#include<iostream>
#include<map>
using namespace std;
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;
		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++;
			}
			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++;
			}
		}
		if(!ok)continue;
		int m=mp.size();
		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;
			if(one==0)now=2;
			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;
}