library

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:heavy_check_mark: test/yukicoder/1397.test.cpp

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/no/1397"
#include "my_template.hpp"
#include "other/io.hpp"
#include "other/connected_dp.hpp"
#include "mod/modint.hpp"

using mint = modint998;

void solve() {
  LL(W, H, N);
  if (N % 2 != 0) return print(0);
  auto [states, edges] = connected_dp_squares::polygon_dp_graph(H);
  const int S = len(states);
  const int E = len(edges);
  vc<int> count_line(E);
  FOR(e, E) {
    auto& now = states[edges[e].fi];
    auto& nxt = states[edges[e].se];
    vc<bool> A(H + 1), B(H + 1);
    FOR(i, -1, H) {
      int j = i + 1;
      bool a1 = (i == -1 ? 0 : now[i] != -1);
      bool a2 = (j == H ? 0 : now[j] != -1);
      A[j] = a1 != a2;
      bool b1 = (i == -1 ? 0 : nxt[i] != -1);
      bool b2 = (j == H ? 0 : nxt[j] != -1);
      B[j] = b1 != b2;
    }
    int x = 0;
    FOR(i, H + 1) if (!A[i] && B[i])++ x;
    count_line[e] = x;
  }

  // print(S, E);
  // state, horizonal edges
  vv(mint, dp, S, N / 2 + 1);
  dp[0][0] = 1;
  FOR(W + 1) {
    vv(mint, newdp, S, N / 2 + 1);
    FOR(e, E) {
      auto [a, b] = edges[e];
      int k = count_line[e];
      FOR(n, N / 2 - k + 1) newdp[b][n + k] += dp[a][n];
    }
    swap(dp, newdp);
  }
  print(dp[1][N / 2]);
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}
#line 1 "test/yukicoder/1397.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1397"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.

void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio

using fastio::read;
using fastio::print;
using fastio::flush;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "ds/hashmap.hpp"

// u64 -> Val

template <typename Val, int LOG = 20, bool KEEP_IDS = false>
struct HashMap {
  static constexpr int N = (1 << LOG);
  u64* key;
  Val* val;
  vc<int> IDS;
  bitset<N> used;
  const int shift;
  const u64 r = 11995408973635179863ULL;
  HashMap() : key(new u64[N]), val(new Val[N]), shift(64 - LOG) {}
  u32 hash(u64 x) {
    static const u64 FIXED_RANDOM
        = std::chrono::steady_clock::now().time_since_epoch().count();
    return (u64(x + FIXED_RANDOM) * r) >> shift;
  }

  int index(const u64& k) {
    int i = 0;
    for (i = hash(k); used[i] && key[i] != k; (i += 1) &= (N - 1)) {}
    return i;
  }

  Val& operator[](const u64& k) {
    int i = index(k);
    if (!used[i]) {
      used[i] = 1, key[i] = k, val[i] = Val{};
      if constexpr (KEEP_IDS) IDS.eb(i);
    }
    return val[i];
  }

  Val get(const u64& k, Val default_value) {
    int i = index(k);
    if (!used[i]) return default_value;
    return val[i];
  }

  bool count(const u64& k) {
    int i = index(k);
    return used[i] && key[i] == k;
  }

  void reset() {
    static_assert(KEEP_IDS);
    for (auto&& i: IDS) used[i] = 0;
    IDS.clear();
  }

  // f(key, val)

  template <typename F>
  void enumerate_all(F f) {
    static_assert(KEEP_IDS);
    for (auto&& i: IDS) f(key[i], val[i]);
  }
};
#line 2 "random/hash_vector.hpp"

#line 2 "random/base.hpp"

u64 RNG_64() {
  static uint64_t x_
      = uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                     chrono::high_resolution_clock::now().time_since_epoch())
                     .count())
        * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "mod/modint61.hpp"

