Money Sums

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