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 \ge 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 \le n \le 1000)- the length of the sequence ai.The second line contains n integers a1,a2,...,an (|ai| \le 109).

Output 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 ai would be Fibonacci-ish.In the second sample, the optimal way to rearrange elements is , , , , 28.