CF633D.Fibonacci-ish

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题目描述

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
$f_{0}$ and $f_{1}$ are arbitrary
$f_{n+2}=f_{n+1}+f_{n}$ 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.

输入格式

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 $a_{1},a_{2},...,a_{n}$ ( $|a_{i}|<=10^{9}$ ).

输出格式

Print the length of the longest possible Fibonacci-ish prefix of the given sequence after rearrangement.

输入输出样例

输入#1
```
3
1 2 -1
```
输出#1
```
3
```
输入#2
```
5
28 35 7 14 21
```
输出#2
```
4
```

说明/提示

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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