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Consider a connected undirected graph in which the difference between the number of edges and the number of vertices is at most $50$. Please find the determinant of its adjacency matrix modulo $998\,244\,353$.
The first line contains two integers $n$ and $m$: the number of vertices and edges in the graph ($1 \le n \le 2 \cdot 10^{5}$, $n - 1 \le m \le n + 50$).
The next $m$ lines describe edges of the graph. Each of them contains two integers $u$ and $v$ ($1 \le u, v \le n$): the two vertices connected by an edge.
It is guaranteed that the graph does not contain self-loops and multiple edges. It is guaranteed that the graph is connected.
Print a single integer: the determinant of the graph's adjacency matrix modulo $998\,244\,353$.
4 3 1 2 2 3 3 4
1
5 10 1 2 1 3 1 4 1 5 2 3 2 4 2 5 3 4 3 5 4 5
4
1 0
0
2 1 2 1
998244352