Problem Statement

You are given a simple connected undirected graph $G$ with $N$ vertices and $M$ edges. Here, $N \geq 2$. The vertices are numbered $1$ to $N$, and the edges are numbered $1$ to $M$; edge $i$ connects vertices $U_i$ and $V_i$. Each edge has a value called a cost, and the cost of edge $i$ is $2^i$.

You will now choose some edges of $G$ to delete so that the number of connected components of $G$ becomes exactly $2$. (It can be proved that this is always achievable under the constraints of this problem.)

Find the minimum possible sum of costs of the deleted edges, modulo $998244353$. (Note that you are not minimizing the remainder modulo $998244353$.)

Constraints

• $2 \leq N \leq 2\times 10^5$
• $N-1 \leq M \leq \min\left(\frac{N(N-1)}{2}, 2\times 10^5\right)$
• $1 \leq U_i < V_i \leq N$
• $(U_i, V_i) \neq (U_j, V_j)$ if $i \neq j$
• $G$ is connected.
• 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 minimum possible sum of costs of the deleted edges, modulo $998244353$.