Problem2055--Fibonacci-ish

2055: Fibonacci-ish

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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. f0 and f1 are arbitrary
  3. 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.

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.

Examples
Input
3
1 2 -1
Output
3
Input
5
28 35 7 14 21
Output
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.

Source/Category

 
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