Problem Statement

AtCoder Town has $N$ intersections and $M$ roads.
Road $i$ connects Intersections $A_i$ and $B_i$.

Takahashi, the mayor, has decided to install zero or more surveillance cameras at the intersections.
Each intersection can be installed with zero or one surveillance camera.

How many of the $2^N$ ways to install surveillance cameras monitor an even number of roads?

Here, Road $i$ is said to be monitored when the following condition is satisfied:

a surveillance camera is installed at one or both of Intersections $A_i$ and $B_i$.

Constraints

• $2 \\leq N \\leq 40$
• $1 \\leq M \\leq \\frac{N(N-1)}{2}$
• $1 \\leq A_i \\lt B_i \\leq N$
• $(A_i,B_i) \\neq (A_j,B_j)$ if $i \\neq j$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\\vdots$ $A_M$ $B_M$

Output

Print the answer.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

6

The sets of towns to install surveillance cameras to satisfy the condition are: $\\{ \\} , \\{ 2 \\} , \\{ 1,2 \\} ,\\{1,3\\},\\{2,3\\},\\{1,2,3\\}$.
Note that it is allowed to install no surveillance camera.

Sample Input 2

20 3
5 6
3 4
1 2

Sample Output 2

458752

The town may not be connected.