#include #include using namespace std; using namespace atcoder; //using mint = modint1000000007; //const int mod = 1000000007; using mint = modint998244353; const int mod = 998244353; //const int INF = 1e9; //const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i,l,r)for(int i=(l);i<(r);++i) #define rrep(i, n) for (int i = (n-1); i >= 0; --i) #define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i) #define all(x) (x).begin(),(x).end() #define allR(x) (x).rbegin(),(x).rend() #define endl "\n" #define P pair template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } #ifndef KMW_T_MATH_MODINT_MATRIX_TREE_HPP #define KMW_T_MATH_MODINT_MATRIX_TREE_HPP #include /** * @brief 行列木定理(spanning tree数) * * 典型用途: * グラフの全域木の数を求める * * 計算量: * O(N^3) * * @tparam Mint modint型 * * 制約 / 注意: * - ラプラシアン行列を渡す * - 0行0列を削除した (N-1)x(N-1) 行列を使う * - mod は素数 */ namespace kmw_t::math::modint { template Mint count_spanning_tree(std::vector> mat) { int n = (int)mat.size(); Mint det = 1; for (int i = 1; i < n; ++i) { if (mat[i][i] == Mint(0)) { // pivot探す for (int j = i + 1; j < n; ++j) { if (mat[j][i] != Mint(0)) { std::swap(mat[i], mat[j]); det = -det; break; } } } if (mat[i][i] == Mint(0)) return 0; Mint inv = mat[i][i].inv(); det *= mat[i][i]; for (int j = i + 1; j < n; ++j) { Mint factor = mat[j][i] * inv; for (int k = i; k < n; ++k) { mat[j][k] -= factor * mat[i][k]; } } } return det; } } // namespace kmw_t::math::modint #endif // KMW_T_MATH_MODINT_MATRIX_TREE_HPP int popcount(long long n) { n = (n & 0x5555555555555555) + (n >> 1 & 0x5555555555555555); n = (n & 0x3333333333333333) + (n >> 2 & 0x3333333333333333); n = (n & 0x0f0f0f0f0f0f0f0f) + (n >> 4 & 0x0f0f0f0f0f0f0f0f); n = (n & 0x00ff00ff00ff00ff) + (n >> 8 & 0x00ff00ff00ff00ff); n = (n & 0x0000ffff0000ffff) + (n >> 16 & 0x0000ffff0000ffff); n = (n & 0x00000000ffffffff) + (n >> 32 & 0x00000000ffffffff); return n; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int n, k; cin >> n >> k; vector e(k, vector

()); rep(i, k) { int t; cin >> t; rep(j, t) { int a, b; cin >> a >> b; a--, b--; e[i].push_back({ a,b }); } } mint ans = 0; rep(i, 1 << k) { vector> mat(n, vector(n)); rep(j, k) { if (1 & (i >> j)) { for (auto vp : e[j]) { auto[x, y] = vp; mat[x][x]++; mat[y][y]++; mat[x][y]--; mat[y][x]--; } } } auto get = kmw_t::math::modint::count_spanning_tree(mat); if (k % 2 == popcount(i) % 2)ans += get; else ans -= get; } cout << ans.val() << endl; return 0; }