q = a / b; let r = a % b; if r != 0 && ((r > 0) != (b > 0)) { q - 1 } else { q } }}; } // 数学的な ceil(a / b)。b != 0。 macro_rules! div_ceil { ($a:expr, $b:expr $(,)?) => {{ let a = $a; let b = $b; let q = a / b; let r = a % b; if r != 0 && ((r > 0) == (b > 0)) { q + 1 } else { q } }}; } // ============================================================================= // Integer / floating-point binary search // ============================================================================= // pred(ok) == true, pred(ng) == false を保ち、最後に true 側の境界を返す。 // ok < ng と ok > ng の双方に対応する。 macro_rules! binsearch { (ok = $ok:expr, ng = $ng:expr, $pred:expr $(,)?) => {{ let mut ok = $ok; let mut ng = $ng; let mut pred = $pred; while ok.abs_diff(ng) > 1 { let mid = if ok < ng { ok + (ng - ok) / 2 } else { ng + (ok - ng) / 2 }; if pred(mid) { ok = mid; } else { ng = mid; } } ok }}; } // false ... true の単調列に対し、最初の true を返す。 // ng は false 側の番兵、ok は true 側の番兵。 macro_rules! first_true { ($ng:expr, $ok:expr, $pred:expr $(,)?) => { binsearch!(ok = $ok, ng = $ng, $pred) }; } // true ... false の単調列に対し、最後の true を返す。 // ok は true 側の番兵、ng は false 側の番兵。 macro_rules! last_true { ($ok:expr, $ng:expr, $pred:expr $(,)?) => { binsearch!(ok = $ok, ng = $ng, $pred) }; } // 浮動小数点版。回数を明示することで停止条件の曖昧さを避ける。 macro_rules! binsearch_f64 { (ok = $ok:expr, ng = $ng:expr, iter = $iter:expr, $pred:expr $(,)?) => {{ let mut ok = $ok; let mut ng = $ng; let mut pred = $pred; for _ in 0..$iter { let mid = (ok + ng) * 0.5; if pred(mid) { ok = mid; } else { ng = mid; } } ok }}; } // ============================================================================= // Sorted slice bounds // ============================================================================= macro_rules! lb { ($slice:expr, $value:expr $(,)?) => {{ let value = $value; ($slice).partition_point(|x| x < &value) }}; } macro_rules! ub { ($slice:expr, $value:expr $(,)?) => {{ let value = $value; ($slice).partition_point(|x| x <= &value) }}; } // UTIL macro_rules! neighbors4 { ($y:expr, $x:expr, $h:expr, $w:expr $(,)?) => {{ const DY: [isize; 4] = [-1, 0, 1, 0]; const DX: [isize; 4] = [0, 1, 0, -1]; (0..4).filter_map(move |dir| { let ny = $y as isize + DY[dir]; let nx = $x as isize + DX[dir]; if 0 <= ny && ny < $h as isize && 0 <= nx && nx < $w as isize { Some((ny as usize, nx as usize)) } else { None } }) }}; } macro_rules! run_length { ($iter:expr $(,)?) => {{ let mut result = Vec::new(); for value in $iter { match result.last_mut() { Some((last, count)) if *last == value => { *count += 1usize; } _ => { result.push((value, 1usize)); } } } result }}; } macro_rules! vector_compress { ($iter:expr $(,)?) => {{ let values: Vec<_> = ($iter).into_iter().collect(); let mut coordinates = values.clone(); coordinates.sort(); coordinates.dedup(); let compressed = values .iter() .map(|value| coordinates.binary_search(value).unwrap()) .collect::>(); (compressed, coordinates) }}; } // ============================================================================= // Map / Set literals and counters // ============================================================================= macro_rules! map { ($($key:expr => $value:expr),* $(,)?) => {{ let mut map = ::std::collections::BTreeMap::new(); $(map.insert($key, $value);)* map }}; } macro_rules! set { ($($value:expr),* $(,)?) => {{ let mut set = ::std::collections::BTreeSet::new(); $(set.insert($value);)* set }}; } macro_rules! count_map { ($iter:expr $(,)?) => {{ let mut count = BTreeMap::new(); for value in $iter { *count.entry(value).or_insert(0usize) += 1; } count }}; } macro_rules! map_add { ($map:expr, $key:expr $(,)?) => { map_add!