struct modint61 {
  static constexpr u64 mod = (1ULL << 61) - 1;
  u64 val;
  constexpr modint61() : val(0ULL) {}
  constexpr modint61(u32 x) : val(x) {}
  constexpr modint61(u64 x) : val(x % mod) {}
  constexpr modint61(int x) : val((x < 0) ? (x + static_cast<ll>(mod)) : x) {}
  constexpr modint61(ll x)
      : val(((x %= static_cast<ll>(mod)) < 0) ? (x + static_cast<ll>(mod))
                                              : x) {}
  static constexpr u64 get_mod() { return mod; }
  modint61 &operator+=(const modint61 &a) {
    val = ((val += a.val) >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 &operator-=(const modint61 &a) {
    val = ((val -= a.val) >= mod) ? (val + mod) : val;
    return *this;
  }
  modint61 &operator*=(const modint61 &a) {
    const unsigned __int128 y = static_cast<unsigned __int128>(val) * a.val;
    val = (y >> 61) + (y & mod);
    val = (val >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 &operator/=(const modint61 &a) { return (*this *= a.inverse()); }
  modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }
  modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }
  modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }
  modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }
  bool operator==(const modint61 &p) const { return val == p.val; }
  bool operator!=(const modint61 &p) const { return val != p.val; }
  modint61 inverse() const {
    ll a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint61(u);
  }
  modint61 pow(ll n) const {
    assert(n >= 0);
    modint61 ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul, n >>= 1;
    }
    return ret;
  }
};

#ifdef FASTIO
void rd(modint61 &x) {
  fastio::rd(x.val);
  assert(0 <= x.val && x.val < modint61::mod);
}

void wt(modint61 x) { fastio::wt(x.val); }
#endif
#line 5 "random/hash_vector.hpp"

template <typename T>
u64 hash_vector(vc<T> X) {
  using mint = modint61;
  static vc<mint> hash_base;
  int n = len(X);
  while (len(hash_base) <= n) { hash_base.eb(RNG(mint::get_mod())); }
  mint H = 0;
  FOR(i, n) H += hash_base[i] * mint(X[i]);
  H += hash_base[n];
  return H.val;
}
#line 3 "other/connected_dp.hpp"

namespace connected_dp_squares {
// pair<新しい状態、今の成分 → 新しい成分>
vc<pair<vc<int>, vc<int>>> next_states(const vc<int>& now) {
  int N = len(now);
  vc<pair<vc<int>, vc<int>>> res;
  FOR(s, 1 << N) {
    vc<int> par(N + N);
    FOR(i, N) par[i] = (s & 1 << i ? i : -1);
    FOR(i, N) par[N + i] = (now[i] == -1 ? -1 : now[i] + N);
    auto find = [&](int x) -> int {
      while (par[x] != x) { x = par[x] = par[par[x]]; }
      return x;
    };
    auto merge = [&](int a, int b) -> void {
      a = find(a), b = find(b);
      if (a == b) return;
      if (a > b) swap(a, b);
      par[b] = a;
    };

    FOR(i, N - 1) if (par[i] != -1 && par[i + 1] != -1) merge(i, i + 1);
    FOR(i, N) if (par[i] != -1 && par[N + i] != -1) merge(i, N + i);
    FOR(i, N + N) if (par[i] != -1) par[i] = find(i);
    FOR(i, N, N + N) if (par[i] >= N) par[i] = -1;
    res.eb(vc<int>(par.begin(), par.begin() + N),
           vc<int>(par.begin() + N, par.end()));
  }
  return res;
}

vc<int> reverse_state(const vc<int>& now) {
  int N = len(now);
  vc<int> max_i(N, -1);
  FOR(i, N) if (now[i] != -1) max_i[now[i]] = i;
  vc<int> rev(N, -1);
  FOR(i, N) {
    if (now[i] == -1) continue;
    int x = max_i[now[i]];
    rev[N - 1 - i] = N - 1 - x;
  }
  return rev;
}

// 0, 1 :空の列、領域の手前、後ろ
// 連結領域をひとつ作る。
// 状態:-1 が選んでいない。0,1,2,3 等は同じ成分には同じ値が入る。
// [states, edges]
pair<vvc<int>, vc<pair<int, int>>> connedted_dp_graph(int N,
                                                      bool merge_reverse) {
  static HashMap<int, 20, true> MP;
  MP.reset();
  vvc<int> states;
  vc<pair<int, int>> edges;

  states.eb(vc<int>(N, -1));
  states.eb(vc<int>(N, -1));
  MP[hash_vector<int>(states[0])] = 0;

