#P633D. Fibonacci-ish
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ID: 3475
Type: RemoteJudge
3000ms
512MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Fibonacci-ish
No submission language available for this problem.
Description
Yash has recently learnt about the Fibonacci sequence and is very excited about it. He calls a sequence Fibonacci-ish if
- the sequence consists of at least two elements
- f0 and f1 are arbitrary
- fn + 2 = fn + 1 + fn for all n ≥ 0.
You are given some sequence of integers a1, a2, ..., an. Your task is rearrange elements of this sequence in such a way that its longest possible prefix is Fibonacci-ish sequence.
The first line of the input contains a single integer n (2 ≤ n ≤ 1000) — the length of the sequence ai.
The second line contains n integers a1, a2, ..., an (|ai| ≤ 109).
Print the length of the longest possible Fibonacci-ish prefix of the given sequence after rearrangement.
Input
The first line of the input contains a single integer n (2 ≤ n ≤ 1000) — the length of the sequence ai.
The second line contains n integers a1, a2, ..., an (|ai| ≤ 109).
Output
Print the length of the longest possible Fibonacci-ish prefix of the given sequence after rearrangement.
Samples
3
1 2 -1
3
5
28 35 7 14 21
4
Note
In the first sample, if we rearrange elements of the sequence as - 1, 2, 1, the whole sequence ai would be Fibonacci-ish.
In the second sample, the optimal way to rearrange elements is 
, 
, 
, 
, 28.