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.

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.

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.

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.

见题面 Input 部分

见题面 Output 部分