Problem Statement

Given is an undirected graph with N vertices and M edges.
The vertices are called Vertex $1, Vertex 2, \ldots, Vertex N$, and the edges are called Edge $1, Edge 2, \ldots, Edge M. Edge i (1 \leq i \leq M) connects Vertex U_i$ and Vertex V_i.
It is guaranteed that the graph is simple: it has no self-loops and no multi-edges.
There are 2^M ways to direct every edge in this graph. We want each vertex to have exactly one edge going from that vertex to another vertex. How many ways are there to direct the edges in that way? Since the answer may be enormous, print it modulo 998244353.

Input

Input is given from Standard Input in the following format:
N M
U_1 V_1
U_2 V_2
$\vdots$
U_M V_M

Output

Print the answer.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $1 \leq M \leq 2\times 10^5$
• $1 \leq U_i,V_i \leq N$
• $U_i \neq V_i$
• All values in input are integers.
• The given graph is simple.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

There are two ways to direct the edges to achieve the objective:

• $1\rightarrow 2 , 2\rightarrow 3 , 1\leftarrow 3$
• $1\leftarrow 2 , 2\leftarrow 3 , 1\rightarrow 3$

Sample Input 2

2 1
1 2

Sample Output 2

0

It is obviously impossible to make every vertex have one edge going from that vertex.

Sample Input 3

7 7
1 2
2 3
3 4
4 2
5 6
6 7
7 5

Sample Output 3

4

见题面 Input 部分

见题面 Output 部分