#ifndef LOCAL #define FAST_IO #endif // ============ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64)x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64)x; return os; } #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; // ============ #ifdef DEBUGF #else #define DBG(x) (void)0 #endif // ============ #include #include #include // ============ constexpr bool is_prime(unsigned n) { if (n == 0 || n == 1) { return false; } for (unsigned i = 2; i * i <= n; ++i) { if (n % i == 0) { return false; } } return true; } constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) { unsigned ret = 1, self = x; while (y != 0) { if (y & 1) { ret = (unsigned) ((unsigned long long) ret * self % mod); } self = (unsigned) ((unsigned long long) self * self % mod); y /= 2; } return ret; } template constexpr unsigned primitive_root() { static_assert(is_prime(mod), "`mod` must be a prime number."); if (mod == 2) { return 1; } unsigned primes[32] = {}; int it = 0; { unsigned m = mod - 1; for (unsigned i = 2; i * i <= m; ++i) { if (m % i == 0) { primes[it++] = i; while (m % i == 0) { m /= i; } } } if (m != 1) { primes[it++] = m; } } for (unsigned i = 2; i < mod; ++i) { bool ok = true; for (int j = 0; j < it; ++j) { if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) { ok = false; break; } } if (ok) return i; } return 0; } // y >= 1 template constexpr T safe_mod(T x, T y) { x %= y; if (x < 0) { x += y; } return x; } // y != 0 template constexpr T floor_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return x / y; } else { return -((-x + y - 1) / y); } } // y != 0 template constexpr T ceil_div(T x, T y) { if (y < 0) { x *= -1; y *= -1; } if (x >= 0) { return (x + y - 1) / y; } else { return -(-x / y); } } // ============ template class ModInt { static_assert(mod != 0, "`mod` must not be equal to 0."); static_assert( mod < (1u << 31), "`mod` must be less than (1u << 31) = 2147483648."); unsigned val; public: static constexpr unsigned get_mod() { return mod; } constexpr ModInt() : val(0) {} template > * = nullptr> constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {} template > * = nullptr> constexpr ModInt(T x) : val((unsigned) (x % mod)) {} static constexpr ModInt raw(unsigned x) { ModInt ret; ret.val = x; return ret; } constexpr unsigned get_val() const { return val; } constexpr ModInt operator+() const { return *this; } constexpr ModInt operator-() const { return ModInt(0u) - *this; } constexpr ModInt &operator+=(const ModInt &rhs) { val += rhs.val; if (val >= mod) val -= mod; return *this; } constexpr ModInt &operator-=(const ModInt &rhs) { val -= rhs.val; if (val >= mod) val += mod; return *this; } constexpr ModInt &operator*=(const ModInt &rhs) { val = (unsigned long long)val * rhs.val % mod; return *this; } constexpr ModInt &operator/=(const ModInt &rhs) { val = (unsigned long long)val * rhs.inv().val % mod; return *this; } friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) += rhs; } friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) -= rhs; } friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) *= rhs; } friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) { return ModInt(lhs) /= rhs; } constexpr ModInt pow(unsigned long long x) const { ModInt ret = ModInt::raw(1); ModInt self = *this; while (x != 0) { if (x & 1) ret *= self; self *= self; x >>= 1; } return ret; } constexpr ModInt inv() const { static_assert(is_prime(mod), "`mod` must be a prime number."); assert(val != 0); return this->pow(mod - 2); } friend std::istream &operator>>(std::istream &is, ModInt &x) { long long val; is >> val; x.val = val % mod + (val < 0 ? mod : 0); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } friend bool operator==(const ModInt &lhs, const ModInt &rhs) { return lhs.val == rhs.val; } friend bool operator!