#include<bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair <int, int>
#define app push_back
#define all(a) a.begin(), a.end()
#define bp __builtin_popcountll
#define ll long long
#define mp make_pair
#define f first
#define s second
#define Time (double)clock()/CLOCKS_PER_SEC
#define debug(x) std::cout << #x << ": " << x << '\n';

const int N = 1e5+7;
vector <int> g[N];

const int MOD = 998244353;
int mod(int n) {
    n %= MOD;
    if (n < 0) return n + MOD;
    else return n;
}   
int fp(int a, int p) {
    int ans = 1, c = a;
    for (int i = 0; (1ll << i) <= p; ++i) {
        if ((p >> i) & 1) ans = mod(ans * c);
        c = mod(c * c);
    }   
    return ans;
}   
int dv(int a, int b) { return mod(a * fp(b, MOD - 2)); }
int f[N], inv[N];
void prec() {
    f[0] = 1;
    for (int i = 1; i < N; ++i)
        f[i] = mod(f[i - 1] * i);
    inv[N - 1] = fp(f[N - 1], MOD - 2);
    for (int i = N - 2; i >= 0; --i)
        inv[i] = mod(inv[i + 1] * (i + 1));
}
int C(int n, int k) {
    return mod(f[n] * mod(inv[k] * inv[n - k]));
}   

bool used[N];
void dfs(int u) {
    used[u] = 1;
    for (int v : g[u])
        if (!used[v])
            dfs(v);
}
signed main() {
    #ifdef HOME
    freopen("input.txt", "r", stdin);
    #else
    #define endl '\n'
    ios_base::sync_with_stdio(0); cin.tie(0);
    #endif
    
    prec();
    int n, m;
    cin >> n >> m;

    vector <ii> ed;
    for (int i = 0; i < m; ++i) {
        int u, v;
        cin >> u >> v;
        ed.app(mp(u, v));
    }   

    int ans = 0;
    for (int sz = 3; sz <= n; ++sz) {
        ans = mod(ans + C(n, sz) * mod(f[sz - 1] * inv[2]));
    }   

    //debug(ans);

    for (int mask = 1; mask < (1 << m); ++mask) {
        vector <int> c;
        for (int i = 0; i < m; ++i)
            if ((mask >> i) & 1) {
                g[ed[i].f].app(ed[i].s);
                g[ed[i].s].app(ed[i].f);
                c.app(ed[i].f);
                c.app(ed[i].s);
            }   

        sort(all(c));
        c.resize(unique(all(c)) - c.begin());

        bool bad = 0;
        for (int u : c) {   
            if (g[u].size() > 2)
                bad = 1;
        }   

        //calc
        memset(used, 0, sizeof used);
        int pa = 0;
        for (int u : c) {
            if (!used[u]) {
                ++pa;
                dfs(u);
            }   
        }   
        int cnt = c.size();

        for (auto e : c)
            g[e].clear();

        if (!bad && pa == 1 && cnt == bp(mask)) {
            //one cycle
            ans = mod(ans - 1);
            continue;
        }   

        if (bp(mask) != cnt - pa) {
            bad = 1;
        }   
        if (bad)
            continue;

        int delt = 0;            
        if (pa == 1) {
            if (cnt >= 3) {
                delt = 1;
            }
            int t = 1;
            for (int add = 1; cnt + add <= n; ++add) {
                t = mod(t * add);
                if (cnt + add >= 3) 
                    delt = mod(delt + t * C(n - cnt, add));
            }   
        }   
        else {
            int t = mod(f[pa - 1] * fp(2, pa - 1));
            if (cnt >= 3) {
                delt = t;
            }   
            for (int add = 1; cnt + add <= n; ++add) {
                t = mod(t * (pa + add - 1));
                if (cnt + add >= 3) {
                    delt = mod(delt + t * C(n - cnt, add));
                }
            }   
        }

        //debug(mask);
        //debug(delt);

        if (bp(mask) & 1)
            ans = mod(ans - delt);
        else
            ans = mod(ans + delt);
    }   
    cout << ans << endl;
}