#define MOD_TYPE 2 #include using namespace std; #include // #include // #include // #include using namespace atcoder; #if 0 #include #include using Int = boost::multiprecision::cpp_int; using lld = boost::multiprecision::cpp_dec_float_100; #endif #if 0 #include #include #include #include using namespace __gnu_pbds; using namespace __gnu_cxx; template using extset = tree, rb_tree_tag, tree_order_statistics_node_update>; #endif #if 1 #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #endif #pragma region Macros using ll = long long int; using ld = long double; using pii = pair; using pll = pair; using pld = pair; template using smaller_queue = priority_queue, greater>; #if MOD_TYPE == 1 constexpr ll MOD = ll(1e9 + 7); #else #if MOD_TYPE == 2 constexpr ll MOD = 998244353; #else constexpr ll MOD = 1000003; #endif #endif using mint = static_modint; constexpr int INF = (int)1e9 + 10; constexpr ll LINF = (ll)4e18; const double PI = acos(-1.0); constexpr ld EPS = 1e-10; constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0}; constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0}; #define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i) #define rep(i, n) REP(i, 0, n) #define REPI(i, m, n) for (int i = m; i < (int)(n); ++i) #define repi(i, n) REPI(i, 0, n) #define RREP(i, m, n) for (ll i = n - 1; i >= m; i--) #define rrep(i, n) RREP(i, 0, n) #define YES(n) cout << ((n) ? "YES" : "NO") << "\n" #define Yes(n) cout << ((n) ? "Yes" : "No") << "\n" #define all(v) v.begin(), v.end() #define NP(v) next_permutation(all(v)) #define dbg(x) cerr << #x << ":" << x << "\n"; #define UNIQUE(v) v.erase(unique(all(v)), v.end()) struct io_init { io_init() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << setprecision(20) << setiosflags(ios::fixed); }; } io_init; template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } inline ll floor(ll a, ll b) { if (b < 0) a *= -1, b *= -1; if (a >= 0) return a / b; return -((-a + b - 1) / b); } inline ll ceil(ll a, ll b) { return floor(a + b - 1, b); } template inline void Fill(A (&array)[N], const T &val) { fill((T *)array, (T *)(array + N), val); } template vector compress(vector &v) { vector val = v; sort(all(val)), val.erase(unique(all(val)), val.end()); for (auto &&vi : v) vi = lower_bound(all(val), vi) - val.begin(); return val; } template constexpr istream &operator>>(istream &is, pair &p) noexcept { is >> p.first >> p.second; return is; } template constexpr ostream &operator<<(ostream &os, pair p) noexcept { os << p.first << " " << p.second; return os; } ostream &operator<<(ostream &os, mint m) { os << m.val(); return os; } ostream &operator<<(ostream &os, modint m) { os << m.val(); return os; } template constexpr istream &operator>>(istream &is, vector &v) noexcept { for (int i = 0; i < v.size(); i++) is >> v[i]; return is; } template constexpr ostream &operator<<(ostream &os, vector &v) noexcept { for (int i = 0; i < v.size(); i++) os << v[i] << (i + 1 == v.size() ? "" : " "); return os; } template constexpr void operator--(vector &v, int) noexcept { for (int i = 0; i < v.size(); i++) v[i]--; } random_device seed_gen; mt19937_64 engine(seed_gen()); inline ll randInt(ll l, ll r) { return engine() % (r - l + 1) + l; } struct BiCoef { vector fact_, inv_, finv_; BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); for (int i = 2; i < n; i++) { fact_[i] = fact_[i - 1] * i; inv_[i] = -inv_[MOD % i] * (MOD / i); finv_[i] = finv_[i - 1] * inv_[i]; } } mint C(ll n, ll k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n - k]; } mint P(ll n, ll k) const noexcept { return C(n, k) * fact_[k]; } mint H(ll n, ll k) const noexcept { return C(n + k - 1, k); } mint Ch1(ll n, ll k) const noexcept { if (n < 0 || k < 0) return 0; mint res = 0; for (int i = 0; i < n; i++) res += C(n, i) * mint(n - i).pow(k) * (i & 1 ? -1 : 1); return res; } mint fact(ll n) const noexcept { if (n < 0) return 0; return fact_[n]; } mint inv(ll n) const noexcept { if (n < 0) return 0; return inv_[n]; } mint finv(ll n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; BiCoef bc(1000010); #pragma endregion // ------------------------------- template struct Matrix { vector> A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector(m, 0)) {} Matrix(size_t n) : A(n, vector(n, 0)){}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector &operator[](int k) const { return (A.at(k)); } inline vector &operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix mat(n); for (int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector> C(n, vector(m, 0)); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) for (int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); while (k > 0) { if (k & 1) B *= *this; *this *= *this; k >>= 1LL; } A.swap(B.A); return (*this); } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); } friend ostream &operator<<(ostream &os, Matrix &p) { size_t n = p.height(), m = p.width(); for (int i = 0; i < n; i++) { os << "["; for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "]\n" : ","); } } return (os); } T determinant() { Matrix B(*this); assert(width() == height()); T ret = 1; for (int i = 0; i < width(); i++) { int idx = -1; for (int j = i; j < width(); j++) { if (B[j][i] != 0) idx = j; } if (idx == -1) return (0); if (i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for (int j = 0; j < width(); j++) { B[i][j] /= vv; } for (int j = i + 1; j < width(); j++) { T a = B[j][i]; for (int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; void solve() { int n, k; cin >> n >> k; vector> E(k); rep(i, k) { int t; cin >> t; rep(j, t) { int a, b; cin >> a >> b; a--, b--; if (a > b) swap(a, b); E[i].push_back({a, b}); } } mint ans = 0; rep(msk, 1 << k) { vector> M(n, vector(n)); rep(x, k) { if (((1 << x) & msk) == 0) continue; for (auto [a, b] : E[x]) { M[a][a]++; M[b][b]++; M[a][b]--; M[b][a]--; } } rep(i, n) M[i].pop_back(); M.pop_back(); Matrix D; D.A = M; mint cnt = D.determinant(); if ((k - __builtin_popcount(msk) + 1) & 1) ans += cnt; else ans -= cnt; } cout << ans << "\n"; } int main() { solve(); }