// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define double ld #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define rep1(i,n) for (int i = 1; i <= (int)(n); i++) #define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = (int)(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define pb push_back #define eb emplace_back #define mp make_pair #define fst first #define snd second template auto constexpr inf = numeric_limits::max()/2-1; auto constexpr INF32 = inf; auto constexpr INF64 = inf; auto constexpr INF = inf; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template using pque_max = priority_queue; template using pque_min = priority_queue, greater >; template ::value>::type> ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; } template ::value>::type> istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << "(" << p.first << ", " << p.second << ")"; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(v.begin(), v.end(), x)-v.begin(); } template int ubd(C const& v, T const& x) { return upper_bound(v.begin(), v.end(), x)-v.begin(); } const int dx[] = { 1,0,-1,0 }; const int dy[] = { 0,1,0,-1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } template struct Random { mt19937_64 mt{random_device{}()}; //mt19937_64 mt{(unsigned)time(0)}; Int a,b; // [a,b] Random(Int a, Int b) : a(a), b(b) {} Int operator()() { return uniform_int_distribution(a,b)(mt); } }; template Int rand(Int a, Int b) { // [a,b] static mt19937_64 mt{random_device{}()}; return uniform_int_distribution(a,b)(mt); } // <<< // >>> modint template class modint { static_assert(md < (1u<<31), ""); using M = modint; using i64 = int64_t; uint32_t x; public: static constexpr uint32_t mod = md; constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { } constexpr i64 val() const { return x; } constexpr explicit operator i64() const { return x; } constexpr bool operator==(M r) const { return x == r.x; } constexpr bool operator!=(M r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; } constexpr M& operator/=(M r) { return *this *= r.inv(); } constexpr M operator+(M r) const { return M(*this) += r; } constexpr M operator-(M r) const { return M(*this) -= r; } constexpr M operator*(M r) const { return M(*this) *= r; } constexpr M operator/(M r) const { return M(*this) /= r; } friend constexpr M operator+(i64 x, M y) { return M(x)+y; } friend constexpr M operator-(i64 x, M y) { return M(x)-y; } friend constexpr M operator*(i64 x, M y) { return M(x)*y; } friend constexpr M operator/(i64 x, M y) { return M(x)/y; } constexpr M inv() const { assert(x > 0); return pow(md-2); } constexpr M pow(i64 n) const { assert(not (x == 0 && n == 0)); if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } #ifdef LOCAL friend string to_s(M r) { return to_s(r.val(), mod); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; // <<< constexpr int64_t MOD = 998244353; //constexpr int64_t MOD = 1e9+7; using mint = modint; mint sgn(int n) { return n%2 == 0 ? +1 : -1; } // >>> mod table template struct ModTable { static constexpr int32_t Size = 1e6 + 10; static_assert(Size <= mod, ""); using ll = int64_t; int32_t fact[Size], finv[Size], inv[Size]; ModTable() { fact[0] = fact[1] = finv[0] = finv[1] = inv[1] = 1; for (int i = 2; i < Size; i++) { fact[i] = ll(fact[i-1])*i % mod; inv[i] = mod - ll(inv[mod%i])*(mod/i) % mod; finv[i] = ll(finv[i-1])*inv[i] % mod; } } }; const ModTable mod_tab; modint fact(int n) { assert(0 <= n); assert(n < ModTable::Size); return mod_tab.fact[n]; } modint finv(int n) { assert(0 <= n); assert(n < ModTable::Size); return mod_tab.finv[n]; } modint C(int n, int k) { if (n < 0 || k < 0 || n < k) return 0; return fact(n)*finv(k)*finv(n-k); } modint P(int n, int k) { assert(k >= 0); return fact(n)*finv(n-k); } // <<< // >>> union find struct UnionFind { int n, sz; // id : 0...n-1 vector par; UnionFind(int n = 0) : n(n), sz(n), par(n,-1) { } int root(int x) { assert(0 <= x); assert(x < n); return par[x] < 0 ? x : par[x] = root(par[x]); } bool unite(int x, int y) { x = root(x), y = root(y); if (x == y) return false; sz--; if (par[x] < par[y]) swap(x,y); par[y] += par[x]; par[x] = y; return true; } bool same(int x, int y) { return root(x) == root(y); } int size(int x) { return -par[root(x)]; } int size() const { return sz; } struct groups_t { vector > grp; vector > id; }; groups_t groups() { vector > g(n); rep (i,n) if (par[i] < 0) g[i].reserve(-par[i]); rep (i,n) g[root(i)].push_back(i); vector > grp; grp.reserve(size()); rep (i,n) if (g[i].size()) grp.emplace_back(move(g[i])); vector > id(n); rep (i,grp.size()) rep (j,grp[i].size()) { id[grp[i][j]] = make_pair(i,j); } return { grp, id }; } }; // <<< int32_t main() { int n,m; cin >> n >> m; vector a(m),b(m); rep (i,m) cin >> a[i] >> b[i], --a[i],--b[i]; auto memo = make_v(2*m+1,m+1); rep (k,2*m+1) rep (r,m+1) { if (k == 0 || r == 0) continue; auto &res = memo[k][r]; rep (i,n-k+1) if (k+i >= 3) res += C(n-k,i) * fact(r+i-1); res *= mint(2).pow(r-1); } rep (i,n+1) if (i >= 3) memo[0][0] += C(n,i) * fact(i-1) / 2; vector deg(n); mint ans = 0; UnionFind uf(n); rep (s,1LL<>i&1) { uf.unite(a[i],b[i]); r++; if (deg[a[i]] == 0) k++; if (deg[b[i]] == 0) k++; if (deg[a[i]] == 1) r--; if (deg[b[i]] == 1) r--; if (++deg[a[i]] > 2) ok = false; if (++deg[b[i]] > 2) ok = false; } int loop = uf.size() - (n-k) - r; if (loop > 1) continue; if (loop == 1) { ans += sgn(popcnt(s)); continue; } if (not ok) continue; dump(s,k,r,memo[k][r]); ans += sgn(popcnt(s)) * memo[k][r]; rep (i,m) if (s>>i&1) { --deg[a[i]],--deg[b[i]]; uf.par[a[i]] = -1; uf.par[b[i]] = -1; } uf.sz = n; } cout << ans << endl; }