//---------- begin union_find ---------- pub struct DSU { p: Vec, } impl DSU { pub fn new(n: usize) -> DSU { assert!(n < std::i32::MAX as usize); DSU { p: vec![-1; n] } } pub fn init(&mut self) { self.p.iter_mut().for_each(|p| *p = -1); } pub fn root(&self, mut x: usize) -> usize { assert!(x < self.p.len()); while self.p[x] >= 0 { x = self.p[x] as usize; } x } pub fn same(&self, x: usize, y: usize) -> bool { assert!(x < self.p.len() && y < self.p.len()); self.root(x) == self.root(y) } pub fn unite(&mut self, x: usize, y: usize) -> Option<(usize, usize)> { assert!(x < self.p.len() && y < self.p.len()); let mut x = self.root(x); let mut y = self.root(y); if x == y { return None; } if self.p[x] > self.p[y] { std::mem::swap(&mut x, &mut y); } self.p[x] += self.p[y]; self.p[y] = x as i32; Some((x, y)) } pub fn parent(&self, x: usize) -> Option { assert!(x < self.p.len()); let p = self.p[x]; if p >= 0 { Some(p as usize) } else { None } } pub fn sum(&self, mut x: usize, mut f: F) -> usize where F: FnMut(usize), { while let Some(p) = self.parent(x) { f(x); x = p; } x } pub fn size(&self, x: usize) -> usize { assert!(x < self.p.len()); let r = self.root(x); (-self.p[r]) as usize } } //---------- end union_find ---------- // ---------- begin ModInt ---------- mod modint { #[allow(dead_code)] pub struct Mod; impl ConstantModulo for Mod { const MOD: u32 = 998_244_353; } #[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::fmt::Debug 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) } } } // ---------- 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 input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 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") }; } // ---------- end input macro ---------- use std::io::Write; use modint::*; type M = ModInt; fn dfs(bit: usize, k: usize, id: usize, key: &mut Vec, state: &mut Vec>) { if k == key.len() { state.push(key.clone()); // println!("{:?}", key); return; } if bit >> k & 1 == 0 { key[k] = 0; dfs(bit, k + 1, id, key, state); } else if k > 0 && bit >> (k - 1) & 1 == 1 { key[k] = key[k - 1]; dfs(bit, k + 1, id, key, state); } else { for i in 1..=(id + 1) { key[k] = i; dfs(bit, k + 1, id.max(i), key, state); } } } fn run() { input! { r: usize, c: usize, n: usize, } let mut state = vec![]; for i in 0..(1 << c) { dfs(i, 0, 0, &mut vec![0; c], &mut state); } state.sort(); let mut trans = vec![vec![]; state.len()]; for (i, u) in state.iter().enumerate() { for (j, d) in state.iter().enumerate() { let mut dsu = DSU::new(2 * c); let mut ok = true; for k in 0..c { for l in 0..k { if u[k] == u[l] && u[k] > 0 { dsu.unite(k, l); let mut val = false; let mut elem = false; for j in l..=k { if u[j] == 0 { elem = true; val |= d[j] == 0; } } ok &= val || !elem; } } if k > 0 && d[k] == d[k - 1] && d[k] > 0 { dsu.unite(k + c - 1, k + c); } if u[k] > 0 && d[k] > 0 { dsu.unite(k, k + c); } } for k in 0..c { for l in 0..k { if d[k] > 0 && d[l] > 0 { ok &= dsu.same(k + c, l + c) ^ (d[k] != d[l]); } } } for k in 0..c { if u[k] > 0 { let mut val = j == 0; for l in 0..c { val |= d[l] > 0 && dsu.same(k, l + c); } ok &= val; } } for k in 1..c { ok &= !(u[k] == 0 && d[k - 1] == 0 && d[k] > 0 && u[k - 1] > 0); ok &= !(d[k] == 0 && u[k - 1] == 0 && u[k] > 0 && d[k - 1] > 0); } if j == 0 { ok &= u.iter().all(|u| *u <= 1); } if ok { let mut bit = 0; for i in 0..c { if u[i] > 0 { bit |= 1 << i; } if d[i] > 0 { bit |= 1 << (i + c); } } let mut add = 0; for i in 0..c { if (bit >> i & 1) ^ (bit >> (i + c) & 1) == 1 { if i == 0 || (bit >> (i - 1) & 1) ^ (bit >> (i - 1 + c) & 1) == 0 { add += 1; } } } for i in 0..c { if (bit >> (i + c) & 1) ^ (bit >> (i + c + 1) & 1) == 1 { let mut cond = false; if i + 1 < c { cond = (bit >> i & 1) ^ (bit >> (c - 1).min(i + 1) & 1) == 0; } else { cond = (bit >> i) & 1 == 0; } if cond { add += 1; } } } if bit >> c & 1 == 1 && bit & 1 == 0 { add += 1; } trans[i].push((j, add)); } } } type Map = std::collections::BTreeMap<(usize, usize), M>; let mut map = Map::new(); let mut ans = M::zero(); for _ in 0..=r { let mut next = Map::new(); for ((key, cnt), val) in map { for &(u, add) in trans[key].iter() { if add + cnt <= n { *next.entry((u, add + cnt)).or_insert(M::zero()) += val; } } } for &(key, cnt) in trans[0].iter() { if key > 0 { *next.entry((key, cnt)).or_insert(M::zero()) += M::one(); } } map = next; for c in 0..=n { map.remove(&(0, c)).map(|p| { if c == n { ans += p; } }); } } println!("{}", ans); } fn main() { run(); }