#include <bits/stdc++.h>
using namespace std;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
using Int = long long;
const char newl = '\n';


template<typename T,T MOD = 1000000007>
struct Mint{
  static constexpr T mod = MOD;
  T v;
  Mint():v(0){}
  Mint(signed v):v(v){}
  Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}

  Mint pow(long long k){
    Mint res(1),tmp(v);
    while(k){
      if(k&1) res*=tmp;
      tmp*=tmp;
      k>>=1;
    }
    return res;
  }

  static Mint add_identity(){return Mint(0);}
  static Mint mul_identity(){return Mint(1);}

  Mint inv(){return pow(MOD-2);}

  Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
  Mint& operator/=(Mint a){return (*this)*=a.inv();}

  Mint operator+(Mint a) const{return Mint(v)+=a;}
  Mint operator-(Mint a) const{return Mint(v)-=a;}
  Mint operator*(Mint a) const{return Mint(v)*=a;}
  Mint operator/(Mint a) const{return Mint(v)/=a;}

  Mint operator-() const{return v?Mint(MOD-v):Mint(v);}

  bool operator==(const Mint a)const{return v==a.v;}
  bool operator!=(const Mint a)const{return v!=a.v;}
  bool operator <(const Mint a)const{return v <a.v;}

  static Mint comb(long long n,int k){
    Mint num(1),dom(1);
    for(int i=0;i<k;i++){
      num*=Mint(n-i);
      dom*=Mint(i+1);
    }
    return num/dom;
  }
};
template<typename T,T MOD> constexpr T Mint<T, MOD>::mod;
template<typename T,T MOD>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}


template<typename M_>
class Enumeration{
  using M = M_;
protected:
  static vector<M> fact,finv,invs;
public:
  static void init(int n){
    n=min<decltype(M::mod)>(n,M::mod-1);

    int m=fact.size();
    if(n<m) return;

    fact.resize(n+1,1);
    finv.resize(n+1,1);
    invs.resize(n+1,1);

    if(m==0) m=1;
    for(int i=m;i<=n;i++) fact[i]=fact[i-1]*M(i);
    finv[n]=M(1)/fact[n];
    for(int i=n;i>=m;i--) finv[i-1]=finv[i]*M(i);
    for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1];
  }

  static M Fact(int n){
    init(n);
    return fact[n];
  }
  static M Finv(int n){
    init(n);
    return finv[n];
  }
  static M Invs(int n){
    init(n);
    return invs[n];
  }

  static M C(int n,int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k]*finv[k];
  }

  static M P(int n,int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k];
  }

  // put n identical balls into k distinct boxes
  static M H(int n,int k){
    if(n<0||k<0) return M(0);
    if(!n&&!k) return M(1);
    init(n+k);
    return C(n+k-1,n);
  }
};
template<typename M>
vector<M> Enumeration<M>::fact=vector<M>();
template<typename M>
vector<M> Enumeration<M>::finv=vector<M>();
template<typename M>
vector<M> Enumeration<M>::invs=vector<M>();


template<typename V>
V compress(V vs){
  sort(vs.begin(),vs.end());
  vs.erase(unique(vs.begin(),vs.end()),vs.end());
  return vs;
}
template<typename T>
map<T, int> dict(const vector<T> &vs){
  map<T, int> res;
  for(int i=0;i<(int)vs.size();i++)
    res[vs[i]]=i;
  return res;
}
map<char, int> dict(const string &s){
  return dict(vector<char>(s.begin(),s.end()));
}


struct UnionFind{
  int num;
  vector<int> rs,ps;
  UnionFind(){}
  UnionFind(int n):num(n),rs(n,1),ps(n,0){iota(ps.begin(),ps.end(),0);}
  int find(int x){
    return (x==ps[x]?x:ps[x]=find(ps[x]));
  }
  bool same(int x,int y){
    return find(x)==find(y);
  }
  void unite(int x,int y){
    x=find(x);y=find(y);
    if(x==y) return;
    if(rs[x]<rs[y]) swap(x,y);
    rs[x]+=rs[y];
    ps[y]=x;
    num--;
  }
  int size(int x){
    return rs[find(x)];
  }
  int count() const{
    return num;
  }
};

//INSERT ABOVE HERE
signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n,m;
  cin>>n>>m;

  vector<int> as(m),bs(m);
  for(int i=0;i<m;i++) cin>>as[i]>>bs[i],as[i]--,bs[i]--;

  using M = Mint<int, 998244353>;
  using E = Enumeration<M>;
  E::init(1e6);

  M ans{0};

  // empty
  for(int k=3;k<=n;k++)
    ans+=E::C(n,k)*E::Fact(k-1)/M(2);

  // cerr<<ans<<endl;

  using P = pair<int, int>;
  map<P, M> memo;
  auto calc=[&](int cnt,int num){
    // cerr<<cnt<<' '<<num<<endl;
    if(memo.count(P(cnt,num))) return memo[P(cnt,num)];
    M &res=memo[P(cnt,num)];
    res=0;
    M tmp{1};
    for(int j=0;j<=num;j++){
      res+=E::C(num,j)*tmp;
      tmp*=M(cnt+j);
    }
    // cerr<<res<<endl;
    return res;
  };

  int sz=1<<m;
  vector<int> cs(n,0);
  for(int bit=1;bit<sz;bit++){
    vector<int> ss;
    for(int i=0;i<m;i++){
      if((bit>>i)&1){
        cs[as[i]]++;
        cs[bs[i]]++;
        ss.emplace_back(as[i]);
        ss.emplace_back(bs[i]);
      }
    }
    ss=compress(ss);
    auto dc=dict(ss);
    UnionFind uf(ss.size());

    int flg=0;
    for(int i=0;i<m;i++){
      flg|=cs[as[i]]>2;
      flg|=cs[bs[i]]>2;
    }

    for(int i=0;i<m;i++)
      cs[as[i]]=cs[bs[i]]=0;

    if(flg) continue;

    for(int i=0;i<m;i++){
      if((bit>>i)&1){
        int a=dc[as[i]];
        int b=dc[bs[i]];
        flg|=uf.same(a,b);
        uf.unite(a,b);
      }
    }

    int vs=ss.size();
    int es=__builtin_popcount(bit);

    if(vs>=3 and uf.count()==1 and vs==es){
      if(__builtin_parity(bit)) ans-=M(1);
      else ans+=M(1);
      continue;
    }

    if(flg) continue;

    int cnt=vs-es;
    int num=n-vs;
    M res=calc(cnt,num);

    assert(cnt==uf.count());

    if(es==1) res-=M(1);

    res*=M(2).pow(cnt-1);
    res*=E::Fact(cnt-1);

    if(__builtin_parity(bit)) ans-=res;
    else ans+=res;
  }

  cout<<ans<<newl;
  return 0;
}