($map, $key, 1) }; ($map:expr, $key:expr, $delta:expr $(,)?) => {{ let key = $key; let delta = $delta; let map = &mut $map; *map.entry(key).or_insert(0) += delta; }}; } macro_rules! M { (a :expr ) => { M::new({ a }) }; } #[derive(Copy, Clone, Debug)] pub struct M(i64); impl M { fn new(x: i64) -> Self { M(x.rem_euclid(MOD)) } fn pow(self, n: usize) -> Self { match n { 0 => M::new(1), _ => { let mut a = self.pow(n >> 1); a *= a; if n & 1 == 1 { a *= self; } a } } } fn inv(self) -> Self { self.pow((MOD - 2) as usize) } } impl std::ops::Neg for M { type Output = M; fn neg(self) -> Self::Output { Self::new(-self.0) } } impl std::ops::AddAssign for M { fn add_assign(&mut self, rhs: Self) { self.0 += rhs.0; self.0 %= MOD; } } impl std::ops::AddAssign for M { fn add_assign(&mut self, rhs: i64) { *self += M::new(rhs); } } impl std::ops::AddAssign for M { fn add_assign(&mut self, rhs: usize) { *self += M::new(rhs as i64); } } impl std::ops::Add for M where M: std::ops::AddAssign, { type Output = Self; fn add(self, other: T) -> Self { let mut res = self; res += other; res } } impl std::ops::SubAssign for M { fn sub_assign(&mut self, rhs: Self) { self.0 -= rhs.0; if self.0 < 0 { self.0 %= MOD; self.0 += MOD; } } } impl std::ops::SubAssign for M { fn sub_assign(&mut self, rhs: i64) { *self -= M::new(rhs); if (*self).0 < 0 { self.0 %= MOD; self.0 += MOD; } } } impl std::ops::SubAssign for M { fn sub_assign(&mut self, rhs: usize) { *self -= M::new(rhs as i64); if (*self).0 < 0 { self.0 %= MOD; self.0 += MOD; } } } impl std::ops::Sub for M where M: std::ops::SubAssign, { type Output = Self; fn sub(self, other: T) -> Self { let mut res = self; res -= other; res } } impl std::ops::MulAssign for M { fn mul_assign(&mut self, rhs: Self) { self.0 %= MOD; self.0 *= (rhs.0 % MOD); self.0 %= MOD; } } impl std::ops::MulAssign for M { fn mul_assign(&mut self, rhs: i64) { *self *= M::new(rhs); } } impl std::ops::MulAssign for M { fn mul_assign(&mut self, rhs: usize) { *self *= M::new(rhs as i64); } } impl std::ops::Mul for M where M: std::ops::MulAssign, { type Output = Self; fn mul(self, other: T) -> Self { let mut res = self; res *= other; res } } impl std::ops::DivAssign for M { fn div_assign(&mut self, rhs: Self) { *self *= rhs.inv(); } } impl std::ops::DivAssign for M { fn div_assign(&mut self, rhs: i64) { *self /= M::new(rhs); } } impl std::ops::DivAssign for M { fn div_assign(&mut self, rhs: usize) { *self /= M::new(rhs as i64); } } impl std::ops::Div for M where M: std::ops::DivAssign, { type Output = Self; fn div(self, other: T) -> Self { let mut res = self; res /= other; res } } impl std::fmt::Display for M { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::ops::Deref for M { type Target = i64; fn deref(&self) -> &Self::Target { &self.0 } } impl std::ops::DerefMut for M { fn deref_mut(&mut self) -> &mut Self::Target { &mut self.0 } } #[allow(dead_code)] pub fn gcd(a: usize, b: usize) -> usize { if b == 0 { a } else { gcd(b, a % b) } } #[allow(dead_code)] pub fn lcm(a: usize, b: usize) -> usize { a / gcd(a, b) * b } #[allow(dead_code)] /// (gcd, x, y) pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { (a, 1, 0) } else { let (gcd, x, y) = extgcd(b, a % b); (gcd, y, x - (a / b) * y) } } #[allow(dead_code)] /// x ^ n % m pub fn mod_pow(x: usize, n: usize, m: usize) -> usize { let mut res = 1; let mut x = x % m; let mut n = n; while n > 0 { if n & 1 == 1 { res = (res * x) % m; } x = (x * x) % m; n >>= 1; } res } pub struct Combination { m: usize, f_table: Vec, moi: Vec, } impl Combination { // 0 <= size <= 10^8 is constrained. pub fn new(mod_num: usize, table_size: usize) -> Self { Self { m: mod_num, f_table: vec![0; table_size], moi: vec![0; 0], } } pub fn build(&mut self) { let size = self.f_table.len(); self.f_table = self.fact_table(size, self.m); self.moi = self.fact_inv_table(size, self.m); } fn fact_table(&mut self, len: usize, m: usize) -> Vec { let mut res = vec![1; len + 1]; for i in 2..len + 1 { res[i] = (res[i - 1] * i) % m; } res } fn fact_inv_table(&mut self, len: usize, m: usize) -> Vec { let mut res = vec![1; len + 1]; let mut inv = vec![1; len + 1]; //inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD for i in 2..len { inv[i] = (m - inv[m % i] * (m / i) % m) % m; res[i] = inv[i] * res[i - 1]; // res[i] = self.mod_inverse(i, m) * res[i - 1]; // res[i] = 1; res[i] %= m; } res } pub fn p(&mut self, n: usize, k: usize) -> i64 { let p = MOD as usize; if k == 0 { return 1; } if n < k { 0 } else { let (a1, e1) = self.mod_fact(n, p); let (a2, e2) = self.mod_fact(k, p); let (a3, e3) = self.mod_fact(n - k, p); if e1 > e2 + e3 { 0 } else { let moi = self.mod_inverse(a3 % p, p); (a1 * self.mod_inverse(a3 % p, p) % p) as i64 } } } pub fn c(&mut self, n: usize, k: usize) -> i64 { let p = MOD as usize; if n == 0 && k == 0 { return 1; } if n == 0 { return 0; } if k == 0 { return 1; } if n < k { 0 } else { let (a1, e1) = self.mod_fact(n, p); let (a2, e2) = self.mod_fact(k, p); let (a3, e3) = self.mod_fact(n - k, p); if e1 > e2 + e3 { 0 } else { (((a1 * &self.moi[k]) % p * &self.moi[n - k]) % p) as i64 } } } pub fn h(&mut self, n: usize, k: usize) -> i64 { return self.c(n + k - 1, k); } pub fn factorial(&mut self, n: usize) -> i64 { return self.p(n, n); } fn extgcd(&mut self, a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { (a, 1, 0) } else { let (gcd, x, y) = extgcd(b, a % b); (gcd, y, x - (a / b) * y) } } fn mod_inverse(&mut self, a: usize, m: usize) -> usize { let (_, x, _) = self.extgcd(a as i64, m as i64); ((m as i64 + x) as usize % m) % m } fn mod_fact(&mut self, n: usize, p: usize) -> (usize, usize) { if n == 0 { (1, 0) } else { let (a, b) = self.mod_fact(n / p, p); let pow = b + n / p; if n / p % 2 != 0 { (a * (p - self.f_table[(n % p) as usize]) % p, pow) } else { (a * self.f_table[(n % p) as usize] % p, pow) } } } } fn main() { sc!(n); let mut c: Combination = Combination::new(MOD as usize, 201010); c.build(); let mut res = M(0); let ft = c.fact_table(n + 1, UMOD); for i in 1..=n { if 2 * i > n + 1 || 3 * i < n { continue; } let t = c.c(i + 1, n + 1 - i * 2); res += M(t) * ft[i] * ft[n - i]; } p!(res); }