/*
Contest: - 
Problem: Yukicoder 1116 
Author: tzc_wk
Time: 2020.8.17
*/
#include <bits/stdc++.h>
using namespace std;
#define fi			first
#define se			second
#define pb			push_back
#define fz(i,a,b)	for(int i=a;i<=b;i++)
#define fd(i,a,b)	for(int i=a;i>=b;i--)
#define foreach(it,v) for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define all(a)		a.begin(),a.end()
#define fill0(a)	memset(a,0,sizeof(a))
#define fill1(a)	memset(a,-1,sizeof(a))
#define fillbig(a)	memset(a,0x3f,sizeof(a))
#define y1			y1010101010101
#define y0			y0101010101010
typedef pair<int,int> pii;
typedef long long ll;
inline int read(){
	int x=0,neg=1;char c=getchar();
	while(!isdigit(c)){
		if(c=='-') neg=-1;
		c=getchar();
	}
	while(isdigit(c)) x=x*10+c-'0',c=getchar();
	return x*neg;
}
int n=read(),m=read();
const ll MOD=998244353;
const ll MAGIC=499122177;
ll p2[100005],fac[100005],inv[100005];
ll qpow(ll x,int e){
	ll ans=1;while(e){if(e&1) ans=ans*x%MOD;x=x*x%MOD;e>>=1;} return ans;
}
inline void prework(){
	p2[0]=1;for(int i=1;i<=n;i++) p2[i]=p2[i-1]*2ll%MOD;
	fac[0]=1;for(int i=1;i<=n;i++) fac[i]=fac[i-1]*i%MOD;
	for(int i=0;i<=n;i++) inv[i]=qpow(fac[i],MOD-2);
}
inline ll getc(int x,int y){
	return fac[x]*inv[y]%MOD*inv[x-y]%MOD;
}
inline ll geta(int x,int y){
	return fac[x]*inv[x-y]%MOD;
}
struct edge{
	int u,v;
} e[16];
int key[32],hs[32],cnt=0,num=0;
int f[32],deg[32],siz[32];
inline int find(int x){
	return (f[x]==x)?x:f[x]=find(f[x]);
}
ll dp[100005][16];
inline ll solve(int msk){
	fill0(deg);fill0(f);fill0(siz);fz(i,1,num) f[i]=i,siz[i]=1;
	int cyc=0;
	for(int i=1;i<=m;i++){
		if(msk>>(i-1)&1){
			int x=e[i].u,y=e[i].v;
			deg[x]++;deg[y]++;
			x=find(x);y=find(y);
			if(x!=y) f[y]=x,siz[x]+=siz[y];
			else cyc++;
		}
	}
	for(int i=1;i<=num;i++) if(deg[i]>2) return 0;
	int one=0,chain=0,chain_siz=0;
	for(int i=1;i<=num;i++) if(find(i)==i){
		if(siz[i]>1) chain++,chain_siz=siz[i];
		else one++;
	} one+=n-num;
//	cout<<cyc<<" "<<chain<<" "<<one<<endl;
	if(cyc>=2) return 0;
	if(cyc==1&&chain>1) return 0;
	if(cyc==1&&chain==1) return 1;
	if(chain==0){
		ll ans=0;
		for(int i=3;i<=n;i++) ans=(ans+getc(n,i)*fac[i-1]%MOD*MAGIC%MOD)%MOD;
		return ans; 
	}
	ll ans=fac[chain-1]*p2[chain-1]%MOD*dp[one][chain]%MOD;
	if(chain==1&&chain_siz==2) ans--;
	if(ans<0) ans+=MOD;
	return ans;
}
inline ll count(int x){return (__builtin_popcount(x)%2)?-1ll:1ll;}
int main(){
	prework();
	for(int i=n;i>=max(n-30,0);i--){
		for(int j=1;j<=min(n,15);j++){
			if(i+j>n) continue;
			for(int k=0;k<=i;k++) dp[i][j]=(dp[i][j]+getc(k+j-1,j-1)*geta(i,k)%MOD)%MOD;
		}
	}
//	puts("IN");
	for(int i=1;i<=m;i++) e[i].u=read(),e[i].v=read();
	for(int i=1;i<=m;i++) key[++cnt]=e[i].u,key[++cnt]=e[i].v; 
	sort(key+1,key+cnt+1);
	for(int i=1;i<=cnt;i++) if(key[i]!=key[i-1]) hs[++num]=key[i];
	for(int i=1;i<=m;i++) e[i].u=lower_bound(hs+1,hs+num+1,e[i].u)-hs;
	for(int i=1;i<=m;i++) e[i].v=lower_bound(hs+1,hs+num+1,e[i].v)-hs;
	ll ans=0;
	for(int i=0;i<(1<<m);i++){
//		cout<<i<<" "<<solve(i)<<endl;
		ans=(ans+solve(i)*count(i)+MOD)%MOD;
	}
	printf("%lld\n",ans);
	return 0;
}
/*
100000 4
12721 93243
93243 68356
68356 12721
39874 19231
*/