  int p = -1;
  while (1) {
    if (++p == len(states)) break;
    if (p == 1) {
      edges.eb(1, 1);
      continue;
    }
    vc<int> now = states[p];
    for (auto&& [nxt, convert]: next_states(now)) {
      // 今の成分数、消える成分数
      int a = 0, b = 0;
      FOR(v, N) if (now[v] == v) {
        ++a;
        if (convert[v] == -1) ++b;
      }
      // 消える成分があってよいのは、終状態にいくときのみ
      if (b >= 2) continue;
      if (b == 1) {
        if (MAX(nxt) != -1) continue;
        edges.eb(p, 1);
        continue;
      }
      u64 h = hash_vector<int>(nxt);
      if (merge_reverse) { chmin(h, hash_vector<int>(reverse_state(nxt))); }
      if (!MP.count(h)) { MP[h] = len(states), states.eb(nxt); }
      edges.eb(p, MP[h]);
    }
  }
  return {states, edges};
}

// 0, 1 :空の列、領域の手前、後ろ
// 多角形(空洞なし)をひとつ作る。
// 状態:-1 が選んでいない。0,1,2,3 等は同じ成分には同じ値が入る。
// [states, edges]
pair<vvc<int>, vc<pair<int, int>>> polygon_dp_graph(int N) {
  static HashMap<int, 20, true> MP;
  MP.reset();
  vvc<int> states;
  vc<pair<int, int>> edges;

  states.eb(vc<int>(N, -1));
  states.eb(vc<int>(N, -1));
  MP[hash_vector<int>(states[0])] = 0;

  int p = -1;
  while (1) {
    if (++p == len(states)) break;
    if (p == 1) {
      edges.eb(1, 1);
      continue;
    }
    vc<int> now = states[p];
    for (auto&& [nxt, convert]: next_states(now)) {
      // 今の成分数、消える成分数
      int a = 0, b = 0;
      FOR(v, N) if (now[v] == v) {
        ++a;
        if (convert[v] == -1) ++b;
      }
      // 消える成分があってよいのは、終状態にいくときのみ
      if (b >= 2) continue;
      if (b == 1) {
        if (MAX(nxt) != -1) continue;
        edges.eb(p, 1);
        continue;
      }
      bool ok = [&](vc<int>& now, vc<int>& nxt, vc<int>& convert) -> bool {
        // 頂点のみで接するのはダメ
        FOR(i, N - 1) {
          bool a1 = now[i] != -1, a2 = now[i + 1] != -1;
          bool b1 = nxt[i] != -1, b2 = nxt[i + 1] != -1;
          if (a1 && !a2 && !b1 && b2) return false;
          if (!a1 && a2 && b1 && !b2) return false;
        }
        // empty region を閉じることと、異なる連結成分がマージされることが同値
        int close = 0;
        int after = 0;
        vc<bool> is_new(N, 1);
        FOR(i, N) if (convert[i] != -1) is_new[convert[i]] = 0;
        FOR(i, N) if (nxt[i] == i && !is_new[i])++ after;
        vc<int> I;
        FOR(i, N) if (now[i] != -1) I.eb(i);
        FOR(k, len(I) - 1) {
          int i = I[k], j = I[k + 1];
          if (j == i + 1) continue;
          bool cl = 1;
          FOR(p, i + 1, j) if (nxt[p] == -1) cl = 0;
          if (cl) close++;
        }
        return a - close == after;
      }(now, nxt, convert);
      if (!ok) continue;
      u64 h = hash_vector<int>(nxt);
      int idx = MP.index(h);
      if (!MP.used[idx]) {
        MP.used[idx] = 1, MP.IDS.eb(idx), MP.key[idx] = h,
        MP.val[idx] = len(states);
        states.eb(nxt);
      }
      edges.eb(p, MP.val[idx]);
    }
  }
  return {states, edges};
}

