#include <bits/stdc++.h>
using namespace std;
#define modulo 998244353
#define mod(mod_x) ((((long long)mod_x+modulo))%modulo)
#define Inf 1000000000000000000

int beki(long long a,long long b,int M = modulo){
	int x = 1;
	while(b!=0){
		if(b&1){
			x=((long long)x*a)%M;
		}
		a=((long long)a*a)%M;
		b>>=1;
	}
	return x;
}


int gyakugen(int a){
	return beki(a,modulo-2);
}

struct combi{
	deque<int> kaijou;
	deque<int> kaijou_;
	
	combi(int n){
		kaijou.push_back(1);
		for(int i=1;i<=n;i++){
			kaijou.push_back(mod(kaijou[i-1]*i));
		}
		
		int b=gyakugen(kaijou[n]);
		
		kaijou_.push_front(b);
		for(int i=1;i<=n;i++){
			int k=n+1-i;
			kaijou_.push_front(mod(kaijou_[0]*k));
		}
	}
	
	int combination(int n,int r){
		if(r>n)return 0;
		int a = mod(kaijou[n]*kaijou_[r]);
		a=mod(a*kaijou_[n-r]);
		return a;
	}
	
	int junretsu(int a,int b){
		int x = mod(kaijou_[a]*kaijou_[b]);
		x=mod(x*kaijou[a+b]);
		return x;
	}
	
	int catalan(int n){
		return mod(combination(2*n,n)*gyakugen(n+1));
	}
	
};

int N,M;
combi C(1000000);

int get(int n,int b){
	static vector<vector<int>> dp(100005,vector<int>(18,-1));
	if(dp[n][b]!=-1)return dp[n][b];
	int sum = 0;
	if(b>=1){
		for(int i=0;i<=n;i++){
			if(N-n + i < 3)continue;
			int t = C.combination(n,i)*C.kaijou[b+i];
			t = mod(t * gyakugen(b+i));
			sum = mod(sum +t);
		}
		
		int ret  = mod(sum*beki(2,max(0,b-1)));

		dp[n][b] = ret;
		return ret;
	}
	else{
		int ret =0;
		for(int i=3;i<=n;i++){
			int t = mod(C.combination(n,i) * C.kaijou[i]);
			t = mod(t * gyakugen(2));
			t = mod(t * gyakugen(i));
			ret = mod(ret + t);
		}
		dp[n][b] = ret;
		return ret;
		
	}
}

bool check(vector<pair<int,int>> p){
	int now = p[0].second;
	int goal = p[0].first;
	p.erase(p.begin());
	for(int i=0;i<30;i++){
		for(int j=0;j<p.size();j++){
			if(p[j].first==now){
				now = p[j].second;
			}
			else if(p[j].second==now){
				now = p[j].first;
			}
			p.erase(p.begin()+j);
			break;
		}
		if(p.size()==0)return true;
	}
	return false;
}

int main(){
	
	cin>>N>>M;
	
	vector<pair<int,int>> p(M);
	for(int i=0;i<M;i++){
		cin>>p[i].first>>p[i].second;
		p[i].first--;
		p[i].second--;
		if(p[i].first>p[i].second)swap(p[i].first,p[i].second);
	}
	
	int ans = 0;
	
	for(int i=0;i<(1<<M);i++){
		vector<pair<int,int>> q;
		int cnt = 0;
		map<int,int> mp;
		for(int j=0;j<M;j++){
			if((i>>j)&1){
				mp[p[j].first]++;
				mp[p[j].second]++;
				q.push_back(p[j]);
				cnt++;
			}
		}
		
		bool f = true;
		int c1 = 0;
		for(auto a:mp){
			if(a.second>=3){
				f=false;
				break;
			}
			if(a.second==1){
				c1++;
			}
		}
		if(!f)continue;
		int t;
		if(c1==0&&mp.size()!=0){
			if(!check(q))continue;
			t = 1;
		}
		else{
			
			t = get(N-mp.size(),c1/2);
			
		}	
		if(cnt%2==0)ans = mod(ans + t);
		else ans  =mod(ans - t);		
		
	}
	
	cout<<ans<<endl;
	
	return 0;
}