// ---------- begin ModInt ---------- mod modint { #[allow(dead_code)] pub struct Mod; impl ConstantModulo for Mod { const MOD: u32 = 1_000_000_007; } #[allow(dead_code)] pub struct StaticMod; static mut STATIC_MOD: u32 = 0; impl Modulo for StaticMod { fn modulo() -> u32 { unsafe { STATIC_MOD } } } #[allow(dead_code)] impl StaticMod { pub fn set_modulo(p: u32) { unsafe { STATIC_MOD = p; } } } use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub trait ConstantModulo { const MOD: u32; } impl Modulo for T where T: ConstantModulo, { fn modulo() -> u32 { T::MOD } } pub struct ModInt(pub u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { ModInt::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut d = self.0 + rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut d = T::modulo() + self.0 - rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64; ModInt::new_unchecked(v as u32) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.0 == 0 { Self::zero() } else { Self::new_unchecked(T::modulo() - self.0) } } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let m = T::modulo() as i64; ModInt::new((val % m + m) as u32) } } #[allow(dead_code)] impl ModInt { pub fn new_unchecked(d: u32) -> Self { ModInt(d, PhantomData) } pub fn zero() -> Self { ModInt::new_unchecked(0) } pub fn one() -> Self { ModInt::new_unchecked(1) } pub fn is_zero(&self) -> bool { self.0 == 0 } } #[allow(dead_code)] impl ModInt { pub fn new(d: u32) -> Self { ModInt::new_unchecked(d % T::modulo()) } 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.0 != 0); self.pow(T::modulo() as u64 - 2) } } #[allow(dead_code)] pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 { let mut t = 1 % m; let mut s = r % m; while n > 0 { if n & 1 == 1 { t = t * s % m; } s = s * s % m; n >>= 1; } t } } // ---------- end ModInt ---------- // ---------- begin Precalc ---------- mod precalc { use super::modint::*; #[allow(dead_code)] pub struct Precalc { inv: Vec>, fact: Vec>, ifact: Vec>, } #[allow(dead_code)] impl Precalc { pub fn new(n: usize) -> Precalc { 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 { assert!(n > 0); self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn perm(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[n - k] } pub fn comb(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } } // ---------- end Precalc ---------- // ---------- begin NTT ---------- #[allow(dead_code)] mod transform { use super::modint::*; pub trait NTTFriendly: ConstantModulo { fn order() -> usize; fn zeta() -> u32; } pub fn ntt(f: &mut [ModInt]) { 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; } for (k, &z) in zeta.iter().rev().enumerate().rev() { let m = 1 << k; for f in f.chunks_exact_mut(2 * m) { let mut q = ModInt::one(); let (x, y) = f.split_at_mut(m); for (x, y) in x.iter_mut().zip(y.iter_mut()) { let a = *x; let b = *y; *x = a + b; *y = (a - b) * q; q *= z; } } } } pub fn intt(f: &mut [ModInt]) { 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; } for (k, &z) in zeta.iter().rev().enumerate() { let m = 1 << k; for f in f.chunks_exact_mut(2 * m) { let mut q = ModInt::one(); let (x, y) = f.split_at_mut(m); for (x, y) in x.iter_mut().zip(y.iter_mut()) { let a = *x; let b = *y * q; *x = a + b; *y = a - b; q *= z; } } } let ik = ModInt::new_unchecked((T::MOD + 1) >> 1).pow(len as u64); for f in f.iter_mut() { *f *= ik; } } pub fn multiply(a: &[ModInt], b: &[ModInt]) -> Vec> { 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 ---------- // ---------- begin polynomial ---------- #[allow(dead_code)] mod poly { use super::modint::*; use