#include<bits/stdc++.h>
#define int long long
#define reduce(x) (x>=mod?x-mod:x)
using namespace std;
constexpr int M=5e3+5,mod=998244353;
int n,m,x,y,ans,num,Index;vector<int>G[M];
vector<pair<int,int>>g[M];bool vis[M],flag[M<<1];
int tmp[M],bel[M],dfn[M],low[M],siz[M],cnt[M],pw1[M],pw2[M],f[M][M];
int read(){
	int x=0,f=1;char ch=getchar();
	while (!isdigit(ch)) {if (ch=='-') f=-1;ch=getchar();}
	while (isdigit(ch)) x=x*10+ch-48,ch=getchar();
	return x*f;
}
int qpow(long long x){return 1ll*pw1[x%n]*pw2[x/n]%mod;}
void dfs1(int x,int f){
	dfn[x]=low[x]=++Index;
	for (auto [u,v]:g[x]){
		if (!dfn[u]){dfs1(u,v);
			low[x]=min(low[x],low[u]);
			if (dfn[x]<low[u]) flag[v]=1;
		}
		else if (v!=f)
			low[x]=min(low[x],dfn[u]);
	}
}
void dfs2(int x){
	siz[bel[x]=num]++;vis[x]=1;
	for (auto [u,v]:g[x])
		if (!vis[u]&&!flag[v]) dfs2(u);
}
void dfs3(int x,int fa){
	f[x][siz[x]]=qpow(1ll*siz[x]*(siz[x]-1)/2-cnt[x]/2);
	for (auto v:G[x]){
		if (v==fa) continue;dfs3(v,x);
		for (int i=1;i<=siz[x]+siz[v];i++) tmp[i]=0;
		for (int i=1;i<=siz[x];i++) if (f[x][i])
			for (int j=1;j<=siz[v];j++) if (f[v][j])
				tmp[i+j]=(tmp[i+j]+1ll*f[x][i]*f[v][j]%mod*qpow(1ll*i*j-1))%mod,
				tmp[i]=reduce(tmp[i]+mod-1ll*f[x][i]*f[v][j]%mod);
		siz[x]+=siz[v]; for (int i=1;i<=siz[x];i++) f[x][i]=tmp[i];
	}
}
signed main(){
	n=read();m=read();
	for (int i=1;i<=m;i++){
		x=read();y=read();
		g[x].push_back({y,i});
		g[y].push_back({x,i});
	} dfs1(1,0);
	for (int i=1;i<=n;i++)
		if (!vis[i]) ++num,dfs2(i);
	for (int i=pw1[0]=1;i<=n;i++) pw1[i]=reduce(pw1[i-1]<<1);
	for (int i=pw2[0]=1;i<=n;i++) pw2[i]=1ll*pw2[i-1]*pw1[n]%mod;
	for (int i=1;i<=n;i++)
		for (auto [j,_]:g[i])
			if (bel[i]^bel[j])
				G[bel[i]].push_back(bel[j]);
			else cnt[bel[i]]++;
	dfs3(1,0);
	for (int i=1;i<=n;i++)
		ans=reduce(ans+f[1][i]);
	return printf("%d\n",ans),0;
}