#include<iostream>
#include<map>
using namespace std;
#include<vector>
struct UF{
	int n;
	vector<int>parent,rank;
	UF(int n_=0):n(n_),parent(n_),rank(n_,1)
	{
		for(int i=0;i<n_;i++)parent[i]=i;
	}
	int find(int a){return parent[a]!=a?parent[a]=find(parent[a]):a;}
	bool same(int a,int b){return find(a)==find(b);}
	bool unite(int a,int b)
	{
		a=find(a),b=find(b);
		if(a==b)return false;
		if(rank[a]<rank[b])
		{
			parent[a]=b;
			rank[b]+=rank[a];
		}
		else
		{
			parent[b]=a;
			rank[a]+=rank[b];
		}
		return true;
	}
	int size(int a){return rank[find(a)];}
};
const long mod=998244353;
long power(long a,long b){return b?power(a*a%mod,b/2)*(b%2?a:1)%mod:1;}
long fac[1<<17],inv[1<<17];
long comb(int N,int K){return fac[N]*inv[K]%mod*inv[N-K]%mod;}
int N,M;
int a[15],b[15];
map<pair<int,int>,long>memo;
main()
{
	cin>>N>>M;
	for(int i=0;i<M;i++)cin>>a[i]>>b[i];
	fac[0]=1;
	for(int i=1;i<=N;i++)fac[i]=fac[i-1]*i%mod;
	inv[N]=power(fac[N],mod-2);
	for(int i=N;i--;)inv[i]=inv[i+1]*(i+1)%mod;
	long ans=0;
	for(int k=3;k<=N;k++)
	{
		(ans+=comb(N,k)*fac[k-1]%mod)%=mod;
	}
	for(int i=1;i<1<<M;i++)
	{
		map<int,int>mp;
		map<int,int>id;
		int sz=0;
		bool ok=true;
		int one=0,edge=0;
		for(int j=0;j<M;j++)if(i>>j&1)
		{
			edge++;
			if(mp[a[j]]==2)
			{
				ok=false;
				break;
			}
			else if(mp[a[j]]==1)
			{
				mp[a[j]]=2;
				one--;
			}
			else
			{
				mp[a[j]]=1;
				one++;
				id[a[j]]=sz++;
			}
			if(mp[b[j]]==2)
			{
				ok=false;
				break;
			}
			else if(mp[b[j]]==1)
			{
				mp[b[j]]=2;
				one--;
			}
			else
			{
				mp[b[j]]=1;
				one++;
				id[b[j]]=sz++;
			}
		}
		if(!ok)continue;
		int m=mp.size();
		UF uf(m);
		int rc=0;
		for(int j=0;j<M;j++)if(i>>j&1)
		{
			int x=id[a[j]],y=id[b[j]];
			if(!uf.unite(x,y))rc++;
		}
		if(rc>=1)
		{
			if(rc==1&&one==0)
			{
				if(edge%2==1)ans=(ans+mod-2)%mod;
				else ans=(ans+2)%mod;
			}
			continue;
		}
		long now;
		pair<int,int>p=make_pair(m,one);
		if(memo.find(p)!=memo.end())now=memo[p];
		else
		{
			now=0;
			for(int k=0;k<=N-m;k++)
			{
				if(m+k>=3)(now+=comb(N-m,k)*fac[k+one/2-1]%mod)%=mod;
			}
			now=now*power(2,one/2)%mod;
			memo[p]=now;
		}
		if(edge%2==1)ans=(ans+mod-now)%mod;
		else ans=(ans+now)%mod;
	}
	cout<<ans*power(2,mod-2)%mod<<endl;
}