結果
問題 | No.2134 $\sigma$-algebra over Finite Set |
ユーザー | nok0 |
提出日時 | 2022-11-22 20:23:00 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
RE
|
実行時間 | - |
コード長 | 33,103 bytes |
コンパイル時間 | 2,696 ms |
コンパイル使用メモリ | 220,360 KB |
実行使用メモリ | 7,680 KB |
最終ジャッジ日時 | 2024-09-24 07:27:28 |
合計ジャッジ時間 | 4,123 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
(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 | 2 ms
6,816 KB |
testcase_01 | AC | 87 ms
6,820 KB |
testcase_02 | AC | 87 ms
6,940 KB |
testcase_03 | AC | 2 ms
6,940 KB |
testcase_04 | AC | 17 ms
6,944 KB |
testcase_05 | AC | 2 ms
6,940 KB |
testcase_06 | AC | 18 ms
6,944 KB |
testcase_07 | AC | 18 ms
6,944 KB |
testcase_08 | AC | 2 ms
6,944 KB |
testcase_09 | AC | 1 ms
6,940 KB |
testcase_10 | AC | 25 ms
7,680 KB |
testcase_11 | AC | 25 ms
7,680 KB |
testcase_12 | AC | 39 ms
7,424 KB |
testcase_13 | AC | 57 ms
7,680 KB |
testcase_14 | AC | 9 ms
6,944 KB |
testcase_15 | RE | - |
testcase_16 | AC | 8 ms
6,944 KB |
testcase_17 | AC | 2 ms
6,940 KB |
testcase_18 | AC | 2 ms
6,944 KB |
ソースコード
#line 1 "/home/nok0/documents/programming/library/atcoder/modint.hpp" #include <cassert> #include <numeric> #include <type_traits> #ifdef _MSC_VER #include <intrin.h> #endif #line 1 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp" #include <utility> #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template <int n> constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template <int m> constexpr int primitive_root = primitive_root_constexpr(m); // @param n `n < 2^32` // @param m `1 <= m < 2^32` // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64) unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; // y_max < m * (n + 1) // floor(y_max / m) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #line 1 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp" #line 7 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp" namespace atcoder { namespace internal { #ifndef _MSC_VER template <class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; #else template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; #endif template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; } // namespace internal } // namespace atcoder #line 14 "/home/nok0/documents/programming/library/atcoder/modint.hpp" namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>; } // namespace internal template <int m, std::enable_if_t<(1 <= m)>* = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>; }; template <int id> struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template <int id> internal::barrett dynamic_modint<id>::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>; template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>; template <class> struct is_dynamic_modint : public std::false_type {}; template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {}; template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>; } // namespace internal } // namespace atcoder #line 3 "/home/nok0/documents/programming/library/math/factorial.hpp" #include <vector> #line 6 "/home/nok0/documents/programming/library/math/factorial.hpp" template<class T> struct factorial { public: static int MAX; static std::vector<T> fac, finv, inv; factorial() {} T binom(int n, int r) { if (n < r or n < 0 or r < 0) return T(0); assert(n < MAX); return fac[n] * finv[r] * finv[n - r]; } T large_binom(int n, int r) { if (n < r or n < 0 or r < 0) return T(0); assert(r < MAX); T ret = finv[r]; for (int i = 1; i <= r; ++i) ret *= (n + 1 - i); return ret; } static void set_size(int n = 3000000) { MAX = (n > 1 ? n : 1) + 1; if ((int)fac.size() >= MAX) return; fac.resize(MAX); finv.resize(MAX); inv.resize(MAX); const int MOD = T::mod(); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++) { fac[i] = fac[i - 1] * i; inv[i] = (T)MOD - inv[MOD % i] * (MOD / i); finv[i] = finv[i - 1] * inv[i]; } } }; template<class T> int factorial<T>::MAX = 0; template<class T> std::vector<T> factorial<T>::fac; template<class T> std::vector<T> factorial<T>::finv; template<class T> std::vector<T> factorial<T>::inv; #line 2 "/home/nok0/documents/programming/library/math/modint_iostream.hpp" #include <iostream> #line 5 "/home/nok0/documents/programming/library/math/modint_iostream.hpp" template<int m> std::istream &std::operator>>(std::istream &is, atcoder::static_modint<m> &a) { long long v; is >> v; a = v; return is; } template<int m> std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) { long long v; is >> v; a = v; return is; } template<int m> std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); } template<int m> std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); } #line 2 "/home/nok0/documents/programming/library/template/header.hpp" #include <bits/stdc++.h> #line 3 "/home/nok0/documents/programming/library/template/def_const.hpp" const int inf = 1000000000; const long long INF = 1000000000000000000ll; #line 4 "/home/nok0/documents/programming/library/template/debug.hpp" namespace viewer { void view(const long long &e) { if(e == INF) std::cerr << "INF"; else if(e == -INF) std::cerr << "-INF"; else std::cerr << e; } void view(const int &e) { if(e == inf) std::cerr << "inf"; else if(e == -inf) std::cerr << "-inf"; else std::cerr << e; } template <typename T> void view(const T &e) { std::cerr << e; } template <typename T, typename