A10354. Fibonacci-ish

Yash has recently learnt about the Fibonacci sequence and is very excited about it. He calls a sequence Fibonacci-ish if

1. the sequence consists of at least two elements
2. $f_{0}$ and $f_{1}$ are arbitrary
3. $f_{n+2}=f_{n+1}+f_{n}$ for all $n>=0$ .

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.

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 , , , , $28$ .