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.