結果
問題 | No.2907 Business Revealing Dora Tiles |
ユーザー | maspy |
提出日時 | 2024-09-27 21:29:55 |
言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 2,276 ms / 3,000 ms |
コード長 | 28,005 bytes |
コンパイル時間 | 4,808 ms |
コンパイル使用メモリ | 308,264 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-09-27 21:30:45 |
合計ジャッジ時間 | 46,960 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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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 | 3 ms
6,816 KB |
testcase_01 | AC | 4 ms
6,940 KB |
testcase_02 | AC | 3 ms
6,944 KB |
testcase_03 | AC | 4 ms
6,944 KB |
testcase_04 | AC | 4 ms
6,944 KB |
testcase_05 | AC | 4 ms
6,940 KB |
testcase_06 | AC | 10 ms
6,940 KB |
testcase_07 | AC | 3 ms
6,940 KB |
testcase_08 | AC | 4 ms
6,944 KB |
testcase_09 | AC | 4 ms
6,940 KB |
testcase_10 | AC | 3 ms
6,940 KB |
testcase_11 | AC | 84 ms
6,940 KB |
testcase_12 | AC | 3 ms
6,944 KB |
testcase_13 | AC | 3 ms
6,940 KB |
testcase_14 | AC | 4 ms
6,944 KB |
testcase_15 | AC | 5 ms
6,940 KB |
testcase_16 | AC | 3 ms
6,944 KB |
testcase_17 | AC | 3 ms
6,940 KB |
testcase_18 | AC | 29 ms
6,940 KB |
testcase_19 | AC | 4 ms
6,940 KB |
testcase_20 | AC | 3 ms
6,940 KB |
testcase_21 | AC | 135 ms
6,944 KB |
testcase_22 | AC | 68 ms
6,944 KB |
testcase_23 | AC | 2,276 ms
6,940 KB |
testcase_24 | AC | 973 ms
6,944 KB |
testcase_25 | AC | 941 ms
6,940 KB |
testcase_26 | AC | 991 ms
6,940 KB |
testcase_27 | AC | 954 ms
6,944 KB |
testcase_28 | AC | 961 ms
6,944 KB |
testcase_29 | AC | 930 ms
6,944 KB |
testcase_30 | AC | 971 ms
6,940 KB |
testcase_31 | AC | 950 ms
6,940 KB |
testcase_32 | AC | 959 ms
6,940 KB |
testcase_33 | AC | 976 ms
6,944 KB |
testcase_34 | AC | 936 ms
6,940 KB |
testcase_35 | AC | 950 ms
6,940 KB |
testcase_36 | AC | 956 ms
6,940 KB |
testcase_37 | AC | 924 ms
6,944 KB |
testcase_38 | AC | 915 ms
6,940 KB |
testcase_39 | AC | 960 ms
6,944 KB |
testcase_40 | AC | 935 ms
6,944 KB |
testcase_41 | AC | 931 ms
6,940 KB |
testcase_42 | AC | 931 ms
6,940 KB |
testcase_43 | AC | 933 ms
6,944 KB |
testcase_44 | AC | 1,596 ms
6,944 KB |
testcase_45 | AC | 1,488 ms
6,944 KB |
testcase_46 | AC | 1,805 ms
6,940 KB |
testcase_47 | AC | 860 ms
6,944 KB |
testcase_48 | AC | 1,273 ms
6,944 KB |
testcase_49 | AC | 1,766 ms
6,940 KB |
testcase_50 | AC | 1,021 ms
6,944 KB |
testcase_51 | AC | 130 ms
6,944 KB |
testcase_52 | AC | 945 ms
6,944 KB |
testcase_53 | AC | 1,119 ms
6,944 KB |
testcase_54 | AC | 1,456 ms
6,944 KB |
testcase_55 | AC | 1,136 ms
6,940 KB |
testcase_56 | AC | 1,108 ms
6,944 KB |
testcase_57 | AC | 1,124 ms
6,940 KB |
testcase_58 | AC | 955 ms
6,940 KB |
testcase_59 | AC | 1,252 ms
6,940 KB |
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 5 "main.cpp" // #include "nt/nim_product.hpp" #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" // https://judge.yosupo.jp/submission/153427 #define ctz32(a) ((a) ? __builtin_ctz((a)) : (32)) typedef uint16_t u16; static const u32 nf[16] = {0x0001u, 0x071cu, 0x6bd1u, 0x1224u, 0x6ba8u, 0x1333u, 0x1553u, 0x0007u, 0x071eu, 0x0925u, 0xc586u, 0x5dbdu, 0xc463u, 0x5efdu, 0x2aa1u, 0x155au}; static const u32 fn[16] = {0x0001u, 0x0102u, 0x0183u, 0x8041u, 0x015cu, 0x5f24u, 0xde2cu, 0x957eu, 0x01f4u, 0xf7d8u, 0x76b0u, 0x5d52u, 0xa977u, 0x20d1u, 0xc1a4u, 0x271fu}; static inline u32 to_field(u32 x) { u32 y = 0; for (; x; x &= x - 1) y ^= nf[ctz32(x)]; return y; } static inline u32 to_nimber(u32 x) { u32 y = 0; for (; x; x &= x - 1) y ^= fn[ctz32(x)]; return y; } static inline u32 to_double(u32 x) { return x << 1 ^ (x < 32768 ? 0 : 93099U); } u16 ln[65536]; u16 expo[196605]; u16 *Hexpo = expo + 62133; u16 *H2expo = expo + 58731; __attribute__((constructor)) void _construct_nimber_product_() { *expo = 1; for (int i = 1; i < 65535; ++i) expo[i] = to_double(expo[i - 1]); for (int i = 1; i < 65535; ++i) { expo[i] = to_nimber(expo[i]); ln[expo[i]] = i; } memcpy(expo + 65535, expo, 131070); memcpy(expo + 131070, expo, 131070); } u16 product_16(u16 A, u16 B) { return A && B ? expo[ln[A] + ln[B]] : 0; } u16 H_16(u16 A) { return A ? Hexpo[ln[A]] : 0; } u16 H2_16(u16 A) { return A ? H2expo[ln[A]] : 0; } u16 Hproduct_16(u16 A, u16 B) { return A && B ? Hexpo[ln[A] + ln[B]] : 0; } u32 product_32(u32 A, u32 B) { u16 a = A & 65535; u16 b = B & 65535; u16 c = A >> 16; u16 d = B >> 16; u16 e = product_16(a, b); return (u32)(product_16((u16)(a ^ c), (u16)(b ^ d)) ^ e) << 16 | (Hproduct_16(c, d) ^ e); } u32 H_32(u32 A) { u16 a = A & 65535; u16 b = A >> 16; return H_16((u16)(a ^ b)) << 16 | H2_16(b); } u64 product(u64 A, u64 B) { u32 a = A & UINT_MAX; u32 b = B & UINT_MAX; u32 c = A >> 32; u32 d = B >> 32; u32 e = product_32(a, b); return (u64)(product_32(a ^ c, b ^ d) ^ e) << 32 | (H_32(product_32(c, d)) ^ e); } u64 nim_product(u64 a, u64 b) { return product(a, b); } /* 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; }