#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<tuple>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = 998244353;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define Per(i,sta,n) for(int i=n-1;i>=sta;i--)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef long double ld;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;
int dx[4]={1,-1,0,0};
int dy[4]={0,0,1,-1};

template<int mod>
struct ModInt {
    long long x;
 
    ModInt() : x(0) {}
    ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    explicit operator int() const {return x;}
 
    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }
 
    ModInt operator-() const { return ModInt(-x); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
 
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
 
    ModInt inverse() const{
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        return ModInt(u);
    }

    ModInt power(long long p) const{
        int a = x;
        if (p==0) return 1;
        if (p==1) return ModInt(a);
        if (p%2==1) return (ModInt(a)*ModInt(a)).power(p/2)*ModInt(a);
        else return (ModInt(a)*ModInt(a)).power(p/2);
    }

    ModInt power(const ModInt p) const{
        return ((ModInt)x).power(p.x);
    }

    friend ostream &operator<<(ostream &os, const ModInt<mod> &p) {
        return os << p.x;
    }
    friend istream &operator>>(istream &is, ModInt<mod> &a) {
        long long x;
        is >> x;
        a = ModInt<mod>(x);
        return (is);
    }
};

using modint = ModInt<mod>;

struct ModFac{
  public:
    vector<modint> f,i_f;
    int n;

    ModFac(int n_){
      n=n_;
      f.resize(n+1,1);
      i_f.resize(n+1,1);
      for(int i=0;i<n;i++){
        f[i+1]=f[i]*(modint)(i+1);
      }
      i_f[n]=f[n].power(mod-2);
      for(int i=n-1;i>=0;i--){
        i_f[i]=i_f[i+1]*(modint)(i+1);
      }
    }
    ModFac(modint n_){
      n=(int)n_;
      f.resize(n+1,1);
      i_f.resize(n+1,1);
      for(int i=0;i<n;i++){
        f[i+1]=f[i]*(modint)(i+1);
      }
      i_f[n]=f[n].power(mod-2);
      for(int i=n-1;i>=0;i--){
        i_f[i]=i_f[i+1]*(modint)(i+1);
      }
    }
    
    modint factorial(int x){
      //cout << f.size() << endl;
      return f[x];
    }
        
    modint inv_factorial(int x){
      return i_f[x];
    }
    
    modint comb(int m,int k){
      if (m<0 or k<0) return 0;
      if (m<k) return 0;
      return f[m]*i_f[k]*i_f[m-k];
    }
};


int n,m;
P E[20];
set<int> se;
vector<P> G[100010];
map<int,bool> visited; 
map<P,pair<modint,bool>> memo;
ModFac MF(110000);

void dfs(int s,int edges,int &node,int &edge,int &max_branch){
  visited[s]=true;
  int branch=0;
  node+=1;
  for(P e:G[s]){
    if(!(edges&(1 << e.second))) continue;
    branch+=1;
    edge+=1;
    if(visited[e.first]) continue;
    dfs(e.first,edges,node,edge,max_branch);
  }
  max_branch=max(max_branch,branch);
}

modint f(int M,int K){
  if(memo[P(M,K)].second) return memo[P(M,K)].first;
  modint res=0;
  rep(i,M+1){
    res+=MF.comb(M,i)*MF.factorial(i+K);
  }
  memo[P(M,K)].first=res;memo[P(M,K)].second=true;
  return res;
}

void solve(){
  cin >> n >> m;
  rep(i,m){
    int a,b;cin >> a >> b;a--;b--;
    se.insert(a);se.insert(b);
    E[i]=P(a,b);
    G[a].push_back(P(b,i));
    G[b].push_back(P(a,i));
  }
  int U=(1 << m);
  modint ans=0;
  rep(S,U){
    modint res=0;
    visited.clear();
    int num_cycle=0,num_pass=0,num_NG=0,others=n;
    //cout << bitset<15>(S) << endl;
    for(int a:se){
      if(visited[a]) continue;
      int node=0,edge=0,max_branch=0;
      dfs(a,S,node,edge,max_branch);
      edge/=2;
      if(node==1) continue;
      if(node==edge+1 && max_branch<=2) num_pass+=1;
      if(node==edge && max_branch==2) num_cycle+=1;
      if(max_branch>=3) num_NG+=1;
      others-=node;
    }
    //cout << num_pass << " " << num_cycle << " " << num_NG << endl;
    //cout << others << endl;
    //if(num_cycle>=2) cout << bitset<15>(S) << endl;
    if(num_NG) continue;
    if(num_cycle==1 && num_pass==0) res=1;
    if(num_cycle==0 && num_pass>=1) {
      res=((modint)2).power(num_pass-1)*f(others,num_pass-1);
      if(n-others==2) res-=1;
    }
    //cout << res << endl;
    int cnt=0;
    rep(i,m){
      if(S&(1 << i)) cnt+=1;
    }
    if(cnt%2==1) ans+=res;
    else ans-=res;
  }
  modint ALL=0;
  Rep(i,3,n+1){
    ALL+=MF.factorial(n)/((modint)(2*i)*MF.factorial(n-i));
  }
  //cout << ALL << endl;
  cout << ALL-ans << endl;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(50);
    solve();
}