#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#include <time.h>
#include <stack>
#include <array>
#define popcount __builtin_popcount
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
const ll MOD=998244353;
ll powmod(ll a, ll k){
    ll ap=a, ans=1;
    while(k){
        if(k&1){
            ans*=ap;
            ans%=MOD;
        }
        ap=ap*ap;
        ap%=MOD;
        k>>=1;
    }
    return ans;
}
ll inv(ll a){
    return powmod(a, MOD-2);
}
ll f[1000010], invf[1000010];
void fac(int n){
    f[0]=1;
    for(ll i=1; i<=n; i++) f[i]=f[i-1]*i%MOD;
    invf[n]=inv(f[n]);
    for(ll i=n-1; i>=0; i--) invf[i]=invf[i+1]*(i+1)%MOD;
}
ll comb(int x, int y){
    if(!(0<=y && y<=x)) return 0;
    return f[x]*invf[y]%MOD*invf[x-y]%MOD;
}
struct unionfind{
    vector<int> par, sz;
    unionfind() {}
    unionfind(int n):par(n), sz(n, 1){
        for(int i=0; i<n; i++) par[i]=i;
    }
    int find(int x){
        if(par[x]==x) return x;
        return par[x]=find(par[x]);
    }
    void unite(int x, int y){
        x=find(x); y=find(y);
        if(x==y) return;
        if(sz[x]>sz[y]) swap(x, y);
        par[x]=y;
        sz[y]+=sz[x];
    }
    bool same(int x, int y){
        return find(x)==find(y);
    }
    int size(int x){
        return sz[find(x)];
    }
};
int n, m;
int a[20], b[20];
ll dp[1<<15];
map<P, ll> memo;
int main()
{
	cin>>n>>m;
	for(int i=0; i<m; i++){
		cin>>a[i]>>b[i];
		a[i]--; b[i]--;
	}
	fac(n);
	unionfind uf(n);
	for(int i=0; i<(1<<m); i++){
		map<int, int> deg;
		int c=0, l=0;
		int myon=0;
		for(int j=0; j<m; j++){
			if(i&(1<<j)){
				c++;
				deg[a[j]]++;
				deg[b[j]]++;
				if(uf.same(a[j], b[j])){
					myon++;
				}
				uf.unite(a[j], b[j]);
			}
		}
		if(myon>1) continue;
		for(auto p:deg) uf.par[p.first]=p.first, uf.sz[p.first]=1;
		if(myon){
			bool cyc=1;
			for(auto p:deg){
				if(p.second!=2) cyc=0;
			}
			if(cyc) dp[i]=1;
			continue;
		}
		int t=deg.size();
		for(auto p:deg){
			if(p.second==1) l++;
		}
		if(l!=2*(t-c)) continue;
		if(memo.find({t, c})!=memo.end()){
			dp[i]=memo[{t, c}];
			continue;
		}
		for(int k=max(0, 3-t); k<=n-t; k++){
			(dp[i]+=comb(n-t, k)*f[t-c+k-1])%=MOD;
		}
		dp[i]=dp[i]*powmod(2, t-c)%MOD*((MOD+1)/2)%MOD;
		memo[{t, c}]=dp[i];
	}
	for(int i=(1<<m)-1; i>=0; i--){
		int x=(1<<m)-1-i;
		for(int j=x; j>0; j=(j-1)&x){
			dp[i]+=MOD-dp[i^j];
		}
		dp[i]%=MOD;
	}
	cout<<dp[0]<<endl;
	return 0;
}