Description

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).

Constraints -- Each case will contain between 1 and 300 elements inclusive. -- Each integer will be between -1,000,000 and 1,000,000 inclusive.

Input

There are multiple cases, and each case contains 2 lines: the first line contains the count of integers, the following line contains all the integers 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

Output

5
3
3

Source: StandLove