#include <bits/stdc++.h>
/*#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
*/#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")    
using namespace std;
/*namespace mp = boost::multiprecision;
using Bint = mp::cpp_int;
using Real = mp::number<mp::cpp_dec_float<1024>>;
*/#define lli long long int
#define uli unsigned long long int
#define INF 9999999999999999
#define rep(i,m,n) for(lli i = m;i < n;i++)
#define rrep(i,m,n) for(lli i=m-1;i>=n;i--)
#define pb(n) push_back(n)
#define UE(N) N.erase(unique(N.begin(),N.end()),N.end());
#define Sort(n) sort(n.begin(), n.end())
#define Rev(n) reverse(n.begin(),n.end())
#define Out(S) cout << S << endl
#define NeOut(S) cout << S
#define HpOut(S) cout << setprecision(50) << S << endl
#define Vec(K,L,N,S) vector<L> K(N,S)
#define DV(K,L,N,M,S) vector<vector<L>> K(N,vector<L>(M,S))
#define TV(K,L,N,M,R,S) vector<vector<vector<L>>> K(N,vector<vector<L>>(M,vector<L>(R,S)))
#define pint pair<lli,lli>
#define paf(L,R) pair<L,R>
#define mod 998244353
#define MAX 10000000
#define ALL(a)  a.begin(),a.end()
#define chmax(a, b) a = (((a)<(b)) ? (b) : (a))
#define chmin(a, b) a = (((a)>(b)) ? (b) : (a))
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % mod;
        inv[i] = mod - inv[mod%i] * (mod / i) % mod;
        finv[i] = finv[i - 1] * inv[i] % mod;
    }
}
lli nCr(lli n, lli r){
    if (n < r) return 0;
    if (n < 0 || r < 0) return 0;
    return fac[n] * (finv[r] * finv[n - r] % mod) % mod;
}
lli modpow(lli n,lli k,lli m){
  if(k==0)return 1;
  else if(k%2==1)return modpow(n,k-1,m)*n%m;
  else{
    lli temp=modpow(n,k/2,m);
    return temp*temp%m;
  }
}
int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);
  lli A,B,X,Y,Z,N,M,num=0,sum=0,flag=0;string S,T;
  cin >> N >> M;
  COMinit();
  Vec(G,pint,0,pint(0,0));
  map<int,int>m1;
  while(M--){
    cin >> A >> B;
    G.pb(pint(A-1,B-1));
    m1[A-1]++;
    m1[B-1]++;
  }
  Vec(pk,pint,m1.size(),pint(0,0));
  for(auto v:m1)pk.pb(pint(pk.size(),v.first));
  map<int,int>m2;
  for(auto v:pk)m2[v.second]=v.first;
  rep(i,0,M){
    G[i].first=m2[G[i].first];
    G[i].second=m2[G[i].second];
  }
  M=G.size();
  Vec(dp,lli,N+1,1);
  Vec(dp2,lli,N+1,1);
  rep(i,2,N+1)dp[i]=i*(dp[i-1]+1)%mod;
  rep(i,2,N+1)dp2[i]=i*(dp2[i-1])%mod;
  rep(i,3,N+1)sum=(sum+dp2[i-1]*nCr(N,i)/2)%mod;
  for(lli i=1;i<(1<<M);i++){
    DV(Gp,int,30,0,0);
    X=0,Y=0,Z=0;
    flag=1;
    Vec(dist,lli,30,-1);
    rep(j,0,M)if(i&(1<<j)){
      Gp[G[j].first].pb(G[j].second);
      Gp[G[j].second].pb(G[j].first);
      dist[G[j].first]=0;
      dist[G[j].second]=0;
      X++;  
    }
    rep(j,0,30)Y+=dist[j]+1;
    rep(j,0,30)if(Gp[j].size()>2)flag=0;
    if(!flag)continue;
    rep(j,0,30){
      if(!Gp[j].size())continue;
      if(dist[j])continue;
      dist[j]=1;
      queue<int>que;
      que.push(j);
      while(!que.empty()){
        auto v=que.front();que.pop();
        for(auto nv:Gp[v]){
          if(dist[nv])continue;
          dist[nv]=dist[v];
          que.push(nv);
        }
      }
      Z++;
    }
    if(Y-Z>=X){
      if(X==1)sum+=pow(-1,X%2)*dp[N-2];
      else{
        num=0;
        rep(j,0,N-Y+1)num=(num+dp2[j]*nCr(N-Y,j)*nCr(j+Z-1,Z-1))%mod;
        sum+=pow(-1,X%2)*(dp2[Z-1]*modpow(2,Z-1,mod)%mod*num%mod);
      }
    }
    else if(X==Y&&Z==1)sum+=pow(-1,X%2);
    //cout << X << " " << Y << " " << Z << " " << sum << endl;
    sum=(sum+mod)%mod;
  }
  Out(sum);

}