Note

The time limit is $5$ seconds, but it is quite tight.

Problem Statement

Freely choose a non-negative integer $T$ ( $0\leq T\leq 998\, 244\, 352$ ) and solve the following problem.

You are given an undirected simple graph with $N$ vertices and $M$ edges. The vertices and the edges are each numbered in order starting from $1$. The $i$-th edge connects vertices $U_i$ and $V_i$.

Among the ways to choose $4$ vertices of this graph, consider the induced subgraph on the chosen vertices, and let

• $A$ be the number of ways whose induced subgraph has no edges, and
• $B$ be the number of ways whose induced subgraph has exactly $4$ edges that form a cycle of length $4$.

Find $A+TB$ modulo $998\, 244\, 353$.

Constraints

• $1\leq N\leq 2\times 10^5$
• $0\leq M\leq 2\times 10^5$
• $U_i \neq V_i$
• If $i\neq j$, then $\lbrace U_i,V_i\rbrace \neq \lbrace U_j,V_j\rbrace$
• All input values are integers.

Input

$N$ $M$
$U_1$ $V_1$
$U_2$ $V_2$
$\vdots$
$U_M$ $V_M$

Output

Output the value of $T$ and the remainder of $A+TB$ divided by $998\, 244\, 353$, in this order, separated by a space, on $1$ line. End the output with a newline.

Sample

6 4
1 2
2 3
3 4
4 1

10000 20001

3 3
1 2
2 3
1 3

99999 0

10 17
1 4
1 6
1 10
3 4
3 5
4 5
4 6
4 9
4 10
5 7
5 8
5 9
6 8
6 10
7 9
7 10
9 10

0 13