} // namespace connected_dp_squares
#line 2 "mod/modint_common.hpp"

struct has_mod_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {0, 1};
  assert(0 <= n);
  if (n >= mod) n %= mod;
  while (len(dat) <= n) {
    int k = len(dat);
    int q = (mod + k - 1) / k;
    dat.eb(dat[k * q - mod] * mint::raw(q));
  }
  return dat[n];
}

template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  assert(0 <= n && n < mod);
  static vector<mint> dat = {1, 1};
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
  return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
  return dat[n];
}

template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
  return (mint(1) * ... * fact_inv<mint>(xs));
}

template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
  return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}

template <typename mint>
mint C_dense(int n, int k) {
  static vvc<mint> C;
  static int H = 0, W = 0;
  auto calc = [&](int i, int j) -> mint {
    if (i == 0) return (j == 0 ? mint(1) : mint(0));
    return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
  };
  if (W <= k) {
    FOR(i, H) {
      C[i].resize(k + 1);
      FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    FOR(i, H, n + 1) {
      C[i].resize(W);
      FOR(j, W) { C[i][j] = calc(i, j); }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  if constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (!large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
  assert(n >= 0);
  assert(0 <= k && k <= n);
  if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / C<mint, 1>(n, k);
}

// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
  assert(n >= 0);
  if (d < 0) return mint(0);
  if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
  return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "mod/modint.hpp"

template <int mod>
struct modint {
  static constexpr u32 umod = u32(mod);
  static_assert(umod < u32(1) << 31);
  u32 val;

  static modint raw(u32 v) {
    modint x;
    x.val = v;
    return x;
  }
  constexpr modint() : val(0) {}
  constexpr modint(u32 x) : val(x % umod) {}
  constexpr modint(u64 x) : val(x % umod) {}
  constexpr modint(u128 x) : val(x % umod) {}
  constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
  bool operator<(const modint &other) const { return val < other.val; }
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += umod - p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = u64(val) * p.val % umod;
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
  modint operator+(const modint &p) const { return modint(*this) += p; }
  modint operator-(const modint &p) const { return modint(*this) -= p; }
  modint operator*(const modint &p) const { return modint(*this) *= p; }
  modint operator/(const modint &p) const { return modint(*this) /= p; }
  bool operator==(const modint &p) const { return val == p.val; }
  bool operator!=(const modint &p) const { return val != p.val; }
  modint inverse() const {
    int a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint(u);
  }
  modint pow(ll n) const {
    assert(n >= 0);
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  static constexpr int get_mod() { return mod; }
  // (n, r), r は 1 の 2^n 乗根
  static constexpr pair<int, int> ntt_info() {
    if (mod == 120586241) return {20, 74066978};
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 880803841) return {23, 211};
    if (mod == 943718401) return {22, 663003469};
    if (mod == 998244353) return {23, 31};
    if (mod == 1045430273) return {20, 363};
    if (mod == 1051721729) return {20, 330};
    if (mod == 1053818881) return {20, 2789};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
  fastio::rd(x.val);
  x.val %= mod;
  // assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
  fastio::wt(x.val);
}
#endif

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 6 "test/yukicoder/1397.test.cpp"

using mint = modint998;

void solve() {
  LL(W, H, N);
  if (N % 2 != 0) return print(0);
  auto [states, edges] = connected_dp_squares::polygon_dp_graph(H);
  const int S = len(states);
  const int E = len(edges);
  vc<int> count_line(E);
  FOR(e, E) {
    auto& now = states[edges[e].fi];
    auto& nxt = states[edges[e].se];
    vc<bool> A(H + 1), B(H + 1);
    FOR(i, -1, H) {
      int j = i + 1;
      bool a1 = (i == -1 ? 0 : now[i] != -1);
      bool a2 = (j == H ? 0 : now[j] != -1);
      A[j] = a1 != a2;
      bool b1 = (i == -1 ? 0 : nxt[i] != -1);
      bool b2 = (j == H ? 0 : nxt[j] != -1);
      B[j] = b1 != b2;
    }
    int x = 0;
    FOR(i, H + 1) if (!A[i] && B[i])++ x;
    count_line[e] = x;
  }

  // print(S, E);
  // state, horizonal edges
  vv(mint, dp, S, N / 2 + 1);
  dp[0][0] = 1;
  FOR(W + 1) {
    vv(mint, newdp, S, N / 2 + 1);
    FOR(e, E) {
      auto [a, b] = edges[e];
      int k = count_line[e];
      FOR(n, N / 2 - k + 1) newdp[b][n + k] += dp[a][n];
    }
    swap(dp, newdp);
  }
  print(dp[1][N / 2]);
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}
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