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

Input

• The first input line has an integer ~n~: the number of coins.

The next line has ~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. After this, print all possible sums in increasing order.

Constraints

• ~1 \le n \le 100~
• ~1 \le x\_i \le 1000~

Example Input

4
4 2 5 2

Example Output

9
2 4 5 6 7 8 9 11 13