Given a set of integers a_1, a_2, ..., a_n, determine the number of distinct sums that can be obtained by summing the elements of all possible non-empty subsets of this set. In other words, find the cardinality of the set of all such sums.
The first line contains an integer n~(1 \le n \le 20). The second line contains integers a_1, a_2, ..., a_n~(-10^5 \le a_i \le 10^5).
Print one number — the cardinality of the set of all possible sums of elements of non-empty subsets.
Example 1
Example 2