You have $n$ coins with certain values. Your task is to find all money sums you can create using these coins. \InputFile 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. \OutputFile In the first line print the number of distinct money sums. In the second line print all possible sums in increasing order.