#include<atcoder/all>
#include <iostream> // cout, endl, cin
#include <string> // string, to_string, stoi
#include <vector> // vector
#include <algorithm> // min, max, swap, sort, reverse, lower_bound, upper_bound
#include <utility> // pair, make_pair
#include <tuple> // tuple, make_tuple
#include <cstdint> // int64_t, int*_t
#include <cstdio> // printf
#include <map> // map
#include <queue> // queue, priority_queue
#include <set> // set
#include <stack> // stack
#include <deque> // deque #include <unordered_map> // unordered_map #include <unordered_set> // unordered_set #include <bitset> // bitset
#include <cctype> // isupper, islower, isdigit, toupper, tolower
#include <math.h>
#include <iomanip>
#include <functional>
#include<unordered_map>
#include <random>
using namespace std;  
using namespace atcoder;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repi(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
//#define endl '\n'
#define all(x) (x).begin(),(x).end()
#define arr(x) (x).rbegin(),(x).rend()
typedef long long ll;
typedef unsigned long long ull;
const ll inf=1e18;  
//const int inf=1e7;  
using graph = vector<vector<int> > ;
using P= pair<ll,ll>;  
using vi=vector<int>;
using vvi=vector<vi>;
using vll=vector<ll>; 
using vvll=vector<vll>;
using vp=vector<P>;
using vvp=vector<vp>;
using vd=vector<double>;
using vvd =vector<vd>;
//string T="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
//string S="abcdefghijklmnopqrstuvwxyz";
//g++ main.cpp -std=c++17 -I .  
//cout <<setprecision(20);
//cout << fixed << setprecision(10);
//cin.tie(0); ios::sync_with_stdio(false);

const double PI = acos(-1);
int vx[]={0,1,0,-1,-1,1,1,-1},vy[]={1,0,-1,0,1,1,-1,-1};
void putsYes(bool f){cout << (f?"Yes":"No") << endl;}
void putsYES(bool f){cout << (f?"YES":"NO") << endl;}
void putsFirst(bool f){cout << (f?"First":"Second") << endl;}
void debug(int test){cout << "TEST" << " " << test << endl;}
ll pow_pow(ll x,ll n,ll mod){
    if(n==0) return 1; 
    x%=mod;
    ll res=pow_pow(x*x%mod,n/2,mod);
    if(n&1)res=res*x%mod;
    return res;
}
ll gcdll(ll x,ll y){
    if(y==0)return x;
    return gcdll(y,x%y);
}
//ll INFF=1000100100100100100;
ll lcmll(ll x,ll y){
    ll X=(x/gcdll(x,y)),Y=y;
    return X*Y;
}
template<class T> bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    else return false;
}
template<class T> bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    else return false;
}
struct edge{
  int to; ll cost;int dir;
  edge(int to,ll cost,int dir) : to(to),cost(cost),dir(dir){}
};
using ve=vector<edge>;
using vve=vector<ve>;
using mint = modint998244353;
//using mint = modint1000000007;
using vm=vector<mint>;
using vvm=vector<vm>;
const int mod = 998244353;
//int mod = 1e9+7;
constexpr ll MAX = 2001000;
ll fact[MAX],finv[MAX],inv[MAX];
void initcomb(){
  fact[0]=fact[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<MAX;i++){
    fact[i]=fact[i-1]*i%mod;
    inv[i]=mod-inv[mod%i]*(mod/i)%mod;
    finv[i]=finv[i-1]*inv[i]%mod;
  }
}
ll comb(ll n,ll k){
  if(n<k) return 0;
  if(n<0||k<0) return 0;
  return fact[n]*(finv[k]*finv[n-k]%mod)%mod;
}
struct UnionFind { vector<int> par, siz; UnionFind(int n) : par(n, -1) , siz(n, 1) { } int root(int x) { if (par[x] == -1) return x;
        else return par[x] = root(par[x]);
    }
    bool issame(int x, int y) {
        return root(x) == root(y);
    }
    bool unite(int x, int y) {
        x = root(x), y = root(y);
        if (x == y) return false; 
        //if (siz[x] < siz[y]) swap(x, y);
        par[y] = x;
        siz[x] += siz[y];
        return true;
    }
    int size(int x) {
        return siz[root(x)];
    }
};
struct Compress{
   vll a;
   map<ll,ll> d,d2;
   int cnt;
   Compress() :cnt(0) {}
   void add(ll x){a.push_back(x);}
   void init(){
     set<ll>s(a.begin(),a.end());
     for(auto y:s)d[y]=cnt++;
     for(auto&y:a)y=d[y];
     for(auto u:d)d2[u.second]=u.first;
   }
   ll to(ll x){return d[x];} //変換先
   ll from(ll x){return d2[x];}//逆引き
   int size(){return cnt;}
};
vll anss;
mint dp[31][17][100005];
void solve(int test){
  initcomb();
  int n,m; cin >> n >> m;
  vi a(m),b(m);
  rep(i,m)cin >> a[i] >> b[i],a[i]--,b[i]--;
  mint ans=0;
  for(int i=3; i<=n; i++){
    mint now=comb(n,i);
    now*=fact[i-1];
    now/=2;
    ans+=now;
  }
  rep(i,31)if(n-i>=0)dp[i][1][0]=1;
  rep(i,31)repi(j,1,17)rep(k,n+1){
    mint now=dp[i][j][k];
    if(!now.val())continue;
    if(j+1<=16)dp[i][j+1][k]+=now;
    if(k+1<=n-i)dp[i][j][k+1]+=now*(n-i-k);
  }
  rep(i,31)repi(j,1,17)repi(k,1,n+1)dp[i][j][k]+=dp[i][j][k-1];
  repi(bit,1,1<<m){
    vi deg(n);
    UnionFind uf(n);
    int cnt=0;
    rep(i,m)if(bit>>i&1){
      deg[a[i]]++,deg[b[i]]++;
      if(uf.issame(a[i],b[i]))cnt++;
      uf.unite(a[i],b[i]);
    }
    int ok=1;
    rep(i,n)if(deg[i]>2)ok=0;
    if(!ok)continue;
    if(cnt){
      int all=1;
      rep(i,n)if(deg[i]){
        if(deg[i]!=2)all=0;
      }
      if(all && cnt==1){
        if(__builtin_popcount(bit)%2)ans-=1;
        else ans+=1;
        continue;
      }
      else continue;
    }
    int num=0;
    int num2=0;
    rep(i,n)if(i==uf.root(i) && uf.size(i)>=2){
      num++;
      num2+=uf.size(i);
    }
    if(num2>=3){
      mint now=dp[num2][num][n-num2];
      now*=pow_pow(2,num,mod);
      now*=fact[num-1];
      now/=2;
      if(__builtin_popcount(bit)%2)ans-=now;
      else ans+=now;
    }
    else {
      mint now=dp[num2][num][n-num2]-1;
      now*=pow_pow(2,num,mod);
      now*=fact[num-1];
      now/=2;
      if(__builtin_popcount(bit)%2)ans-=now;
      else ans+=now;
    }
  }
  cout << ans.val() << endl;
}
//g++ main.cpp -std=c++17 -I .
int main(){cin.tie(0);ios::sync_with_stdio(false);
 int t=1;//cin >>t;
 rep(test,t)solve(test);
 for(auto ans:anss)cout << ans << endl;
}