Problem Statement

There is an undirected graph $G$ with $N$ vertices and $M$ edges. $G$ does not contain self-loops, but may contain multi-edges. Vertices are numbered from $1$ to $N$, and edges are numbered from $1$ to $M$, with edge $i$ connecting vertices $U_i,V_i$.

Find the number, modulo $998244353$, of cycles contained in $G$.

More formally, find the number, modulo $998244353$, of subsets $\lbrace e_1,e_2,\dots,e_k\rbrace \subseteq \lbrace 1,2,\dots,M\rbrace\ (k\geq 2)$ of the given edge set that satisfy the following condition.

• There exists a permutation $(e_1',e_2',\dots,e_k')$ of $(e_1,e_2,\dots,e_k)$ and a vertex sequence $(v_1,v_2,\dots,v_k)$ such that all of the following hold:
• $v_1,v_2,\dots,v_k$ are pairwise distinct;
  • For all $j\ (1\leq j\leq k)$, edge $e_j'$ connects vertices $v_j,v_{(j\bmod k) + 1}$.

Constraints

• $2\leq N \leq 20$
• $2\leq M \leq 2\times 10^5$
• $1\leq U_i < V_i \leq N$
• All input values are integers.

Input

The 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

Output the answer.