結果

問題 No.1397 Analog Graffiti
ユーザー maspy
提出日時 2022-10-24 21:02:39
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 13 ms / 10,000 ms
コード長 30,360 bytes
コンパイル時間 4,626 ms
コンパイル使用メモリ 268,176 KB
最終ジャッジ日時 2025-02-08 12:21:19
ジャッジサーバーID
（参考情報） 		judge4 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 24
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ソースコード

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プレゼンテーションモードにする

#line 1 "/home/maspy/compro/library/my_template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
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 vec(type, name, ...) vector<type> name(__VA_ARGS__)
#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 FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
  overload4(__VA_ARGS__, FOR4_R, 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
template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}
#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())
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); }
// (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 pick(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T pick(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T pick(pqg<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T pick(vc<T> &que) {
  assert(que.size());
  T a = que.back();
  que.pop_back();
  return a;
}
template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}
template <typename F>
ll binary_search(F check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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);
}
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  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;
}
template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}
// stable
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(A.size());
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
  return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  int n = len(I);
  vc<T> B(n);
  FOR(i, n) B[i] = A[I[i]];
  return B;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail
template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;
struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <class T, is_modint_t<T> * = nullptr>
  bool read_single(T &ref) {
    long long val = 0;
    bool f = read_single(val);
    ref = T(val);
    return f;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <class A, class B, class C>
  bool read_single(tuple<A, B, C> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)));
  }
  template <class A, class B, class C, class D>
  bool read_single(tuple<A, B, C, D> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)) && read_single(get<3>(p)));
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }
  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char &val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string &s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double &x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double &x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <class T, is_modint_t<T> * = nullptr>
  void write(T &ref) {
    write(ref.val);
  }
  template <class T>
  void write(const vector<T> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> &val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <class A, class B, class C>
  void write(const tuple<A, B, C> &val) {
    auto &[a, b, c] = val;
    write(a), write(' '), write(b), write(' '), write(c);
  }
  template <class A, class B, class C, class D>
  void write(const tuple<A, B, C, D> &val) {
    auto &[a, b, c, d] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);
  }
  template <class A, class B, class C, class D, class E>
  void write(const tuple<A, B, C, D, E> &val) {
    auto &[a, b, c, d, e] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
  }
  template <class A, class B, class C, class D, class E, class F>
  void write(const tuple<A, B, C, D, E, F> &val) {
    auto &[a, b, c, d, e, f] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
  }
  template <class T, size_t S>
  void write(const array<T, S> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if(val < 0){
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if(negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __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 "/home/maspy/compro/library/ds/hashmap.hpp"
template <typename Val, int LOG = 20>
struct HashMapLL {
  int N;
  ll* keys;
  Val* vals;
  vc<int> IDS;
  bitset<1 << LOG> used;
  const int shift;
  const uint64_t r = 11995408973635179863ULL;
  HashMapLL()
      : N(1 << LOG), keys(new ll[N]), vals(new Val[N]), shift(64 - __lg(N)) {}
  int hash(ll x) {
    static const uint64_t FIXED_RANDOM
        = std::chrono::steady_clock::now().time_since_epoch().count();
    return (uint64_t(x + FIXED_RANDOM) * r) >> shift;
  }
  int index(const ll& key) {
    int i = 0;
    for (i = hash(key); used[i] && keys[i] != key; (i += 1) &= (N - 1)) {}
    return i;
  }
  Val& operator[](const ll& key) {
    int i = index(key);
    if (!used[i]) IDS.eb(i), used[i] = 1, keys[i] = key, vals[i] = Val{};
    return vals[i];
  }
  Val get(const ll& key, Val default_value) {
    int i = index(key);
    if (!used[i]) return default_value;
    return vals[i];
  }
  bool contain(const ll& key) {
    int i = index(key);
    return used[i] && keys[i] == key;
  }
  bool count(const ll& key) {
    int i = index(key);
    return used[i] && keys[i] == key;
  }
  void reset() {
    for (auto&& i: IDS) used[i] = 0;
    IDS.clear();
  }
  vc<pair<ll, Val>> items() {
    vc<pair<ll, Val>> res;
    res.reserve(len(IDS));
    for (auto&& i: IDS) res.eb(keys[i], vals[i]);
    return res;
  }
};
template <typename KEY, typename VAL, int LOG>
struct HashMap {
  HashMapLL<VAL, LOG> MP;
  function<ll(KEY)> f;
  HashMap(function<ll(KEY)> f) : MP(), f(f) {}
  int index(const KEY& key) { return MP.index(f(key)); }
  VAL& operator[](const KEY& key) { return MP[f(key)]; }
  bool contain(const KEY& key) { return MP.contain(f(key)); }
  bool count(const KEY& key) { return MP.count(f(key)); }
  void reset() { MP.reset(); }
};
#line 2 "/home/maspy/compro/library/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 "/home/maspy/compro/library/mod/modint61.hpp"
struct modint61 {
  static constexpr bool is_modint = true;
  static constexpr ll mod = (1LL << 61) - 1;
  ll val;
  constexpr modint61(const ll x = 0) : val(x) {
    while(val < 0) val += mod;
    while(val >= mod) val -= mod;
  }
  bool operator<(const modint61 &other) const {
