Compose a polygon

Given a set of line segments, determine the minimum number of segments that must be removed so that the remaining segments can form a polygon with non-zero area.

Input

The first line of the input contains an integer n (3 ≤ n ≤ 50), representing the number of segments in the set. The second line lists the lengths of these segments as a sequence of n integers, each between 1 and 10^6 inclusive.

Output

Output the minimum number of segments that need to be removed so that the remaining segments can form a polygon. If no subset of segments can form a polygon, output -1.

Examples