General

# Author Problem Lang Verdict Time Memory Sent Judged
121212991 Out of competition:
* sansen
1542D - 11 Rust Accepted 295 ms 108 KB 2021-07-03 16:36:37 2021-07-03 18:28:00

→ Source
// ---------- begin ModInt ----------
// モンゴメリ乗算を用いる
// ほぼCodeforces用
// 注意
// new_unchecked は値xが 0 <= x < modulo であることを仮定
// ModInt の中身は正規化された値で持ってるので直接読んだり書いたりするとぶっ壊れる
// 奇素数のみ
mod modint {

use std::marker::*;
use std::ops::*;

pub trait Modulo {
fn modulo() -> u32;
fn rem() -> u32;
fn ini() -> u64;
fn reduce(x: u64) -> u32 {
assert!(x < (Self::modulo() as u64) << 32);
let b = (x as u32 * Self::rem()) as u64;
let t = x + b * Self::modulo() as u64;
let mut c = (t >> 32) as u32;
if c >= Self::modulo() {
c -= Self::modulo();
}
c as u32
}
}

pub enum Mod1_000_000_007 {}

impl Modulo for Mod1_000_000_007 {
fn modulo() -> u32 {
1_000_000_007
}
fn rem() -> u32 {
2226617417
}
fn ini() -> u64 {
582344008
}
}

pub enum Mod998_244_353 {}

impl Modulo for Mod998_244_353 {
fn modulo() -> u32 {
998_244_353
}
fn rem() -> u32 {
998244351
}
fn ini() -> u64 {
932051910
}
}

pub fn generate_umekomi_modulo(p: u32) {
assert!(p < (1 << 31) && p > 2 && p & 1 == 1 && (2u32..).take_while(|v| v * v <= p).all(|k| p % k != 0));
let mut t = 1u32;
let mut s = !p + 1;
let mut n = !0u32 >> 2;
while n > 0 {
if n & 1 == 1 {
t *= s;
}
s *= s;
n >>= 1;
}
let mut ini = (1u64 << 32) % p as u64;
ini = (ini << 32) % p as u64;
assert!(t * p == !0);
println!("pub enum Mod{} {{}}", p);
println!("impl Modulo for Mod{} {{", p);
println!("    fn modulo() -> u32 {{");
println!("        {}", p);
println!("    }}");
println!("    fn rem() -> u32 {{");
println!("        {}", t);
println!("    }}");
println!("    fn ini() -> u32 {{");
println!("        {}", ini);
println!("    }}");
println!("}}");
let mut f = vec![];
let mut n = p - 1;
for i in 2.. {
if i * i > n {
break;
}
if n % i == 0 {
f.push(i);
while n % i == 0 {
n /= i;
}
}
}
if n > 1 {
f.push(n);
}
let mut order = 1;
let mut n = p - 1;
while n % 2 == 0 {
n /= 2;
order <<= 1;
}
let z = (2u64..).find(|z| {
f.iter().all(|f| mod_pow(*z, ((p - 1) / *f) as u64, p as u64) != 1)
}).unwrap();
let zeta = mod_pow(z, ((p - 1) / order) as u64, p as u64);
println!("impl transform::NTTFriendly for Mod{} {{", p);
println!("    fn order() -> usize {{");
println!("        {}", order);
println!("    }}");
println!("    fn zeta() -> u32 {{");
println!("        {}", zeta);
println!("    }}");
println!("}}");
}

pub struct ModInt<T>(u32, PhantomData<T>);

impl<T> Clone for ModInt<T> {
fn clone(&self) -> Self {
ModInt::build(self.0)
}
}

impl<T> Copy for ModInt<T> {}

impl<T: Modulo> Add for ModInt<T> {
type Output = ModInt<T>;
fn add(self, rhs: Self) -> Self::Output {
let mut d = self.0 + rhs.0;
if d >= T::modulo() {
d -= T::modulo();
}
Self::build(d)
}
}

impl<T: Modulo> AddAssign for ModInt<T> {
fn add_assign(&mut self, rhs: Self) {
*self = *self + rhs;
}
}

impl<T: Modulo> Sub for ModInt<T> {
type Output = ModInt<T>;
fn sub(self, rhs: Self) -> Self::Output {
let mut d = T::modulo() + self.0 - rhs.0;
if d >= T::modulo() {
d -= T::modulo();
}
Self::build(d)
}
}

impl<T: Modulo> SubAssign for ModInt<T> {
fn sub_assign(&mut self, rhs: Self) {
*self = *self - rhs;
}
}

impl<T: Modulo> Mul for ModInt<T> {
type Output = ModInt<T>;
fn mul(self, rhs: Self) -> Self::Output {
Self::build(T::reduce(self.0 as u64 * rhs.0 as u64))
}
}

