Given a set ~A~ with ~N~ elements, generate all non-empty subsets of ~A~.

Input

• The first line is ~N~ (~1 \leq N \leq 20~)
• The next line contains ~N~ distinct double ~a~ elements of the set. (~1 \leq a \leq 100~)

Output

• The first line is ~M~, the number of non-empty subsets
• The next ~m~ lines are the subsets.

Example Input 1

3
1 2 3

Example Output 1

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