Longest Arithmetic Progression

You are given N nonnegative integers. Choose any subset of them and arrange the chosen numbers in any order to form an arithmetic progression. Find the maximum possible length of such a progression.

An arithmetic progression is a sequence where the difference between every pair of neighboring terms is constant. The common difference may be negative or 0.

The first line contains the number of integers N (1 ≤ N ≤ 2,000).

Each of the next N lines contains one integer. Every integer is at least 0 and less than 1,000,000,000.

Print the length of the longest arithmetic progression that can be formed.