An arithmetic series consists of a sequence of terms such that each term minus its immediate predecessor gives the same result. For example, the sequence 3, 7, 11, 15 is the terms of the arithmetic series 3+7+11+15; each term minus its predecessor equals 4. (Of course there is no requirement on the first term since it has no predecessor.)
Given a collection of integers, we want to find the longest arithmetic series that can be formed by choosing a sub-collection (possibly the entire collection).
Input
There are multiple cases, and each case contains 2 lines: the first line contains the count of integers (between 2 and 1000 inclusive), the following line contains all the integers (between -1,000,000,000 and 1,000,000,000 inclusive) separated by one or more spaces.
Output
Print a single number for each case in a single line.
Sample Input
7
3 8 4 5 6 2 2
4
-1 -5 1 3
4
-10 -20 -10 -10
Sample Output
5
3
3
