結果
| 問題 | No.2907 Business Revealing Dora Tiles |
| ユーザー |
 maspy
|
| 提出日時 | 2024-09-27 21:26:30 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 27,072 bytes |
| コンパイル時間 | 5,314 ms |
| コンパイル使用メモリ | 312,488 KB |
| 実行使用メモリ | 13,760 KB |
| 最終ジャッジ日時 | 2024-09-27 21:26:45 |
| 合計ジャッジ時間 | 10,677 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 24 ms
13,760 KB |
| testcase_01 | AC | 25 ms
6,816 KB |
| testcase_02 | AC | 24 ms
6,944 KB |
| testcase_03 | AC | 26 ms
6,940 KB |
| testcase_04 | AC | 25 ms
6,944 KB |
| testcase_05 | AC | 24 ms
6,944 KB |
| testcase_06 | AC | 38 ms
6,944 KB |
| testcase_07 | AC | 23 ms
6,944 KB |
| testcase_08 | AC | 24 ms
6,940 KB |
| testcase_09 | AC | 24 ms
6,944 KB |
| testcase_10 | AC | 26 ms
6,944 KB |
| testcase_11 | AC | 212 ms
6,940 KB |
| testcase_12 | AC | 24 ms
6,944 KB |
| testcase_13 | AC | 24 ms
6,944 KB |
| testcase_14 | AC | 26 ms
6,944 KB |
| testcase_15 | AC | 27 ms
6,944 KB |
| testcase_16 | AC | 24 ms
6,944 KB |
| testcase_17 | AC | 25 ms
6,940 KB |
| testcase_18 | AC | 84 ms
6,944 KB |
| testcase_19 | AC | 24 ms
6,940 KB |
| testcase_20 | AC | 23 ms
6,940 KB |
| testcase_21 | AC | 392 ms
6,940 KB |
| testcase_22 | AC | 167 ms
6,940 KB |
| testcase_23 | TLE | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
| testcase_52 | -- | - |
| testcase_53 | -- | - |
| testcase_54 | -- | - |
| testcase_55 | -- | - |
| testcase_56 | -- | - |
| testcase_57 | -- | - |
| testcase_58 | -- | - |
| testcase_59 | -- | - |
ソースコード
#line 1 "/home/maspy/compro/library/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 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> = 1'010'000'000;
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 "/home/maspy/compro/library/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 3 "main.cpp"
#line 1 "/home/maspy/compro/library/other/mex.hpp"
int mex(const vc<int>& A) {
int n = len(A);
vc<bool> aru(n + 1);
for (auto& x: A)
if (x < n) aru[x] = 1;
int mex = 0;
while (aru[mex]) ++mex;
return mex;
}
#line 1 "/home/maspy/compro/library/nt/nim_product.hpp"
u64 naive_nim_product(u64 x, u64 y, int k = 6) {
if (x == 0 || y == 0) return 0;
if (x == 1) return y;
if (y == 1) return x;
int B = 1 << (k - 1);
u64 mask = (1ULL << B) - 1;
u64 a = x >> B, b = x & mask;
u64 c = y >> B, d = y & mask;
tie(a, b, c) = mt(naive_nim_product(a, c, k - 1),
naive_nim_product(a ^ b, c ^ d, k - 1),
naive_nim_product(b, d, k - 1));
b = a ^ b ^ c;
return (a << B) ^ naive_nim_product(1ULL << (B - 1), a, k - 1) ^ (b << B) ^ c;
}
u64 nim_product(u64 x, u64 y) {
static bool prepared = false;
// x * y, 256以下
// 2^a * 2^b * x, 8, 8, 256
static u64 memo1[256][256];
static u64 memo2[8][8][256];
if (!prepared) {
prepared = true;
FOR(x, 256) FOR(y, 256) memo1[x][y] = naive_nim_product(x, y, 4);