impl<T: Modulo> MulAssign for ModInt<T> {
fn mul_assign(&mut self, rhs: Self) {
*self = *self * rhs;
}
}

impl<T: Modulo> Neg for ModInt<T> {
type Output = ModInt<T>;
fn neg(self) -> Self::Output {
if self.0 == 0 {
Self::zero()
} else {
Self::build(T::modulo() - self.0)
}
}
}

impl<T: Modulo> std::fmt::Display for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}

impl<T: Modulo> std::fmt::Debug for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}

impl<T: Modulo> std::str::FromStr for ModInt<T> {
type Err = std::num::ParseIntError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
let val = s.parse::<u32>()?;
Ok(ModInt::new(val))
}
}

impl<T: Modulo> From<usize> for ModInt<T> {
fn from(val: usize) -> ModInt<T> {
ModInt::new_unchecked((val % T::modulo() as usize) as u32)
}
}

impl<T: Modulo> From<u64> for ModInt<T> {
fn from(val: u64) -> ModInt<T> {
ModInt::new_unchecked((val % T::modulo() as u64) as u32)
}
}

impl<T: Modulo> From<i64> for ModInt<T> {
fn from(val: i64) -> ModInt<T> {
let m = T::modulo() as i64;
ModInt::new((val % m + m) as u32)
}
}

impl<T> ModInt<T> {
fn build(d: u32) -> Self {
ModInt(d, PhantomData)
}
pub fn zero() -> Self {
Self::build(0)
}
pub fn is_zero(&self) -> bool {
self.0 == 0
}
}

impl<T: Modulo> ModInt<T> {
pub fn new_unchecked(d: u32) -> Self {
Self::build(T::reduce(d as u64 * T::ini()))
}
pub fn new(d: u32) -> Self {
Self::new_unchecked(d % T::modulo())
}
pub fn one() -> Self {
Self::new_unchecked(1)
}
pub fn get(&self) -> u32 {
T::reduce(self.0 as u64)
}
pub fn pow(&self, mut n: u64) -> Self {
let mut t = Self::one();
let mut s = *self;
while n > 0 {
if n & 1 == 1 {
t *= s;
}
s *= s;
n >>= 1;
}
t
}
pub fn inv(&self) -> Self {
assert!(!self.is_zero());
self.pow((T::modulo() - 2) as u64)
}
}

pub fn mod_pow(mut r: u64, mut n: u64, m: u64) -> u64 {
let mut t = 1 % m;
while n > 0 {
if n & 1 == 1 {
t = t * r % m;
}
r = r * r % m;
n >>= 1;
}
t
}
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
use super::modint::*;
pub struct Precalc<T> {
inv: Vec<ModInt<T>>,
fact: Vec<ModInt<T>>,
ifact: Vec<ModInt<T>>,
}
impl<T: Modulo> Precalc<T> {
pub fn new(n: usize) -> Precalc<T> {
let mut inv = vec![ModInt::one(); n + 1];
let mut fact = vec![ModInt::one(); n + 1];
let mut ifact = vec![ModInt::one(); n + 1];
for i in 2..(n + 1) {
fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
}
ifact[n] = fact[n].inv();
if n > 0 {
inv[n] = ifact[n] * fact[n - 1];
}
for i in (1..n).rev() {
ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
inv[i] = ifact[i] * fact[i - 1];
}
Precalc {
inv: inv,
fact: fact,
ifact: ifact,
}
}
pub fn inv(&self, n: usize) -> ModInt<T> {
assert!(n > 0);
self.inv[n]
}
pub fn fact(&self, n: usize) -> ModInt<T> {
self.fact[n]
}
pub fn ifact(&self, n: usize) -> ModInt<T> {
self.ifact[n]
}
pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[n - k]
}
pub fn comb(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[k] * self.ifact[n - k]
}
}
}
// ---------- end Precalc ----------
// ---------- begin NTT ----------
mod transform {
use super::modint::*;
pub trait NTTFriendly: Modulo {
fn order() -> usize;
fn zeta() -> u32;
}
pub fn ntt<T: NTTFriendly>(f: &mut [ModInt<T>]) {
let n = f.len();
assert!(n.count_ones() == 1);
assert!(n <= T::order());
let len = n.trailing_zeros() as usize;
let mut zeta = Vec::with_capacity(len);
let mut r = ModInt::new_unchecked(T::zeta()).pow((T::order() >> len) as u64);
for _ in 0..len {
zeta.push(r);
r = r * r;
}
let mut q = Vec::with_capacity(len / 2);
for (k, &z) in zeta.iter().rev().enumerate().rev() {
let m = 1 << k;
q.clear();
let mut r = ModInt::one();
for _ in 0..m {
q.push(r);
r *= z;
}
for f in f.chunks_exact_mut(2 * m) {
let (x, y) = f.split_at_mut(m);
for ((x, y), q) in x.iter_mut().zip(y.iter_mut()).zip(q.iter()) {
let a = *x;
let b = *y;
*x = a + b;
*y = (a - b) * *q;
}
}
}
}
pub fn intt<T: NTTFriendly>(f: &mut [ModInt<T>]) {
let n = f.len();
assert!(n.count_ones() == 1);
assert!(n <= T::order());
let len = n.trailing_zeros() as usize;
let mut zeta = Vec::with_capacity(len);
let mut r = ModInt::new_unchecked(T::zeta()).inv().pow((T::order() >> len) as u64);
for _ in 0..len {
zeta.push(r);
r = r * r;
}
let mut q = Vec::with_capacity(len / 2);
for (k, &z) in zeta.iter().rev().enumerate() {
let m = 1 << k;
q.clear();
let mut r = ModInt::one();
for _ in 0..m {
q.push(r);
r *= z;
}
for f in f.chunks_exact_mut(2 * m) {
let (x, y) = f.split_at_mut(m);
for ((x, y), q) in x.iter_mut().zip(y.iter_mut()).zip(q.iter()) {
let a = *x;
let b = *y * *q;
*x = a + b;
*y = a - b;
}
}
}
let ik = ModInt::new_unchecked((T::modulo() + 1) >> 1).pow(len as u64);
for f in f.iter_mut() {
*f *= ik;
}
}
pub fn multiply<T: NTTFriendly>(a: &[ModInt<T>], b: &[ModInt<T>]) -> Vec<ModInt<T>> {
if a.is_empty() || b.is_empty() {
return vec![];
}
let n = a.len() + b.len() - 1;
let k = n.next_power_of_two();
assert!(k <= T::order());
let mut f = Vec::with_capacity(k);
let mut g = Vec::with_capacity(k);
f.extend_from_slice(a);
f.resize(k, ModInt::zero());
ntt(&mut f);
g.extend_from_slice(b);
g.resize(k, ModInt::zero());
ntt(&mut g);
for (f, g) in f.iter_mut().zip(g.iter()) {
*f *= *g;
}
intt(&mut f);
f.truncate(n);
f
}
}
// ---------- end NTT ----------