=(const ModInt &lhs, const ModInt &rhs) { return lhs.val != rhs.val; } }; [[maybe_unused]] constexpr unsigned mod998244353 = 998244353; [[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007; // ============ // ============ #include #include #include template class Matrix { std::vector> data; public: Matrix(int n) : data(n, std::vector(n, T(0))) {} Matrix(int h, int w) : data(h, std::vector(w, T(0))) {} // must be rectangular Matrix(std::vector> a) : data(std::move(a)) {} int height() const { return data.size(); } int width() const { return data.empty() ? 0 : data[0].size(); } bool is_square() const { return height() == width(); } const T &operator()(int i, int j) const { return data[i][j]; } T &operator()(int i, int j) { return data[i][j]; } Matrix trans() const { const int h = height(), w = width(); Matrix ret(w, h); for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) { ret.data[j][i] = data[i][j]; } } return ret; } Matrix operator+() const { return *this; } Matrix operator-() const { const int h = height(), w = width(); Matrix ret = *this; for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) { ret.data[i][j] = -ret.data[i][j]; } } return ret; } Matrix &operator+=(const Matrix &rhs) { assert(height() == rhs.height() && width() == rhs.width()); const int h = height(), w = width(); for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) { data[i][j] += rhs.data[i][j]; } } return *this; } Matrix &operator-=(const Matrix &rhs) { assert(height() == rhs.height() && width() == rhs.width()); const int h = height(), w = width(); for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) { data[i][j] -= rhs.data[i][j]; } } return *this; } friend Matrix operator+(const Matrix &lhs, const Matrix &rhs) { return lhs += rhs; } friend Matrix operator-(const Matrix &lhs, const Matrix &rhs) { return lhs -= rhs; } friend Matrix operator*(const Matrix &lhs, const Matrix &rhs) { assert(lhs.width() == rhs.height()); const int n = lhs.height(), m = rhs.height(), k = rhs.width(); Matrix ret(n, k); for (int i = 0; i < n; ++i) { for (int j = 0; j < k; ++j) { for (int l = 0; l < m; ++l) { ret.data[i][j] += lhs.data[i][l] * rhs.data[l][j]; } } } return ret; } Matrix &operator*=(const Matrix &rhs) { return *this = *this * rhs; } static Matrix e(int n) { Matrix mat(n); for (int i = 0; i < n; ++i) { mat.data[i][i] = T(1); } return mat; } Matrix pow(unsigned long long t) { assert(height() == width()); Matrix ret = Matrix::e(height()); Matrix self = *this; while (t > 0) { if (t % 2 == 1) { ret = ret * self; } self = self * self; t /= 2; } return ret; } T det() const { assert(is_square()); const int n = height(); std::vector> a = data; T ans(1); for (int i = 0; i < n; ++i) { int nonzero = -1; for (int j = i; j < n; ++j) { if (a[j][i] != T(0)) { nonzero = j; break; } } if (nonzero == -1) { return T(0); } if (nonzero != i) { std::swap(a[i], a[nonzero]); ans = -ans; } ans *= a[i][i]; { const T inv = T(1) / T(a[i][i]); for (int j = i; j < n; ++j) { a[i][j] *= inv; } } for (int j = i + 1; j < n; ++j) { const T tmp = a[j][i]; for (int k = i; k < n; ++k) { a[j][k] -= tmp * a[i][k]; } } } return ans; } }; // ============ using Mint = ModInt; Mint spanning(i32 n, const Vec> &edge) { Vec deg(n, 0); REP(i, n) REP(j, i) { deg[i] += edge[i][j]; deg[j] += edge[i][j]; } Matrix mat(n - 1, n - 1); REP(i, n - 1) REP(j, n - 1) { if (i == j) { mat(i, j) = Mint(deg[i]); } else { mat(i, j) = -Mint(edge[i][j]); } } return mat.det(); } int main() { i32 n, k; cin >> n >> k; Vec>> edges(k); REP(i, k) { i32 t; cin >> t; edges[i].reserve(t); while (t--) { i32 a, b; cin >> a >> b; --a; --b; edges[i].emplace_back(a, b); } } Mint ans; REP(st, 1, 1 << k) { Vec> edge(n, Vec(n, 0)); REP(i, k) { if (st & (1 << i)) { for (auto [a, b] : edges[i]) { ++edge[a][b]; ++edge[b][a]; } } } Mint cnt = spanning(n, edge); if (__builtin_parity(((1 << k) - 1) ^ st)) { ans -= cnt; } else { ans += cnt; } } cout << ans << '\n'; }