CF445B.DZY Loves Chemistry

DZY loves chemistry, and he enjoys mixing chemicals.

DZY has $n$ chemicals, and $m$ pairs of them will react. He wants to pour these chemicals into a test tube, and he needs to pour them in one by one, in any order.

Let's consider the danger of a test tube. Danger of an empty test tube is $1$ . And every time when DZY pours a chemical, if there are already one or more chemicals in the test tube that can react with it, the danger of the test tube will be multiplied by $2$ . Otherwise the danger remains as it is.

Find the maximum possible danger after pouring all the chemicals one by one in optimal order.

The first line contains two space-separated integers $n$ and $m$ .

Each of the next $m$ lines contains two space-separated integers $x_{i}$ and $y_{i}$ $(1<=x_{i}<y_{i}<=n)$ . These integers mean that the chemical $x_{i}$ will react with the chemical $y_{i}$ . Each pair of chemicals will appear at most once in the input.

Consider all the chemicals numbered from $1$ to $n$ in some order.

Print a single integer — the maximum possible danger.

In the first sample, there's only one way to pour, and the danger won't increase.

In the second sample, no matter we pour the $1$ st chemical first, or pour the $2$ nd chemical first, the answer is always $2$ .

In the third sample, there are four ways to achieve the maximum possible danger: 2-1-3, 2-3-1, 1-2-3 and 3-2-1 (that is the numbers of the chemicals in order of pouring).