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.
Input
The first line contains two integers n and m: the number of vertices and edges in the graph (1 ≤ n ≤ 2 · 10^{5}, n − 1 ≤ m ≤ n + 50).
The next m lines describe edges of the graph.
Each of them contains two integers u and v (1 ≤ u, v ≤ n): the two vertices connected by an edge.
It is guaranteed that the graph does not contain selfloops and multiple edges. It is guaranteed that the graph is connected.
Output
Print a single integer: the determinant of the graph’s adjacency matrix modulo 998 244 353.
Samples
input  output 

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

Problem Author: Alexey Danilyuk
Problem Source: Petrozavodsk Summer 2018. t.me/umnik_team Contest