#include #include #include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; template vector> vec2d(int n, int m, T v){ return vector>(n, vector(m, v)); } template vector>> vec3d(int n, int m, int k, T v){ return vector>>(n, vector>(m, vector(k, v))); } template void print_vector(vector v, char delimiter=' '){ if(v.empty()) { cout << endl; return; } for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter; cout << v.back() << endl; } using mint = atcoder::modint998244353; ostream& operator<<(ostream& os, const mint& m){ os << m.val(); return os; } template struct matrix{ int n, m; vector> dat; matrix(int n_, int m_){ n = n_; m = m_; for(int i = 0; i < n; i++){ dat.push_back(vector(m)); } } matrix(int n, int m, T val): n(n), m(m){ for(int i = 0; i < n; i++){ dat.push_back(vector(m, val)); } } matrix(int n, int m, vector> dat): n(n), m(m), dat(dat){ assert((int)dat.size() == n); for(int i = 0; i < n; i++) assert(dat[i].size() == m); } vector& operator[](int x) { return dat[x]; } }; template bool prod(matrix a, matrix b, matrix &ans){ assert(a.m == b.n); for(int i = 0; i < a.n; i++){ for(int j = 0; j < b.m; j++){ ans.dat[i][j] = 0; for(int k = 0; k < b.n; k++){ ans.dat[i][j] += (a.dat[i][k]*b.dat[k][j]); } } } return true; } template void copy_mat(matrix a, matrix &b){ assert(a.n == b.n); assert(a.m == b.m); for(int i = 0; i < a.n; i++){ for(int j = 0; j < a.m; j++){ b.dat[i][j] = a.dat[i][j]; } } } template void pow_mat(matrix a, ll n, matrix &ans){ assert(n < ((ll)1<<61)); matrix buf(a.n, a.n); matrix tmp(a.n, a.n); copy_mat(a, tmp); for(int i = 0; i < a.n; i++) { for(int j = 0; j < a.n; j++){ ans.dat[i][j] = 0; } ans.dat[i][i] = 1; } while (n > 0) { if (n&1) { prod(tmp, ans, buf); copy_mat(buf, ans); } prod(tmp, tmp, buf); copy_mat(buf, tmp); n >>= 1; } } template void print_mat(matrix a){ for(int i = 0; i < a.n; i++){ for(int j = 0; j < a.m; j++){ cout << a.dat[i][j] << ' '; } cout << endl; } } template ostream& operator<<(ostream& os, const matrix& m){ print_mat(m); return os; } /** * I+a+...+a^nを求めます(ちゃんと検証していないのであってないかも) */ template void sum_pow(matrix a, ll n, matrix &ans){ assert(a.n == a.m); assert(a.n == ans.n); assert(a.n == ans.m); matrix A(2*a.n, 2*a.n); for(int i = 0; i < a.n; i++){ for(int j = 0; j < a.n; j++){ A[i][j] = a[i][j]; if(i == j){ A[i+a.n][j] = 1; A[i+a.n][j+a.n] = 1; } } } matrix B(2*a.n, a.n); for(int i = 0; i < a.n; i++){ B[i][i] = 1; } matrix S(2*a.n, a.n); matrix buf(2*a.n, 2*a.n); pow_mat(A, n+1, buf); prod(buf, B, S); for(int i = 0; i < a.n; i++){ for(int j = 0; j < a.n; j++){ ans[i][j] = S[i+a.n][j]; } } } /** * verified: https://judge.yosupo.jp/submission/35808 */ template T det(matrix a, T unit_prod, T unit_sum){ assert(a.n == a.m); int n = a.n; matrix b(n, n); copy_mat(a, b); int cnt_swap = 0; for(int i = 0; i < n; i++){ if(b[i][i] == unit_sum){ for(int j = i+1; j < n; j++){ if(b[j][i] != unit_sum){ // swap cnt_swap++; for(int k = 0; k < n; k++){ swap(b[i][k], b[j][k]); } break; } } } if(b[i][i] == unit_sum) continue; T inv = unit_prod/b[i][i]; for(int j = i+1; j < n; j++){ for(int k = n-1; k >= 0; k--){ b[j][k] -= b[i][k]*b[j][i]*inv; } } } T ans = unit_prod; for(int i = 0; i < a.n; i++) ans *= b[i][i]; if(cnt_swap%2 == 1) ans *= -1; return ans; } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; int n, k; cin >> n >> k; vector> a(k), b(k); for(int i = 0; i < k; i++){ int t; cin >> t; a[i].resize(t); b[i].resize(t); for(int j = 0; j < t; j++){ cin >> a[i][j] >> b[i][j]; a[i][j]--; b[i][j]--; } } mint ans = 0; for(int s = 0; s < (1< mat(n-1, n-1); mint sgn = 1; for(int i = 0; i < k; i++){ if((s&(1< v) swap(u, v); mat[u][u] += 1; if(v != n-1){ mat[u][v] -= 1; mat[v][u] -= 1; mat[v][v] += 1; } } } ans += det(mat, mint(1), mint(0))*sgn; } cout << ans << endl; }