The Colored Map

Limits: 2 sec., 256 MiB

There are $N$ cities (numbered from 1 to $N$) and $M$ roads on the map of Ukraine. You want to paint each city in either blue or yellow color. If there is a road between two cities they need to be painted in the same color.

After you pain all the cities you calculate the number $X$ which is the number of yellow cities on the map. Find the number of different possible values of $X$ you can get.

Input

The first line contains two integers $N$ and $M$ separated with a single space. Each of the following $M$ lines contains two integers $A_j$ and $B_j$ separated with a single space. It means the $j$-th road connects cities $A_j$ and $B_j$.

Output

The only integer which is the number of different values of $X$ you can get.

Constraints

$1 \le N, M \le 100000 (10^5)$,

$1 \le A_j, B_j \le N$,

$A_j \ne B_j$.

Samples

Input (stdin) сopy	Output (stdout) сopy
7 7 1 4 4 7 2 5 2 6 5 3 4 1 6 5	4

Notes

The cities 1, 4 and 7 should be painted in the same color. Similarly, the cities 2, 3, 5 and 6 should have the same color. Thus, the number $X$ can have four different values: 0, 3, 4 or 7.