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Volumes > C. T. 2011 > problem:


Progression

Volume problems

• Skiers
• Matrix
• Range Minimum Query
• Министерство правды
• Coins and nests
• Ball
• Huge parking
• Islands areas
• Progression
• Passing score
• Jedi vs Sith
• Сортировка времени
• Triangle2

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Time limit 1000/1000/4000/4000 ms. Memory limit 65000/65000/65000/65000 Kb.

Problem description

Bob loves playing with numbers. One day he found a piece of paper with N integer numbers on it. He decided to select some numbers from it without changing their position so that selected numbers form arithmetical progression. Help him in finding the longest arithmetical progression from given numbers.

Input

Line 1: A single integer: N (2 <= N <= 1000).

Line 2: N integers ai which were on the paper (-10000 <= ai <= 10000).

Output

Single integer, length of longest arithmetical progression.

Example

stdin stdout

13
-6 -2 1 2 5 6 7 9 16 13 16 17 20

5

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