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 line has an integer $n(1\le n\le 100)$: the number of coins.

The next line has $n$ integers $x_1,x_2,...,x_n(1\le x_i\le 1000)$: the values of the coins.

Output

In the first line print the number of distinct money sums.

In the second line print all possible sums in increasing order.

Examples