library
This documentation is automatically generated by online-judge-tools/verification-helper
test/3_yukicoder/1397.test.cpp
- View this file on GitHub
- Last update: 2024-09-28 04:06:11+09:00
- Problem: https://yukicoder.me/problems/no/1397
Depends on
ds/hashmap.hpp
- mod/modint.hpp
- mod/modint61.hpp
- mod/modint_common.hpp
- my_template.hpp
- other/connected_dp.hpp
- other/io.hpp
- random/base.hpp
- random/hash_vector.hpp
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/3_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
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
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;
}
template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
vc<T> &res = first;
(res.insert(res.end(), others.begin(), others.end()), ...);
}
#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;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif
#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>
struct HashMap {
// n は入れたいものの個数で ok
HashMap(u32 n = 0) { build(n); }
void build(u32 n) {
u32 k = 8;
while (k < n * 2) k *= 2;
cap = k / 2, mask = k - 1;
key.resize(k), val.resize(k), used.assign(k, 0);
}
// size を保ったまま. size=0 にするときは build すること.
void clear() {
used.assign(len(used), 0);
cap = (mask + 1) / 2;
}
int size() { return len(used) / 2 - cap; }
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
return i;
}
Val& operator[](const u64& k) {
if (cap == 0) extend();
int i = index(k);
if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
return (used[i] ? val[i] : default_value);
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
}
private:
u32 cap, mask;
vc<u64> key;
vc<Val> val;
vc<bool> used;
u64 hash(u64 x) {
static const u64 FIXED_RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
x += FIXED_RANDOM;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return (x ^ (x >> 31)) & mask;
}
void extend() {
vc<pair<u64, Val>> dat;
dat.reserve(len(used) / 2 - cap);
FOR(i, len(used)) {
if (used[i]) dat.eb(key[i], val[i]);
}
build(2 * len(dat));
for (auto& [a, b]: dat) (*this)[a] = b;
}
};
#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 { return modint61(val ? mod - val : u64(0)); }
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 &other) const { return val < other.val; }
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"
// dot case: https://atcoder.jp/contests/ttpc2023/submissions/57905985
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) {
HashMap<int> MP;
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) {
HashMap<int> MP;
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);
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 "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 == 1004535809) return {21, 836905998};
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/3_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;
}