#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#define N_MAX 200002

using namespace std;
typedef long long ll;
typedef pair<int, int> P;

const ll MOD = 998244353;

struct UnionFind {
  vector<int> data;
  UnionFind(int size) : data(size, -1) { }
  bool unionSet(int x, int y) {
    x = root(x); y = root(y);
    if (x != y) {
      if (data[y] < data[x]) swap(x, y);
      data[x] += data[y]; data[y] = x;
    }
    return x != y;
  }
  bool findSet(int x, int y) {
    return root(x) == root(y);
  }
  int root(int x) {
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  int size(int x) {
    return -data[root(x)];
  }
};

ll inv[N_MAX],fac[N_MAX],finv[N_MAX];

void init(){
    fac[0]=fac[1]=1;
    finv[0]=finv[1]=1;
    inv[1]=1;
    for(int i=2;i<N_MAX;i++){
        inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
        fac[i]=fac[i-1]*(ll) i%MOD;
        finv[i]=finv[i-1]*inv[i]%MOD;
    }
}

ll inv_(ll n){
    if(n == 1) return 1;
    else return MOD-inv_(MOD%n)*(MOD/n)%MOD;
}

ll comb(ll n, ll r){
  ll ans;
  if(n < r){
      ans = 0;
  }else{
      ans = (fac[n]*finv[r])%MOD;
      ans = (ans*finv[n-r])%MOD;
      ans = (ans+MOD)%MOD;
  }
  return ans;
}

map<P, ll> mp;

ll calc(ll n, ll k){
    ll ans = 0;
    for(ll i = 0; i <= n-k; i++){
        if(k+i <= 1) continue;
        if(k+i == 2 && k == 0) continue;
        if(k == 1 && i == 1){
            ans += comb(n-k, i);
            continue;
        }
        if(k == 2 && i == 0){
            ans += 2*comb(n-k, i);
            continue;
        }
        ll tmp = (fac[k+i]*(1<<k))%MOD;
        tmp *= inv[2];
        tmp %= MOD;
        tmp *= inv[k+i];
        tmp %= MOD;
        tmp *= comb(n-k, i);
        tmp %= MOD;
        ans += tmp;
    }
    mp[P(n, k)] = ans;
    return ans;
}
int N, M;
int a[15], b[15];

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    init();
    cin >> N >> M;
    for(int i = 0; i < M; i++) {
        cin >> a[i] >> b[i];
    }
    mp[P(2, 2)] = 2;
    mp[P(2, 1)] = 1;

    ll ans = 0;
    for(int i = 0; i < (1<<M); i++){
        set<int> st;
        int c = 0;
        for(int j = 0; j < M; j++){
            if(i&(1<<j)){
                c++;
                st.insert(a[j]); st.insert(b[j]);
            }
        }
        int sz = st.size();
        map<int, int> idx;
        int cur = 0;
        for(int j : st){
            idx[j] = cur;
            cur++;
        }
        UnionFind uf(sz);
        bool ok = true;
        for(int j = 0; j < M; j++){
            if(i&(1<<j)){
                int a_idx = idx[a[j]];
                int b_idx = idx[b[j]];
                if(uf.findSet(a_idx, b_idx)){
                    ok = false;
                }else{
                    uf.unionSet(a_idx, b_idx);
                }
            }
        }
        
        set<int> st_root;
        for(int j = 0; j < sz; j++) {
            int r = uf.root(j);
            st_root.insert(r);
        }
        if(!ok) {
            vector<int> v_cnt(sz);
            for(int j = 0; j < M; j++){
                if(i&(1<<j)){
                    int a_idx = idx[a[j]];
                    int b_idx = idx[b[j]];
                    v_cnt[a_idx]++;
                    v_cnt[b_idx]++;
                }
            }
            bool loop = true;
            for(int j : v_cnt){
                if(j != 2) loop = false;
            }
            if(loop && st_root.size() == 1) {
                ll sgn = (c%2 == 0 ? 1 : -1);
                ans += sgn;
            }
            continue;
        }
        int rem = N-sz+st_root.size();
        int k = st_root.size();
        ll sgn = (c%2 == 0 ? 1 : -1);
        ll tmp;
        if(mp.count(P(rem, k)) == 0){
            tmp = calc(rem, k);
        }else{
            tmp = mp[P(rem, k)];
        }
        if(k == 1 && uf.size(0) >= 3) tmp++;
        ans += (sgn*tmp)%MOD;
        ans %= MOD;
    }
    cout << (ans+MOD)%MOD << endl;
}