Goal
Story:
Hercule Poirot is a man of order and precision. He has a number of cigars, and he keeps them strictly in increasing height order.
As a New Year present, Poirot decides to gift his friend, Captain Hastings, a box of cigars. He has decided to give Hastings a set of cigars, such that the difference between every 2 consecutive cigars is same.
Find out the maximum number of cigars Poirot can gift Hastings.
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The Problem:
Given the lengths of N cigars (sorted in ascending order), find the maximum number of cigars which have a common difference.
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Rules:
There are N cigars.
Each cigar has a length LNT.
Display the largest number of cigars which are increasing with the same difference.
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Example:
Let there be 10 cigars of length:
3, 5, 6, 7, 10, 12, 14, 15, 18, 20
In this case the maximum number of cigars Poirot can gift is 4. (5 - 10 - 15 - 20)
Input
Line 1: An integer N, the number of cigars
Next N Lines: An integer LNT, the length of a cigar
(Note: The lengths of the cigars are sorted in ascending order)
Output
Line 1: An integer MAX, the maximum number of cigars Poirot can gift
Constraints
2 ≤ N ≤ 1000
1 ≤ LNT ≤ 1000
(Note: The lengths of the cigars may not be unique)
Example
Input
10
3
5
6
7
10
12
14
15
18
20
