Answer is here!

#include<bits/stdc++.h>
using ll = long long;
constexpr ll mod = 998244353;
const int maxn = 1e6 + 10;
int n, N;
ll pw[maxn];
std::vector<int> G[maxn], to[maxn];
int low[maxn], dfn[maxn], dt, stk[maxn], top;
int siz[maxn];
void dfs1(int u) {
low[u] = dfn[u] = ++dt, stk[++top] = u;
for (int v : G[u]) {
    if (dfn[v]) low[u] = std::min(low[u], dfn[v]);
    else {
        dfs1(v), low[u] = std::min(low[u], low[v]);
        if (dfn[u] == low[v]) {
            N++, to[u].push_back(n + N), to[n + N].push_back(u);
            int t;
            do {t = stk[top--]; to[t].push_back(n + N), to[n + N].push_back(t);} while (t != v);
            siz[n + N] = to[n + N].size();
        }
    }
}
}
ll f[maxn], g[maxn];
void dfs2(int u, int fa) {
if (u != 1 && to[u].size() == 1)
    return f[u] = g[u] = 1, void();
ll h[3] = {1, 0, 0};
for (int v : to[u]) {
    if (v == fa) continue;
    dfs2(v, u);
    h[2] = (h[2] * (g[v] + 1) + h[1] * g[v]) % mod, h[1] = (h[1] + h[0] * g[v]) % mod;
}
if (u > n) f[u] = pw[siz[u] - 1] * h[2] % mod, g[u] = (pw[siz[u] - 1] * h[1] + f[u]) % mod;
else f[u] = (2ll * h[2] + h[1] + h[0]) % mod, g[u] = (h[1] + f[u]) % mod;
}
int main() {
int m; scanf("%d%d", &n, &m);
for (int i = pw[0] = 1; i <= n; i++) (pw[i] = pw[i - 1] << 1) >= mod && (pw[i] -= mod);
for (int x, y; m--; )
    scanf("%d%d", &x, &y), G[x].push_back(y), G[y].push_back(x);
dfs1(1);
dfs2(1, 0);
ll ans = 0;
for (int i = 1; i <= n + N; i++) (ans += f[i]) %= mod;
printf("%lld\n", (2ll * ans + 1ll) % mod);
return 0;
}

thank you!