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

Output:

9
2 4 5 6 7 8 9 11 13