## 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