Yash has recently learnt about the Fibonacci sequence and is very excited about it. He calls a sequence Fibonacci-ish if
You are given some sequence of integers a _{1}, a _{2}, ..., a _{ n}. 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 a _{ i}.
The second line contains n integers a _{1}, a _{2}, ..., a _{ n} (|a _{ i}| ≤ 10^{9}).
Print the length of the longest possible Fibonacci-ish prefix of the given sequence after rearrangement.
3
1 2 -1
3
5
28 35 7 14 21
4
In the first sample, if we rearrange elements of the sequence as - 1, 2, 1, the whole sequence a _{ i} would be Fibonacci-ish.
In the second sample, the optimal way to rearrange elements is , , , , 28.
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