FOR(a, 8) FOR(b, 8) {
u64 v = naive_nim_product(1ULL << (8 * a), 1ULL << (8 * b));
FOR(x, 256) memo2[a][b][x] = naive_nim_product(v, x);
}
} // end prepare
u64 v = 0;
FOR(a, 8) FOR(b, 8) {
v ^= memo2[a][b][memo1[(x >> (8 * a)) & 255][(y >> (8 * b)) & 255]];
}
return v;
}
#line 1 "/home/maspy/compro/library/linalg/matrix_rank.hpp"
template <typename T>
int matrix_rank(vc<vc<T>> a, int n = -1, int m = -1) {
if (n == 0) return 0;
if (n == -1) { n = len(a), m = len(a[0]); }
assert(n == len(a) && m == len(a[0]));
int rk = 0;
FOR(j, m) {
if (rk == n) break;
if (a[rk][j] == 0) {
FOR(i, rk + 1, n) if (a[i][j] != T(0)) {
swap(a[rk], a[i]);
break;
}
}
if (a[rk][j] == 0) continue;
T c = T(1) / a[rk][j];
FOR(k, j, m) a[rk][k] *= c;
FOR(i, rk + 1, n) {
T c = a[i][j];
FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; }
}
++rk;
}
return rk;
}
#line 2 "/home/maspy/compro/library/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 "/home/maspy/compro/library/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 1 "/home/maspy/compro/library/linalg/transpose.hpp"
template <typename VC>
vc<VC> transpose(const vc<VC>& A, int H = -1, int W = -1) {
if (H == -1) { H = len(A), W = len(A[0]); }
vc<VC> B(W, VC(H, A[0][0]));
FOR(x, H) FOR(y, W) B[y][x] = A[x][y];
return B;
}
#line 1 "/home/maspy/compro/library/linalg/basis.hpp"
// basis[i]: i 番目に追加成功したもの. 別のラベルがあるなら外で管理する.
// rbasis: 上三角化された基底. [i][i]==1.
// way[i][j]: rbasis[i] = sum way[i][j] basis[j]
template <typename mint>
struct Basis {
int n, rank;
vvc<mint> basis;
vvc<mint> rbasis;
vvc<mint> way;
Basis(int max_dim) : n(max_dim), rank(0), basis{} {
rbasis.assign(max_dim, vc<mint>(max_dim));
way.assign(max_dim, vc<mint>(max_dim));
}
// return : (sum==X にできるか, その方法)
pair<bool, vc<mint>> solve(vc<mint> X) {
vc<mint> CF(n);
FOR(i, n) {
if (rbasis[i][i] == mint(1)) {
CF[i] = X[i];
FOR(j, i, n) X[j] -= CF[i] * rbasis[i][j];
}
}
for (auto& x: X) {
if (x != mint(0)) { return {false, {}}; }
}
vc<mint> ANS(rank);
FOR(i, n) { FOR(j, rank) ANS[j] += CF[i] * way[i][j]; }
return {true, ANS};
}
// return : (sum==x にできるか, その方法). false の場合には追加する
pair<bool, vc<mint>> solve_or_add(vc<mint> X) {
vc<mint> Y = X;
vc<mint> CF(n);
FOR(i, n) {
if (rbasis[i][i] == mint(1)) {
CF[i] = X[i];
FOR(j, i, n) X[j] -= CF[i] * rbasis[i][j];
}
}
int p = [&]() -> int {
FOR(i, n) if (X[i] != mint(0)) return i;
return -1;
}();
if (p == -1) {
vc<mint> ANS(rank);
FOR(i, n) { FOR(j, rank) ANS[j] += CF[i] * way[i][j]; }
return {true, ANS};
}
mint c = X[p].inverse();
FOR(j, p, n) X[j] *= c;
FOR(i, n) CF[i] *= c;
basis.eb(Y), rbasis[p] = X;
way[p][rank] = c;
FOR(i, n) { FOR(j, rank) way[p][j] -= CF[i] * way[i][j]; }
++rank;
return {false, {}};
}
// rank==r の時点まで戻す. Frobenius Form 用.
