Money Sums

Input

The first line contains one integer n~(1 \le n \le 100) — the number of coins.

The second line contains $n$ integers x_1, x_2, \ldots, x_n~(1 \le x_i \le 1000) — the denominations of the coins.

Output

In the first line, print the number of distinct sums that can be obtained.

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

Examples