#1194743 (Rust) No.3777 Train Seats

• 問題: No.3777 Train Seats
• ユーザー: Moss_Local
• 提出日時: 2026-10-23 23:18:45
• 言語: Rust (1.99.0 + proconio + num + itertools + ACL)
• 結果: AC
• 実行時間: 6 ms / 2,000 ms
• コード長: 19,447 bytes
• コンパイル時間: 10,345 ms
• コンパイル使用メモリ: 188,780 KB
• 実行使用メモリ: 9,920 KB
• 最終ジャッジ日時: 2026-10-23 23:18:59
• 合計ジャッジ時間: 13,411 ms
• ジャッジサーバーID （参考情報）: judge4_0 / judge3_0

ファイルパターン	結果
sample	AC * 3
other	AC * 50

コンパイルメッセージ

warning: unnecessary parentheses around assigned value
   --> src/main.rs:559:19
    |
559 |         self.0 *= (rhs.0 % MOD);
    |                   ^           ^
    |
    = note: `#[warn(unused_parens)]` (part of `#[warn(unused)]`) on by default
help: remove these parentheses
    |
559 -         self.0 *= (rhs.0 % MOD);
559 +         self.0 *= rhs.0 % MOD;
    |

warning: variable does not need to be mutable
   --> src/main.rs:66:17
    |
 66 |             let mut $x = iter.next()
    |                 ----^^
    |                 |
    |                 help: remove this `mut`
...
786 |     sc!(n);
    |     ------ in this macro invocation
    |
    = note: `#[warn(unused_mut)]` (part of `#[warn(unused)]`) on by default
    = note: this warning originates in the macro `sc` (in Nightly builds, run with -Z macro-backtrace for more info)

ソースコード

// -*- 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: std::str::FromStr>() -> 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<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_mat<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
macro_rules! sc {
    ($($x:ident),+ $(,)?) => {
        sc!(@read usize; $($x),+);
    };

    ($($x:ident : $t:ty),+ $(,)?) => {
        let values = read_vec::<String>();
        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<char> = read::<String>().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::<Vec<_>>()
            .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<T>(values: &[T]) -> Vec<T>
        where
            T: Copy + Default + std::ops::Add<Output = T>,
        {
            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::<Vec<_>>();

        (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<M> for M {
    fn add_assign(&mut self, rhs: Self) {
        self.0 += rhs.0;
        self.0 %= MOD;
    }
}
impl std::ops::AddAssign<i64> for M {
    fn add_assign(&mut self, rhs: i64) {
        *self += M::new(rhs);
    }
}
impl std::ops::AddAssign<usize> for M {
    fn add_assign(&mut self, rhs: usize) {
        *self += M::new(rhs as i64);
    }
}
impl<T> std::ops::Add<T> for M
where
    M: std::ops::AddAssign<T>,
{
    type Output = Self;
    fn add(self, other: T) -> Self {
        let mut res = self;
        res += other;
        res
    }
}
impl std::ops::SubAssign<M> 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<i64> 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<usize> 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<T> std::ops::Sub<T> for M
where
    M: std::ops::SubAssign<T>,
{
    type Output = Self;
    fn sub(self, other: T) -> Self {
        let mut res = self;
        res -= other;
        res
    }
}
impl std::ops::MulAssign<M> for M {
    fn mul_assign(&mut self, rhs: Self) {
        self.0 %= MOD;

        self.0 *= (rhs.0 % MOD);
        self.0 %= MOD;
    }
}
impl std::ops::MulAssign<i64> for M {
    fn mul_assign(&mut self, rhs: i64) {
        *self *= M::new(rhs);
    }
}
impl std::ops::MulAssign<usize> for M {
    fn mul_assign(&mut self, rhs: usize) {
        *self *= M::new(rhs as i64);
    }
}
impl<T> std::ops::Mul<T> for M
where
    M: std::ops::MulAssign<T>,
{
    type Output = Self;
    fn mul(self, other: T) -> Self {
        let mut res = self;
        res *= other;
        res
    }
}
impl std::ops::DivAssign<M> for M {
    fn div_assign(&mut self, rhs: Self) {
        *self *= rhs.inv();
    }
}
impl std::ops::DivAssign<i64> for M {
    fn div_assign(&mut self, rhs: i64) {
        *self /= M::new(rhs);
    }
}
impl std::ops::DivAssign<usize> for M {
    fn div_assign(&mut self, rhs: usize) {
        *self /= M::new(rhs as i64);
    }
}
impl<T> std::ops::Div<T> for M
where
    M: std::ops::DivAssign<T>,
{
    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<usize>,
    moi: Vec<usize>,
}

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<usize> {
        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<usize> {
        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);
}