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 <image>, <image>, <image>, <image>, 28.

n=int(raw_input())
A=map(int,raw_input().split())
"""
n=5
A=[28, 35, 7, 14, 21]
"""

dic={}
for x in A:
    dic[x]=dic.get(x,0)+1

maxx=2
for key1 in dic:
    dic[key1]-=1
    for key2 in dic:
        if dic[key2]>0:
            dic[key2]-=1
            a,b=key1,key2
            seq=[b]
            while dic.get(a+b)>0:
                seq.append(a+b)
                dic[a+b]-=1
                a,b=b,a+b
            maxx=max(len(seq)+1,maxx)
            for x in seq:
                dic[x]+=1
    dic[key1]+=1

print maxx
exit()