super::transform; pub struct Polynomial { pub a: Vec>, } impl Clone for Polynomial { fn clone(&self) -> Self { Polynomial::new(self.a.iter().map(|a| a.clone()).collect()) } } impl Polynomial { pub fn new(a: Vec>) -> Self { let mut a = Polynomial { a: a }; a.fix(); a } pub fn from_slice(a: &[ModInt]) -> Self { let mut b = Vec::with_capacity(a.len()); b.extend_from_slice(a); Self::new(b) } pub fn zero() -> Self { Polynomial::new(vec![]) } pub fn one() -> Self { Polynomial::new(vec![ModInt::one()]) } pub fn get(&self, x: usize) -> ModInt { self.a.get(x).cloned().unwrap_or(ModInt::zero()) } pub fn len(&self) -> usize { self.a.len() } pub fn reverse(&self, n: usize) -> Self { assert!(self.len() >= n); let mut a = Vec::with_capacity(n); a.extend_from_slice(&self.a); a.resize(n, ModInt::zero()); a.reverse(); Self::new(a) } pub fn truncate(&self, n: usize) -> Self { let mut b = self.a.clone(); b.truncate(n); Polynomial::new(b) } pub fn eval(&self, x: ModInt) -> ModInt { let mut ans = ModInt::zero(); for a in self.a.iter().rev() { ans = ans * x + *a; } ans } pub fn fix(&mut self) { while self.a.last().map_or(false, |a| a.is_zero()) { self.a.pop(); } } pub fn derivative(&self) -> Self { if self.len() < 2 { return Polynomial::zero(); } let mut b = vec![ModInt::zero(); self.len() - 1]; for (i, (b, a)) in b.iter_mut().zip(self.a.iter().skip(1)).enumerate() { *b = *a * ModInt::from(i + 1); } Polynomial::new(b) } pub fn integral(&self) -> Self { if self.len() < 1 { return Polynomial::zero(); } let mut b = vec![ModInt::zero(); self.len() + 1]; let mut inv = vec![ModInt::one(); self.len() + 1]; b[1] = self.a[0]; for (i, (b, a)) in b[1..].iter_mut().zip(self.a.iter()).enumerate().skip(1) { let k = i + 1; inv[k] = -inv[T::modulo() as usize % k] * ModInt::from(T::modulo() as usize / k); *b = *a * inv[k]; } Polynomial::new(b) } pub fn add(&self, rhs: &Self) -> Self { let mut ans = vec![ModInt::zero(); std::cmp::max(self.a.len(), rhs.a.len())]; for (ans, a) in ans.iter_mut().zip(self.a.iter()) { *ans = *a; } for (ans, a) in ans.iter_mut().zip(rhs.a.iter()) { *ans += *a; } Polynomial::new(ans) } pub fn add_assign(&mut self, rhs: &Self) { if self.len() < rhs.len() { self.a.resize(rhs.len(), ModInt::zero()); } for (a, b) in self.a.iter_mut().zip(rhs.a.iter()) { *a += *b; } } pub fn sub(&self, rhs: &Self) -> Self { let mut ans = vec![ModInt::zero(); std::cmp::max(self.a.len(), rhs.a.len())]; for (ans, a) in ans.iter_mut().zip(self.a.iter()) { *ans = *a; } for (ans, a) in ans.iter_mut().zip(rhs.a.iter()) { *ans -= *a; } Polynomial::new(ans) } pub fn sub_assign(&mut self, rhs: &Self) { if self.len() < rhs.len() { self.a.resize(rhs.len(), ModInt::zero()); } for (a, b) in self.a.iter_mut().zip(rhs.a.iter()) { *a -= *b; } } } impl Polynomial { pub fn mul(&self, rhs: &Self) -> Self { Self::new(transform::multiply(&self.a, &rhs.a)) } pub fn inverse(&self, n: usize) -> Self { assert!(self.a.len() > 0 && self.a[0].0 > 0); let len = n.next_power_of_two(); assert!(2 * len <= T::order()); let mut b = Vec::with_capacity(len); b.push(self.a[0].inv()); let mut f = Vec::with_capacity(2 * len); let mut g = Vec::with_capacity(2 * len); let mut size = 1; while b.len() < n { size <<= 1; f.clear(); f.extend_from_slice(&b); f.resize(2 * size, ModInt::zero()); g.clear(); if self.a.len() >= size { g.extend_from_slice(&self.a[..size]); } else { g.extend_from_slice(&self.a); } g.resize(2 * size, ModInt::zero()); transform::ntt(&mut f); transform::ntt(&mut g); for (g, f) in g.iter_mut().zip(f.iter()) { *g *= *f * *f; } transform::intt(&mut g); b.resize(size, ModInt::zero()); for (b, g) in b.iter_mut().zip(g.iter()) { *b = *b + *b - *g; } } b.truncate(n); Polynomial::new(b) } pub fn div_rem(&self, rhs: &Self) -> (Self, Self) { let n = self.len(); let m = rhs.len(); assert!