U> void view(const std::pair<T, U> &p) { std::cerr << "("; view(p.first); std::cerr << ", "; view(p.second); std::cerr << ")"; } template <class T0, class T1, class T2> void view(const std::tuple<T0, T1, T2> &p) { std::cerr << "("; view(std::get<0>(p)); std::cerr << ", "; view(std::get<1>(p)); std::cerr << ", "; view(std::get<2>(p)); std::cerr << ")"; } template <class T0, class T1, class T2, class T3> void view(const std::tuple<T0, T1, T2, T3> &p) { std::cerr << "("; view(std::get<0>(p)); std::cerr << ", "; view(std::get<1>(p)); std::cerr << ", "; view(std::get<2>(p)); std::cerr << ", "; view(std::get<3>(p)); std::cerr << ")"; } template <typename T> void view(const std::set<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::unordered_set<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::multiset<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::unordered_multiset<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::vector<T> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T, std::size_t ary_size> void view(const std::array<T, ary_size> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::vector<std::vector<T>> &vv) { std::cerr << "{\n"; for(const auto &v : vv) { std::cerr << "\t"; view(v); std::cerr << '\n'; } std::cerr << "}"; } template <typename T, typename U> void view(const std::vector<std::pair<T, U>> &v) { std::cerr << "{\n"; for(const auto &c : v) { std::cerr << "\t("; view(c.first); std::cerr << ", "; view(c.second); std::cerr << ")\n"; } std::cerr << "}"; } template <class T0, class T1, class T2> void view(const std::vector<std::tuple<T0, T1, T2>> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << '{'; for(const auto &t : v) { std::cerr << "\n\t"; view(t); std::cerr << ","; } std::cerr << "\n}"; } template <class T0, class T1, class T2, class T3> void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << '{'; for(const auto &t : v) { std::cerr << "\n\t"; view(t); std::cerr << ","; } std::cerr << "\n}"; } template <typename T, typename U> void view(const std::map<T, U> &m) { std::cerr << "{\n"; for(const auto &t : m) { std::cerr << "\t["; view(t.first); std::cerr << "] : "; view(t.second); std::cerr << '\n'; } std::cerr << "}"; } template <typename T, typename U> void view(const std::unordered_map<T, U> &m) { std::cerr << "{\n"; for(const auto &t : m) { std::cerr << "\t["; view(t.first); std::cerr << "] : "; view(t.second); std::cerr << '\n'; } std::cerr << "}"; } } // namespace viewer // when compiling : g++ foo.cpp -DLOCAL #ifdef LOCAL void debug_out() {} template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { viewer::view(H); std::cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ std::cerr << "\b\b]\n"; \ } while(0) #define dump(x) \ do { \ std::cerr << __LINE__ << " " << #x << " : "; \ viewer::view(x); \ std::cerr << '\n'; \ } while(0) #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif #line 3 "/home/nok0/documents/programming/library/template/def_name.hpp" #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define popcnt(x) __builtin_popcountll(x) template<class T = int> using V = std::vector<T>; template<class T = int> using VV = std::vector<std::vector<T>>; template<class T> using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>; using ll = long long; using ld = long double; using int128 = __int128_t; using pii = std::pair<int, int>; using pll = std::pair<long long, long long>; #line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp" struct fast_io { fast_io() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(15); } } fast_io_; #line 3 "/home/nok0/documents/programming/library/template/input.hpp" template<class T, class U> std::istream &operator>>(std::istream &is, std::pair<T, U> &p) { is >> p.first >> p.second; return is; } template<class T> std::istream &operator>>(std::istream &is, std::vector<T> &v) { for (T &i : v) is >> i; return is; } std::istream &operator>>(std::istream &is, __int128_t &a) { std::string s; is >> s; __int128_t ret = 0; for (int i = 0; i < (int)s.length(); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0'; a = ret * (s[0] == '-' ? -1 : 1); return is; } namespace scanner { void scan(int &a) { std::cin >> a; } void scan(long long &a) { std::cin >> a; } void scan(std::string &a) { std::cin >> a; } void scan(char &a) { std::cin >> a; } void scan(char a[]) { std::scanf("%s", a); } void scan(double &a) { std::cin >> a; } void scan(long double &a) { std::cin >> a; } template<class T, class U> void scan(std::pair<T, U> &p) { std::cin >> p; } template<class T> void scan(std::vector<T> &a) { std::cin >> a; } void INPUT() {} template<class Head, class... Tail> void INPUT(Head &head, Tail &...tail) { scan(head); INPUT(tail...); } } // namespace scanner #define VEC(type, name, size) \ std::vector<type> name(size); \ scanner::INPUT(name) #define VVEC(type, name, h, w) \ std::vector<std::vector<type>> name(h, std::vector<type>(w)); \ scanner::INPUT(name) #define INT(...) \ int __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define STR(...) \ std::string __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LD(...) \ long double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #line 3 "/home/nok0/documents/programming/library/template/math.hpp" template <class T, class U> inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template <class T, class U> inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template <class T> T divup(T x, T y) { return (x + y - 1) / y; } template <class T> T POW(T a, long long n) { T ret = 1; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } long long POW(long long a, long long n, const int mod) { long long ret = 1; a = (a % mod + mod) % mod; while(n) { if(n & 1) (ret *= a) %= mod; (a *= a) %= mod; n >>= 1; } return ret; } template <class T, class F> T bin_search(T ok, T ng, const F &f) { while(abs(ok - ng) > 1) { T mid = (ok + ng) >> 1; (f(mid) ? ok : ng) = mid; } return ok; } template <class T, class F> T bin_search(T ok, T ng, const F &f, int loop) { for(int i = 0; i < loop; i++) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } #line 3 "/home/nok0/documents/programming/library/template/output.hpp" template<class T, class U> std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) { os << p.first << " " << p.second; return os; } template<class T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) { for (int i = 0; i < int(a.size()); ++i) { if (i) os << " "; os << a[i]; } return os; } std::ostream &operator<<(std::ostream &dest, __int128_t &value) { std::ostream::sentry s(dest); if (s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if (dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } template<class T> void print(const T a) { std::cout << a << '\n'; } template<class Head, class... Tail> void print(Head H, Tail... T) { std::cout << H << ' '; print(T...); } template<class T> void printel(const T a) { std::cout << a << '\n'; } template<class T> void printel(const std::vector<T> &a) { for (const auto &v : a) std::cout << v << '\n'; } template<class Head, class... Tail> void printel(Head H, Tail... T) { std::cout << H << '\n'; printel(T...); } void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); } void No() { std::cout << "No\n"; } void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); } void NO() { std::cout << "NO\n"; } #line 2 "/home/nok0/documents/programming/library/template/rep.hpp" #define foa(v, a) for (auto &v : a) #define repname(a, b, c, d, e, ...) e #define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__) #define rep0(x) for (int rep_counter = 0; rep_counter < (x); ++rep_counter) #define rep1(i, x) for (int i = 0; i < (x); ++i) #define rep2(i, l, r) for (int i = (l); i < (r); ++i) #define rep3(i, l, r, c) for (int i = (l); i < (r); i += (c)) #define repsname(a, b, c, ...) c #define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__) #define reps0(x) for (int reps_counter = 1; reps_counter <= (x); ++reps_counter) #define reps1(i, x) for (int i = 1; i <= (x); ++i) #define rrepname(a, b, c, ...) c #define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__) #define rrep0(x) for (int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter) #define rrep1(i, x) for (int i = (x)-1; i >= 0; --i) #line 3 "/home/nok0/documents/programming/library/template/vector.hpp" template <class T> int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); } template <class T> int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); } template <class T> void UNIQUE(std::vector<T> &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template <class T> std::vector<T> press(std::vector<T> &a) { auto res = a; UNIQUE(res); for(auto &v : a) v = lb(res, v); return res; } #define SORTname(a, b, c, ...) c #define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__) #define SORT0(a) std::sort((a).begin(), (a).end()) #define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; }) template <class T> void ADD(std::vector<T> &a, const T x = 1) { for(auto &v : a) v += x; } template <class T> void SUB(std::vector<T> &a, const T x = 1) { for(auto &v : a) v -= x; } template <class T> struct cum_vector { public: cum_vector() = default; template <class U> cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) { for(int i = 0; i < (int)vec.size(); i++) cum[i + 1] = cum[i] + vec[i]; } T prod(int l, int r) { return cum[r] - cum[l]; } private: std::vector<T> cum; }; std::vector<std::pair<char, int>> rle(const std::string &s) { const int n = s.size(); std::vector<std::pair<char, int>> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and s[l] == s[r]; r++) {} ret.emplace_back(s[l], r - l); l = r; } return ret; } template <class T> std::vector<std::pair<T, int>> rle(const std::vector<T> &v) { int n = v.size(); std::vector<std::pair<T, int>> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and v[l] == v[r]; r++) {} ret.emplace_back(v[l], r - l); l = r; } return ret; } std::vector<int> iota(int n) { std::vector<int> p(n); std::iota(p.begin(), p.end(), 0); return p; } #line 11 "/home/nok0/documents/programming/library/template/all" using namespace std; #line 3 "a.cpp" using mint = atcoder::modint998244353; void main_(); int main() { int t = 1; while(t--) main_(); } void main_() { INT(n, m); if(m == 0) { print(2); return; } bitset<1000> bs; vector bss(n, bs), bss_rev(n, bs); vector u(n, bs); rep(i, n) { rep(j, n) u[i][j] = 1, bss_rev[i][j] = 1; } rep(i, m) { INT(k); VEC(int, a, k); SUB(a); foa(v, a) bss[i][v] = 1, bss_rev[i][v] = 0; } rep(j, n) { rep(i, n) { if(bss[i][j]) { u[j] &= bss[i]; } else { u[j] &= bss_rev[i]; } } } set<V<>> st; rep(i, n) { V<> tmp(n); rep(j, n) { tmp[j] = u[i][j]; } debug(tmp); st.insert(tmp); } print(mint(2).pow(SZ(st))); }