You have $n$ coins with certain values. Your task is to find all money sums you can create using these coins.

Input:

• The first line contains an integer $n:$ the number of coins.
• The second line contains $n$ integers $x_1, x_2, \dots, x_n:$ the values of the coins.

Output:

• First, print an integer $k:$ the number of distinct money sums that can be formed using any subset of the coins (each coin used at most once).
• Then, print all such sums in increasing order, separated by spaces.

Constraints:

• $1 \le n \le 100$
• $1 \le x_i \le 1000$

Example:

Sample Input:

4
4 2 5 2

Sample Output:

  9
  2 4 5 6 7 8 9 11 13