(m > 0); if n < m { return (Polynomial::zero(), self.clone()); } let ia = self.reverse(n).truncate(n - m + 1); let ib = rhs.reverse(m).inverse(n - m + 1); let id = ia.mul(&ib).truncate(n - m + 1); let div = id.reverse(n - m + 1); let rem = self.sub(&rhs.mul(&div)).truncate(m - 1); (div, rem) } pub fn rem(&self, rhs: &Self) -> Self { self.div_rem(rhs).1 } pub fn log(&self, n: usize) -> Self { assert!(self.len() > 0 && self.a[0].0 == 1); self.derivative() .mul(&self.inverse(n)) .truncate(n - 1) .integral() } pub fn exp(&self, n: usize) -> Self { assert!(self.a.get(0).map_or(true, |a| a.is_zero()) && n <= T::order()); let mut b = Polynomial::new(vec![ModInt::one()]); let mut size = 1; while size < n { size <<= 1; let f = b.log(size); let f = Polynomial::from_slice(&self.a[..std::cmp::min(self.len(), size)]).sub(&f); b = b.add(&b.mul(&f)).truncate(size); } b.truncate(n) } pub fn multi_eval(&self, x: &[ModInt]) -> Vec> { let size = x.len().next_power_of_two(); let mut seg = vec![Some(Polynomial::one()); 2 * size]; for (seg, x) in seg[size..].iter_mut().zip(x.iter()) { *seg = Some(Polynomial::from_slice(&[-*x, ModInt::one()])); } for i in (1..size).rev() { seg[i] = Some( seg[2 * i] .as_ref() .unwrap() .mul(seg[2 * i + 1].as_ref().unwrap()), ); } let mut rem = vec![None; 2 * size]; rem[1] = Some(self.rem(&seg[1].take().unwrap())); for i in 1..size { let a = rem[i].take().unwrap(); rem[2 * i] = Some(a.rem(&seg[2 * i].take().unwrap())); rem[2 * i + 1] = Some(a.rem(&seg[2 * i + 1].take().unwrap())); } let mut ans = Vec::with_capacity(x.len()); for a in rem[size..].iter_mut().take(x.len()) { ans.push(a.take().unwrap().get(0)); } ans } pub fn interpolation(x: &[ModInt], y: &[ModInt]) -> Self { assert!(x.len() > 0 && x.len() == y.len()); let size = x.len().next_power_of_two(); let mut p = vec![Polynomial::one(); 2 * size]; for (p, x) in p[size..].iter_mut().zip(x.iter()) { *p = Polynomial::new(vec![-*x, ModInt::one()]); } for i in (1..size).rev() { p[i] = p[2 * i].mul(&p[2 * i + 1]); } let z = p[1].derivative().multi_eval(x); let mut a = vec![Polynomial::zero(); 2 * size]; for (a, (z, y)) in a[size..].iter_mut().zip(z.iter().zip(y.iter())) { *a = Polynomial::new(vec![*y * z.inv()]); } for i in (1..size).rev() { a[i] = a[2 * i] .mul(&p[2 * i + 1]) .add(&a[2 * i + 1].mul(&p[2 * i])); } a.swap_remove(1) } } } // ---------- begin polynomial ---------- //https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より 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") }; } // use std::io::Write; use modint::*; struct P; impl ConstantModulo for P { const MOD: u32 = 998_244_353; } impl transform::NTTFriendly for P { fn order() -> usize { 1 << 23 } fn zeta() -> u32 { let p = Self::MOD as u64; mod_pow(3, (p - 1) >> 23, p) as u32 } } type M = ModInt

; fn run() { input! { s: bytes, } let p = 26; let pc = precalc::Precalc::new(s.len()); let mut cnt = vec![0; p]; for c in s { let k = (c - b'a') as usize; cnt[k] += 1; } let mut dp = vec![M::one()]; for c in cnt { let mut a = vec![M::one(); c + 1]; for (i, dp) in dp.iter_mut().enumerate() { *dp *= pc.ifact(i); } for (i, a) in a.iter_mut().enumerate() { *a *= pc.ifact(i); } let mut res = transform::multiply(&a, &dp); for (i, res) in res.iter_mut().enumerate() { *res *= pc.fact(i); } dp = res; } let mut ans = M::zero(); for a in dp.iter().skip(1) { ans += *a; } println!("{}", ans); } fn main() { run(); }