#include <bits/stdc++.h>
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(),a.end()
#define rrng(a) a.rbegin(),a.rend()
#define maxs(x,y) (x = max(x,y))
#define mins(x,y) (x = min(x,y))
#define isin(x,l,r) ((l) <= (x) && (x) < (r))
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define uni(x) x.erase(unique(rng(x)),x.end())
#define snuke srand((unsigned)clock()+(unsigned)time(NULL));
#define show(x) cout<<#x<<" = "<<x<<endl;
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define bn(x) ((1<<x)-1)
#define dup(x,y) (((x)+(y)-1)/(y))
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef tuple<int,int,int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<T> vt;
inline int getInt() { int x; scanf("%d",&x); return x;}
template<typename T>inline istream& operator>>(istream&i,v(T)&v)
{rep(j,sz(v))i>>v[j];return i;}
template<typename T>string join(const v(T)&v)
{stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);}
template<typename T>inline ostream& operator<<(ostream&o,const v(T)&v)
{if(sz(v))o<<join(v);return o;}
template<typename T1,typename T2>inline istream& operator>>(istream&i,pair<T1,T2>&v)
{return i>>v.fi>>v.se;}
template<typename T1,typename T2>inline ostream& operator<<(ostream&o,const pair<T1,T2>&v)
{return o<<v.fi<<","<<v.se;}
template<typename T>inline ll suma(const v(T)& a) { ll res(0); for (auto&& x : a) res += x; return res;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
#define dame { puts("-1"); return 0;}
#define yn {puts("Yes");}else{puts("No");}
const int MX = 200005;

// coordinate compression
struct X {
  typedef int T;
  vector<T> d;
  X() {}
  // X(vector<T>& a): d(a) {
  //   init();
  //   for (T& na : a) na = (*this)(na);
  // }
  void add(const T& x) { d.pb(x);}
  void init() {
    sort(rng(d));
    d.erase(unique(rng(d)), d.end());
  }
  int size() const { return sz(d);}
  T operator[](int i) const { return d[i];}
  int operator()(const T& x) const { return upper_bound(rng(d),x)-d.begin()-1;}
};
//

// Union find
struct uf {
  vi d;
  uf(){}
  uf(int mx):d(mx,-1){}
  int root(int x) {
    if(d[x] < 0) return x;
    return d[x] = root(d[x]);
  }
  bool unite(int x, int y) {
    x = root(x); y = root(y);
    if(x == y) return false;
    if(d[x] > d[y]) swap(x,y);
    d[x] += d[y]; d[y] = x;
    return true;
  }
  bool same(int x, int y) { return root(x) == root(y);}
  int size(int x) { return -d[root(x)];}
  int operator[](int x) { return root(x);}
  int operator()(int x) { return size(x);}
};
//

// Mod int
const int mod = 998244353;
struct mint {
  ll x;
  mint():x(0){}
  mint(ll x):x((x%mod+mod)%mod){}
  // mint(ll x):x(x){}
  mint& fix() { x = (x%mod+mod)%mod; return *this;}
  mint operator-() const { return mint(0) - *this;}
  mint operator~() const { return mint(1) / *this;}
  mint& operator+=(const mint& a){ if((x+=a.x)>=mod) x-=mod; return *this;}
  mint& operator-=(const mint& a){ if((x+=mod-a.x)>=mod) x-=mod; return *this;}
  mint& operator*=(const mint& a){ (x*=a.x)%=mod; return *this;}
  mint& operator/=(const mint& a){ (x*=a.pow(mod-2).x)%=mod; return *this;}
  mint operator+(const mint& a)const{ return mint(*this) += a;}
  mint operator-(const mint& a)const{ return mint(*this) -= a;}
  mint operator*(const mint& a)const{ return mint(*this) *= a;}
  mint operator/(const mint& a)const{ return mint(*this) /= a;}
  mint pow(ll t) const {
    if(!t) return 1;
    mint res = pow(t/2);
    res *= res;
    return (t&1)?res*x:res;
  }
  bool operator<(const mint& a)const{ return x < a.x;}
  bool operator==(const mint& a)const{ return x == a.x;}
};
mint ex(mint x, ll t) { return x.pow(t);}
istream& operator>>(istream&i,mint&a){i>>a.x;return i;}
ostream& operator<<(ostream&o,const mint&a){o<<a.x;return o;}
typedef vector<mint> vm;
struct comb {
  vm f, g;
  comb(){}
  comb(int mx):f(mx+1),g(mx+1) {
    f[0] = 1;
    rrep(i,mx) f[i] = f[i-1]*i;
    g[mx] = f[mx].pow(mod-2);
    for(int i=mx;i>0;i--) g[i-1] = g[i]*i;
  }
  mint operator()(int a, int b) {
    if (a < b) return 0;
    return f[a]*g[b]*g[a-b];
  }
} c(MX);
//

map<P,mint> mp;
mint f(int n, int e) {
  P p(n,e);
  if (mp.count(p)) return mp[p];
  mint res = 0;
  rep(i,n+1) res += c.f[n]*c.g[n-i]*c(i+e-1,e-1);
  // cerr<<p<<" "<<res<<endl;
  return mp[p] = res;
}

int main() {
  int n,m;
  scanf("%d%d",&n,&m);
  vp es(m);
  X xs;
  rep(i,m) {
    int a,b;
    scanf("%d%d",&a,&b);
    --a; --b;
    es[i] = P(a,b);
    xs.add(a);
    xs.add(b);
  }
  xs.init();
  rep(i,m) es[i].fi = xs(es[i].fi);
  rep(i,m) es[i].se = xs(es[i].se);
  int s = sz(xs);

  vm two(MX,1);
  rep(i,MX-1) two[i+1] = two[i]*2;

  mint owt = mint(1)/2;

  mint ans = 0;
  rep(i,1<<m) {
    vi deg(s);
    uf t(s);
    bool ok = true;
    int cnt = 0;
    rep(j,m) if (i>>j&1) {
      int a = es[j].fi, b = es[j].se;
      deg[a]++;
      deg[b]++;
      if (!t.unite(a,b)) ++cnt;
      if (deg[a] > 2) ok = false;
      if (deg[b] > 2) ok = false;
    }
    if (!ok) continue;
    int w = n-s, e = 0;
    rep(i,s) {
      if (t.root(i) != i) continue;
      if (t.size(i) == 1) ++w;
      else ++e;
    }
    if (cnt && e != 1) continue;
    mint now = 0;
    if (e) {
      now = c.f[e-1]*two[e-1];
      now *= f(w,e);
      if (e == 1 && w == n-2) now -= 1;
    } else {
      srep(i,3,n+1) now += c(n,i)*c.f[i-1]*owt;
    }
    if (cnt) now = 1;
    // cout<<i<<" "<<now<<endl;
    if (pcnt(i)&1) now = -now;
    ans += now;
  }
  cout<<ans<<endl;
  return 0;
}