use modint::*;

type M = ModInt<Mod998_244_353>;

impl transform::NTTFriendly for Mod998_244_353 {
fn order() -> usize {
8388608
}
fn zeta() -> u32 {
15311432
}
}

// ---------- begin scannner ----------
mod scanner {
use std::str::FromStr;
pub struct Scanner<'a> {
it: std::str::SplitWhitespace<'a>,
}
impl<'a> Scanner<'a> {
pub fn new(s: &'a String) -> Scanner<'a> {
Scanner {
it: s.split_whitespace(),
}
}
pub fn next<T: FromStr>(&mut self) -> T {
self.it.next().unwrap().parse::<T>().ok().unwrap()
}
pub fn next_bytes(&mut self) -> Vec<u8> {
self.it.next().unwrap().bytes().collect()
}
pub fn next_chars(&mut self) -> Vec<char> {
self.it.next().unwrap().chars().collect()
}
pub fn next_vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {
(0..len).map(|_| self.next()).collect()
}
}
}
// ---------- end scannner ----------

use std::io::Write;

fn main() {
let mut s = String::new();
let mut sc = scanner::Scanner::new(&s);
let out = std::io::stdout();
let mut out = std::io::BufWriter::new(out.lock());
run(&mut sc, &mut out);
}

fn run<W: Write>(sc: &mut scanner::Scanner, out: &mut std::io::BufWriter<W>) {
let n = sc.next();
let mut op = vec![];
for i in 0..n {
let s = sc.next::<String>();
if s == "+" {
let v = sc.next::<u32>();
op.push((1, (v, i)));
} else {
op.push((0, (0, 0)));
}
}
let mut ans = M::zero();
for (x, &(_, key)) in op.iter().enumerate().filter(|p| (p.1).0 == 1) {
let mut dp = vec![M::one()];
for (y, &(op, val)) in op.iter().enumerate() {
let mut next = vec![M::zero(); dp.len() + 1];
for (i, &way) in dp.iter().enumerate() {
if y != x {
next[i] += way;
}
if op == 0 {
next[i.saturating_sub(1)] += way;
continue;
}
if y <= x {
if val <= key {
next[i + 1] += way;
} else {
next[i] += way;
}
} else {
if val <= key && i > 0 {
next[i + 1] += way;
} else {
next[i] += way;
}
}
}
dp = next;
}
ans += M::new(key.0) * dp[1..].iter().fold(M::zero(), |s, a| s + *a);
}
println!("{}", ans);
}


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