    return val < other.val;
  } // To use std::map
  bool operator==(const modint61 &p) const { return val == p.val; }
  bool operator!=(const modint61 &p) const { return val != p.val; }
  modint61 &operator+=(const modint61 &p) {
    if ((val += p.val) >= mod) val -= mod;
    return *this;
  }
  modint61 &operator-=(const modint61 &p) {
    if ((val += mod - p.val) >= mod) val -= mod;
    return *this;
  }
  modint61 &operator*=(const modint61 &p) {
    ll a = val, b = p.val;
    const ll MASK30 = (1LL << 30) - 1;
    const ll MASK31 = (1LL << 31) - 1;
    const ll MASK61 = (1LL << 61) - 1;
    ll au = a >> 31, ad = a & MASK31;
    ll bu = b >> 31, bd = b & MASK31;
    ll x = ad * bu + au * bd;
    ll xu = x >> 30, xd = x & MASK30;
    x = au * bu * 2 + xu + (xd << 31) + ad * bd;
    xu = x >> 61, xd = x & MASK61;
    x = xu + xd;
    if (x >= MASK61) x -= MASK61;
    val = x;
    return *this;
  }
  modint61 operator-() const { return modint61(get_mod() - val); }
  modint61 &operator/=(const modint61 &p) {
    *this *= p.inverse();
    return *this;
  }
  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; }
  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(int64_t n) const {
    modint61 ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret = ret * mul;
      mul = mul * mul;
      n >>= 1;
    }
    return ret;
  }
  static constexpr ll get_mod() { return mod; }
};
#line 3 "/home/maspy/compro/library/random/hash_vector.hpp"
template <typename T>
ll 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 "/home/maspy/compro/library/connected_dp/squares.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。多角形とは限らない。
pair<vvc<int>, vc<pair<int, int>>> connedted_dp_graph(int N,
                                                      bool merge_reverse) {
  static HashMapLL<int> 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;
      }
      ll 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};
}
} // namespace connected_dp_squares
#line 2 "/home/maspy/compro/library/mod/modint.hpp"
template <int mod>
struct modint {
  static constexpr bool is_modint = true;
  int val;
  constexpr modint(const ll val = 0) noexcept
      : val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}
  bool operator<(const modint &other) const {
    return val < other.val;
  } // To use std::map
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= mod) val -= mod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += mod - p.val) >= mod) val -= mod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = (int)(1LL * val * p.val % mod);
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint(-val); }
  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(int64_t n) const {
    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; }
};
struct ArbitraryModInt {
  static constexpr bool is_modint = true;
  int val;
  ArbitraryModInt() : val(0) {}
  ArbitraryModInt(int64_t y)
      : val(y >= 0 ? y % get_mod()
                   : (get_mod() - (-y) % get_mod()) % get_mod()) {}
  bool operator<(const ArbitraryModInt &other) const {
    return val < other.val;
  } // To use std::map<ArbitraryModInt, T>
  static int &get_mod() {
    static int mod = 0;
    return mod;
  }
  static void set_mod(int md) { get_mod() = md; }
  ArbitraryModInt &operator+=(const ArbitraryModInt &p) {
    if ((val += p.val) >= get_mod()) val -= get_mod();
    return *this;
  }
  ArbitraryModInt &operator-=(const ArbitraryModInt &p) {
    if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();
    return *this;
  }
  ArbitraryModInt &operator*=(const ArbitraryModInt &p) {
    long long a = (long long)val * p.val;
    int xh = (int)(a >> 32), xl = (int)a, d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));
    val = m;
    return *this;
  }
  ArbitraryModInt &operator/=(const ArbitraryModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }
  ArbitraryModInt operator+(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) += p;
  }
  ArbitraryModInt operator-(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) -= p;
  }
  ArbitraryModInt operator*(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) *= p;
  }
  ArbitraryModInt operator/(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) /= p;
  }
  bool operator==(const ArbitraryModInt &p) const { return val == p.val; }
  bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }
  ArbitraryModInt inverse() const {
    int a = val, b = get_mod(), u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return ArbitraryModInt(u);
  }
  ArbitraryModInt pow(int64_t n) const {
    ArbitraryModInt ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
};
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 (int(dat.size()) <= n) {
    int k = dat.size();
    auto q = (mod + k - 1) / k;
    int r = k * q - mod;
    dat.emplace_back(dat[r] * mint(q));
  }
  return dat[n];
}
template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {1, 1};
  assert(0 <= n);
  if (n >= mod) return 0;
  while (int(dat.size()) <= n) {
    int k = dat.size();
    dat.emplace_back(dat[k - 1] * mint(k));
  }
  return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {1, 1};
  assert(0 <= n && n < mod);
  while (int(dat.size()) <= n) {
    int k = dat.size();
    dat.emplace_back(dat[k - 1] * inv<mint>(k));
  }
  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 (dense) return C_dense<mint>(n, k);
  if (!large) return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) { x *= mint(n - i); }
  x *= fact_inv<mint>(k);
  return x;
}
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} の計算
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);
}
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
using amint = ArbitraryModInt;
#line 5 "main.cpp"
using mint = modint998;
pair<vvc<int>, vc<pair<int, int>>> polygon_dp_graph(int N) {
  static HashMapLL<int> 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]: connected_dp_squares::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 = [&]() -> 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;
      }();
      if (!ok) continue;
      ll h = hash_vector<int>(nxt);
      if (!MP.count(h)) {
        MP[h] = len(states);
        states.eb(nxt);
      }
      edges.eb(p, MP[h]);
    }
  }
  return {states, edges};
}
void solve() {
  LL(W, H, N);
  if (N % 2 != 0) return print(0);
  auto [states, edges] = 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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