#include <bits/stdc++.h>
using namespace std;

const int64_t MOD = 998244353;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}
void mul(int64_t& a, int64_t b){
    a = a*b % MOD;
}

int64_t power_mod(int64_t num, int64_t power){
    int64_t prod = 1;
    num %= MOD;
    while(power > 0){
        if(power&1) prod = prod * num % MOD;
        num = num * num % MOD;
        power >>= 1;
    }
    return prod;
}

int64_t extgcd(int64_t a, int64_t b, int64_t& x, int64_t& y){
    int64_t d = a;
    if(b != 0){
        d = extgcd(b, a%b, y, x);
        y -= (a/b) * x;
    }else{
        x = 1; y = 0;
    }
    return d;
}

int64_t inv_mod(int64_t a){
    int64_t x, y;
    extgcd(a, MOD, x, y);
    return (MOD + x%MOD) % MOD;
}

vector<int64_t> fact, fact_inv;

void create_mod_tables(int num){
    fact.assign(num+1, 1);
    fact_inv.assign(num+1, 1);
    for(int i=1; i<=num; i++) fact[i] = fact[i-1] * i % MOD;
    fact_inv[num] = inv_mod(fact[num]);
    for(int i=num; i>0; i--) fact_inv[i-1] = fact_inv[i] * i % MOD;
}

int64_t comb_mod(int n, int k){
    return fact[n] * fact_inv[n-k] % MOD * fact_inv[k] % MOD;
}

int64_t perm_mod(int n, int k){
    return fact[n] * fact_inv[n-k] % MOD;
}

int nth_bit(int64_t num, int n){
    return (num >> n) & 1;
}

struct UnionFind {
    vector<int> par;
    vector<int> sz;

    UnionFind(int n=0){ if(n>0) initialize(n); }
    void initialize(int n){
        par.resize(n);
        sz.assign(n, 1);
        for(int i=0; i<n; i++){
            par[i] = i;
        }
    }

    int find(int x){
        if(par[x] == x){
            return x;
        }else{
            return find(par[x]);
        }
    }

    bool unite(int x, int y){
        x = find(x), y = find(y);
        if(x == y) return false;
        if(sz[x] > sz[y]) swap(x, y);
        par[x] = y;
        sz[y] += sz[x];
        return true;
    }

    bool same(int x, int y){ return find(x) == find(y); }
    int size(int x){ return sz[find(x)]; }
};

template<typename T>
vector<T> compress(vector<T> A){
    sort(A.begin(), A.end());
    A.erase(unique(A.begin(), A.end()), A.end());
    return A;
}

int main(){
    int N, M;
    cin >> N >> M;
    vector<int> A(M), B(M), V;
    for(int i=0; i<M; i++){
        cin >> A[i] >> B[i];
        A[i]--; B[i]--;
        V.push_back(A[i]);
        V.push_back(B[i]);
    }
    V = compress(V);
    int sz = V.size();
    for(int& a : A) a = lower_bound(V.begin(), V.end(), a) - V.begin();
    for(int& a : B) a = lower_bound(V.begin(), V.end(), a) - V.begin();

    create_mod_tables(200000);

    // use, path
    static int64_t P[31][16];
    for(int use=0; use<=2*M; use++) for(int path=0; path<=M; path++){
        int rest = N-use;
        if(rest < 0) continue;
        int64_t p2 = power_mod(2, path);
        mul(p2, inv_mod(2));
        for(int r=0; r<=rest; r++) if(use+r >= 3 && path+r){
            int64_t res = comb_mod(rest, r) * fact[path+r-1] % MOD * p2 % MOD;
            //cerr << use<<path<<r<<" " << res << endl;
            add(P[use][path], res);
        }
    }

    int64_t ans = 0;
    for(int b=0; b<(1<<M); b++){
        vector<int> deg(sz);
        UnionFind uf(sz);
        int64_t C = 1;
        for(int i=0; i<M; i++) if(nth_bit(b, i)){
            uf.unite(A[i], B[i]);
            deg[A[i]]++;
            deg[B[i]]++;
            C *= -1;
        }
        if(b && *max_element(deg.begin(), deg.end()) > 2) continue;
        int use = 0, cmp = 0, one = 0;
        for(int i=0; i<sz; i++) if(deg[i]){
            use++;
            if(uf.find(i) == i) cmp++;
            if(deg[i] == 1) one++;
        }
        int64_t res = 0;
        if(cmp == 1 && one == 0){
            res = 1;
        }else{
            if(cmp*2 != one) continue;
            res = P[use][cmp];
        }
        //cerr << b << res << use << cmp << endl;
        add(ans, MOD+C*res);
    }
    cout << ans << endl;
    return 0;
}