EIU Programming Practices and Exams

Given a set A with N elements.

       The first non-empty subset subset of A corresponds to the bit representation of 1 .

       The 2nd non-empty subset of A corresponds to the bit representation of 2

       …

      The Mth non-empty subset of A corresponds to the bit representation of M

For example: 
{1} {2} {3}
1 => 0 0 1 => {} {} {3}

2 => 0 1 0 => {} {2} {}

…

(See output for more details)

Input

The first line is N (1<=N<=20)

The next line contains N distinct double a elements of the set. (1<=a<=100)

Output

The first line is M, the number of non-empty subsets

The next m lines are the subsets.

Example

Input:

3
3
1 2 3

Output:

3
7
3 
2 
2 3 
1 
1 3 
1 2 
1 2 3