void rollback(int r) {
while (rank > r) {
--rank;
POP(basis);
FOR(i, n) if (way[i][rank] != mint(0)) {
fill(all(rbasis[i]), mint(0));
fill(all(way[i]), mint(0));
}
}
}
};
#line 10 "main.cpp"
/*
結局、表がひとつしかない場合のグランディーが知りたいということに
*/
void test() {
// int H = 4, W = 4;
// vc<int> MP(1 << 20);
// auto dfs = [&](auto& dfs, vvc<int> A) -> int {
// int k = 0;
// FOR(i, H) FOR(j, W) k |= 1 << (W * i + j);
// vc<int> TO;
// FOR(i, 1, H) FOR(j, 1, W) {
// if (A[i][j] == 0) continue;
// FOR(p, i) FOR(q, j) {
// vvc<int> B = A;
// B[p][q] ^= 1;
// B[p][j] ^= 1;
// B[i][q] ^= 1;
// B[i][j] ^= 1;
// TO.eb(dfs(dfs, B));
// }
// }
// return MP[k] = mex(TO);
// };
// vv(int, ANS, H, W);
// FOR(x, H) FOR(y, W) {
// vv(int, A, H, W);
// A[x][y] = 1;
// int ans = dfs(dfs, A);
// print(H, W, x, y, ans);
// flush();
// ANS[x][y] = ans;
// }
// FOR(x, H) print(ANS[x]);
int H = 16, W = 16;
vv(int, dp, H, W);
FOR(x, 1, H) FOR(y, 1, W) {
vc<int> TO;
FOR(a, x) FOR(b, y) { TO.eb(dp[a][y] ^ dp[x][b] ^ dp[a][b]); }
dp[x][y] = mex(TO);
}
FOR(x, H) print(dp[x]);
}
/*
nim product じゃないか！
入力に合わせると
G(x,y) = prod(x-1,y-1)
結局なにこれ？
sum H[i][j]W[j] == 0
つまり nim product field での連立方程式の解ということに
matrix rank
*/
struct F {
u64 val;
constexpr F(u64 x = 0) : val(x) {}
F &operator+=(const F &p) {
val ^= p.val;
return *this;
}
F &operator-=(const F &p) {
val ^= p.val;
return *this;
}
F &operator*=(const F &p) {
val = nim_product(val, p.val);
return *this;
}
F &operator/=(const F &p) {
*this *= p.inverse();
return *this;
}
F operator-() const { return *this; }
F operator+(const F &p) const { return F(*this) += p; }
F operator-(const F &p) const { return F(*this) -= p; }
F operator*(const F &p) const { return F(*this) *= p; }
F operator/(const F &p) const { return F(*this) /= p; }
bool operator==(const F &p) const { return val == p.val; }
bool operator!=(const F &p) const { return val != p.val; }
F inverse() const { return pow(u64(-2)); }
F pow(u64 n) const {
assert(n >= 0);
u64 ret = 1, mul = val;
while (n > 0) {
if (n & 1) ret = nim_product(ret, mul);
mul = nim_product(mul, mul);
n >>= 1;
}
return F(ret);
}
};
using V = array<F, 18>;
using MAT = array<array<F, 18>, 18>;
void add(MAT &B, V X) {
FOR(i, 18) {
if (B[i][i] == F(0)) {
if (X[i] == F(0)) continue;
F c = X[i].inverse();
X[i] = 1;
FOR(j, i + 1, 18) X[j] *= c;
B[i] = X;
}
F c = X[i];
X[i] = 0;
FOR(j, i + 1, 18) X[j] -= B[i][j] * c;
}
}
int basis_rank(MAT &B) {
int ans = 0;
FOR(i, 18) if (B[i][i] == F(1))++ ans;
return ans;
}
void solve() {
LL(W, H);
vv(F, A, H, W, F(0));
FOR(x, H) FOR(y, W) {
U64(w);
A[x][y] = F(w - 1);
}
// ll r = matrix_rank<F>(mat);
// N 変数
// 自由度
/*
連立方程式の解なのだが、どの成分も 0 ではないという条件がつく！！！
雑な方法：すべての subset で求めて包除する
適当な列集合だけとりだしたときのランクということに？
*/
int N = W;
A = transpose(A);
vc<V> rows(N);
FOR(i, N) { FOR(j, H) rows[i][j] = A[i][j]; }
using mint = modint998;
mint ans = 0;
auto dfs = [&](auto &dfs, int s, int k, MAT basis) -> void {
if (k == N) {
ll r = basis_rank(basis);
ll n = popcnt(s) - r;
mint x = mint(2).pow(64 * n);
if ((N - popcnt(s)) % 2 == 0) {
ans += x;
} else {
ans -= x;
}
return;
}
dfs(dfs, s, k + 1, basis);
add(basis, rows[k]);
dfs(dfs, s | 1 << k, k + 1, basis);
};
MAT basis{};
dfs(dfs, 0, 0, basis);
print(ans);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}