DZY Loves Chemistry

Time Limit:1000MS     Memory Limit:262144KB     64bit IO Format:%I64d & %I64u

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Description

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.

Input

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.

Output

Print a single integer — the maximum possible danger.

Sample Input

Input

1 0

Output

1

Input

2 1 1 2

Output

2

Input

3 2 1 2 2 3

Output

4

Hint

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 1st chemical first, or pour the 2nd 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).

1 #include
         
           2  3 int pre[1050]; 4  5 int Find(int x)           6 { 7     int r=x;              8     while(r!=pre[r])      9         r=pre[r];        10     int i=x,j;11     while(pre[i]!=r)     12     {13         j=pre[i];14         pre[i]=r;15         i=j;16     }17     return r;            18 }19 20 void join(int x,int y)               21 {22     int fx=Find(x),fy=Find(y);       23     if(fx!=fy)                       24         pre[fy]=fx;                  25 }26 27 int main()28 {29     int n,m,i,j,x,y;30     while(scanf("%d %d",&n,&m)!=EOF)31     {32         for(i=1;i<=n;i++)            33             pre[i]=i;34         for(i=1;i<=m;i++)            35         {36             scanf("%d %d",&x,&y);37             join(x,y);38         }39         int t[1050]={
       0},k=0;       40         for(i=1;i<=n;i++)            41             t[Find(i)]=1;42         for(i=1;i<=n;i++)43             if(t[i]==1)44                 k++;45         long long ans=1;46         for(i=1;i<=n-k;i++)47             ans=ans*2;48         printf("%I64d\n",ans);49     }50     return 0;51 }